JP3817866B2 - Data conversion device and coefficient determination device thereof - Google Patents

Description

本実施例による係数を決定する方法により、ｗ₁とｗ₂と初期値をいずれも０とする。この場合、誤差としては、合計のユークリッド距離を用いる。まず、ｗ₁について、誤差と、誤差に区間［０…２］の一様乱数を加えたものを算出する。その結果、次表のように算出されたとする。
【００８２】
【表２】

この結果に基づき、ｗ₁は更新しない。次に、ｗ₂について、同様に、誤差と、誤差に同上の乱数を加えたものを算出する。その結果、次表のように算出されたとする。
【００８３】
【表３】

この結果に基づき、ｗ₂も更新しない。この状況は、いずれの変数も変更しない方が誤差が小さいという極少の状況の例である。本実施例では誤差を付加しているので、引続きこの計算を繰り返し、所定の確率によってこのような極少から脱出できる。
【００８４】
この時点で誤差を評価し、２を得る。誤差が大きいので、引続き、ｗ₁について、誤差と、誤差に乱数を加えたものを算出する。その結果、次表のように算出されたとする。
【００８５】
【表４】

この結果に基づき、ｗ₁は１に更新する。更に、ｗ₂について、同様に、誤差と、誤差に乱数を加えたものを算出する。その結果、次表のように算出されたとする。
【００８６】
【表５】

この結果に基づき、ｗ₂は−１に更新する。この時点で誤差を評価し、０を得る。誤差が十分に小さいので、係数の最適化を終了する。
【００８７】
以上に例を以て示したように、本実施例によれば、誤差は次第に減少し、所定の乱数を付加することによって誤差が極少となる点から、所定の確率によって脱出し、より誤差の小さい係数を得ることができる。
【００８８】
以上に示した簡単な例では、最適化を２巡した時点で最適化が終了したが、現実的な係数決定では、より複雑な係数を決定する必要があることが一般的である。この場合、乱数の大きさが大きいまま最適化を進めると、最適化が概ね終了しても、最終的な係数には収束しにくい。そこで、誤差が小さい係数がより高い確率で選択されるように、乱数の大きさを小さくし、収束を進めるようにする。一方、乱数が小さすぎると極少を脱出できなくなる場合がある。本実施例では誤差の履歴により、確率を制御することによってこの課題を解決した。
【００８９】
また、以上に示した簡単な例では所定のステップは、ｓ₁，ｓ₂とも１を用いたが、処理を高速化するためと、極少からより高い確率で脱出できる目的で、誤差の履歴により、所定のステップを制御している。また、ｓ₁，ｓ₂に異なる値を用い、実質的により小さいステップ、すなわちｓ₁、ｓ₂、｜ｓ₁−ｓ₂｜の最大公約数による最適化を可能にする。
【００９０】
以上、簡単な例を以て作用を説明したが、本実施例によれば複雑なデータ変換装置においても、同様の動作をする。
【００９１】
本方式においては、データ変換装置の誤差は、装置内の丸めや精度を含めた誤差による評価を行っている。従って、このような誤差を含めた上で、より誤差の少ない係数を、全探査よりも高速に算出することが可能である。
【００９２】
［実施例２］
つぎにデータ変換装置として離散的な係数をとるニューラルネットワークを用いて色変換を行う実施例２について説明する。図３は本実施例の構成を示し、この図において、図１と対応する箇所には対応する符号を付して詳細な説明を省略する。図３において、入力バッファ１１は入力データとして印刷のＣ（サイアン）、Ｍ（マジェンタ）、Ｙ（イエロー）、Ｋ（墨）の面積率を保持している。ニューラルネットワークを用いた色変換装置２１はＣ、Ｍ、Ｙ、Ｋの面積率をＣＩＥ Ｌ^*ａ^*ｂ^*（Ｄ５０）色座標に変換するものである。ニューラルネットワークの係数は離散的であり、係数更新部１９によって最適化されていく。変換された色座標データは出力バッファ１３にストアされ、色差算出部２２によって出力色座標データと理想色座標データとの色差が算出される。色差自乗平均算出部２３は色差の自乗平均を算出し、これが誤差とされる。
【００９３】
つぎに色変換装置２１の係数の最適化について詳細に説明する。上述のとおり、色変換装置２１は、印刷のＣ、Ｍ、Ｙ、Ｋの面積率を、印刷結果のＣＩＥ Ｌ^*ａ^*ｂ^*（Ｄ５０）色座標に変換するものである。この色変換装置２１の係数決定には、、入力として、ＩＴ８／７．３ ｅｘｔｅｎｄｅｄ ｓｅｔに基づく９２８組のＣＭＹＫ面積率を、理想出力には、各面積率に基づいて印刷を行い、印刷結果をＤ５０光源により測色し、ＣＩＥ Ｌ^*ａ^*ｂ^*色座標としたものを用いる。すなわち、入力データｘと理想出力データｙは、｛ｘ₁，ｙ₁｝，｛ｘ₂，ｙ₂｝，…，｛ｘ_i，ｙ_i｝…，｛ｘ₉₂₈，ｙ₉₂₈｝であり、各入力データｘ_iは、４次元で、ｘ_i＝（Ｃ_i，Ｍ_i，Ｙ_i，Ｋ_i）であり、各理想出力データｙ_iは、３次元で、ｙ_i＝（Ｌ_i，ａ_i，ｂ_i）であるとする。このデータ変換装置のｋ個の係数（ｗ₁，ｗ₂，…，ｗ_p，…，ｗ_k）は、予め全て０に初期化しておく。このデータ変換装置に、データｘ_iを与えた時の出力を、ｇ（ｘ_i｜ｗ₁，ｗ₂，…，ｗ_p，…，ｗ_k）とする。このときの理想出力ｙ_iとの誤差を、ΔＥ色差、すなわち、ＣＩＥ Ｌ^*ａ^*ｂ＊色空間上のユークリッド距離ΔＥ（ｙ_i，ｇ（ｘ_i｜ｗ₁，ｗ₂，…，ｗ_p，…，ｗ_k））とする。本実施例では、この色変換装置の誤差を、各色の自乗平均誤差、すなわち、
【００９４】
【数４】

とする。
【００９５】
いま、ｋ個の係数のうち、ｐ番目の係数ｗ_pに着目し、現在の係数値に対する誤差Ｅ₀、すなわち、Ｅ₀＝Ｅ（ｗ₁，ｗ₂，…，ｗ_p，…，ｗ_k）と、現在の係数値より所定のステップｓ₁だけ大きな係数値に対する誤差Ｅ₊、すなわち、Ｅ₊＝Ｅ（ｗ₁，ｗ₂，…，ｗ_p＋ｓ₁，…，ｗ_k）、及び、現在の係数値より所定のステップｓ₂だけ小さな係数値に対する誤差Ｅ、すなわち、Ｅ_-＝Ｅ（ｗ₁，ｗ₂，…，ｗ_p−ｓ₂，…，ｗ_k）の３種類の誤差を算出する。この実施例では加算の場合の所定のステップを異なる値としているが、加算の場合の所定のステップと、減算の場合の所定のステップは必ずしも異なる値とする必要はない。
【００９６】
次に、これらの誤差に基づいて、より低い誤差のものが、より高い確率で選ばれる適宜の関数によって、いずれか１つを選択する。Ｅ₀が選択された場合、ｗ_pは更新しない。Ｅ₊が選択された場合、ｗ_pにｓ₁を加え、更新する。Ｅ_-が選択された場合、ｗ_pからｓ₂を減じ、更新する。
【００９７】
この操作を各重みｗ_p（ｐ＝１，２，…，ｋ）について適用する。この最適化の操作が１巡した時点で、この色変換装置の誤差を求め、所定の値以下になるか、ほぼ収束する状態、もしくは、所定の回数まで繰り返す。その際、最小の誤差となった場合には、「最適な係数」として係数を記録し、前述の所定のステップｓに、１よりも大きい所定の値を乗じることによって、ｓを増加させる。一方、誤差が最適化を１巡行う前に比較して、増加してしまった場合には、ｓ₁やＳ₂に１よりも小さい所定の値を乗じて、ｓ₁やＳ₂を減少させるが、最小ステップ以下未満の値とはしない。
【００９８】
以上により、学習が終了した時点で、最終的に記録された「最適な係数」を出力する。
【００９９】
［実施例３］
つぎに係数が離散値をとるテーブルと補間とを用いる色変換装置を用いた実施例３について説明する。図４は実施例３の構成を示しており、この図において、図１と対応する箇所には対応する符号を付して詳細な説明を省略する。図４において、入力バッファ１１は入力データとしてＣＩＥ Ｌ^*ａ^*ｂ^* （Ｄ５０）色座標データをストアしている。色変換装置３１は、係数が離散値をとるテーブルと補間とを用いて、ＣＩＥ Ｌ^*ａ^*ｂ^* （Ｄ５０）色座標を入力し、所定の印刷装置のＣ、Ｍ、Ｙ、Ｋの面積率を算出するものである。本実施例では、各格子点に記憶する値は離散値とする。この変換装置３１の詳細は後述する。Ｃ、Ｍ、Ｙ、Ｋの面積率は出力バッファ１３にストアされ、これに基づいて印刷装置３２を駆動して印刷出力を得る。こののち印刷出力を測定してＣＩＥ Ｌ^*ａ^*ｂ^*（Ｄ５０）色座標データを得る。この色座標データは測定値バッファ３３にストアされる。理想出力データメモリ１４には入力データ自体がストアされ、この入力データと測定値バッファ３３の色座標データとの色差が色差算出部２２で算出され、平均色差が平均色差算出部３４で算出され、誤差とされる。
【０１００】
つぎに変換装置３１の係数の最適化について詳細に説明する。変換装置３１は、入力空間上のＬ^*軸、ａ^*軸、ｂ^*軸の各々の代表点、例えば、各軸１０点からなる３次元の表に、予め変換後のＣＭＹＫ各面積率を記録し、色変換に際しては、入力した色座標を含む直方体の各頂点に相当する格子点の変換値を、直方体内の位置に応じて補間を行い、変換結果を得るものであり、補間方法としては、４面体補間法、プリズム補間法、ｃｕｂｉｃ補間法などが知られている。本実施例はこれらの補間方法のいずれの場合でも適用することができる。
【０１０１】
一般的に、各格子点に記憶される変換値は、各代表点の変換値をテーブルの精度によって丸めた値であり、いずれの補間方法においても、入出力の対応によっては補間誤差が発生する。
【０１０２】
所定の係数における、この色変換装置の誤差を次の手順により求めた平均色差とする。十分に細かい所定の間隔、例えば、各次元とも格子点の代表値の間隔の１６分の１の間隔で、所定のの係数によって色変換し、ＣＭＹＫの各面積率を算出する。この算出結果をもとに印刷を行い、測色値と、変換前の色座標との色差を算出し、全入力範囲についての平均の色差を誤差とする。この際、実際に印刷を行って、測色することに換えて、プリンタをモデル化したものを用いて印刷後の予測値を推定しても良い。
【０１０３】
本実施例は、補間後の平均の色差が最小になるように、各格子点の値を最適化することを目的とし、以下の最適化を行う。
【０１０４】
まず、全ての格子点について、各格子点（Ｌ，Ａ，Ｂ）のテーブルに記憶する離散値の係数｛Ｃ（Ｌ，Ａ，Ｂ），Ｍ（Ｌ，Ａ，Ｂ），Ｙ（Ｌ，Ａ，Ｂ），Ｋ（Ｌ，Ａ，Ｂ）｝を、対応する変換値をテーブルの精度によって丸めた値により初期化する。Ｔ及びｓをそれぞれ適宜の初期値とする。各格子点に、色再現範囲内で、彩度の低いものから順に通し番号を付け、引続き、色再現範囲外の格子点について、変換前後の色差が小さい順に通し番号を付ける。つぎに以下の処理プを行う。
処理（１）：通し番号が小さい順に、Ｋの格子点値を、処理（１．１）〜（１．３）の操作により最適化する。
処理（１．１）：現在のＫの値に所定のステップｓを加え、色変換装置の誤差を算出する。
処理（１．２）：現在のＫの値から所定のステップｓ及びステップの最小単位を減じ、色変換装置の誤差を算出する。
【０１０５】
この際、全入力範囲に換えて、この係数が影響を持つ範囲に限って色差の平均を求めてもよい。例えば、４面体補間法、プリズム補間法、ｃｕｂｉｃ補間法では、それぞれ当該格子点を頂点に持つ４面体、３角柱、直方体に含まれる部分のみについて平均を求めても良い。
処理（１．３）：上記処理（１．１）の誤差と処理（１．２）の誤差に所定の区間［０，Ｔ］に一様な分布に基づく乱数をそれぞれに加算し、処理（１．１）の誤差と乱数の和が、処理（１．２）の誤差と乱数の和よりも小さい場合には現在のＫの値に所定のステップｓを加え、更新する。そうでない場合には、現在のＫの値から所定のステップｓ及びステップの最小単位を減じ更新する。
処理（２）：上記処理（１）の操作を、全ての格子点のＫに適用する。この最適化の操作が１巡した時点で、この色変換装置の誤差を求め、所定の値以下になるか、ほぼ収束する状態、もしくは、所定の回数まで繰り返す。その際、最小の誤差となった場合には、「Ｋが最適な係数」として係数を記録し、前述の所定の区間を決定するＴに、１よりも大きい所定の値を乗じることによって、Ｔを増加させる。一方、誤差が最適化を１巡行う前に比較して、増加してしまった場合には、Ｔに１よりも小さい所定の値を乗じて、Ｔを減少させる。所定のステップｓについても同様の操作を行うが、最小ステップ未満の値とはしない。
【０１０６】
次に、「Ｋが最適な係数」を初期値として、Ｔ及びｓをそれぞれ適宜の初期値とし以下の処理を実行する。
処理（３）：通し番号が小さい順に、ＣＭＹの格子点値を、処理（３．１）〜（３．５）の操作により最適化する。
処理（３．１）：現在のＣの値に所定のステップｓを加え、色変換装置の誤差を算出する。
処理（３．２）：現在のＣの値から所定のステップｓ及びステップの最小単位を減じ、色変換装置の誤差を算出する。
処理（３．３）：上記処理（３．１）の誤差と処理（３．２）の誤差に所定の区間［０，Ｔ］に一様な分布に基づく乱数をそれぞれに加算し、処理（３．１）の誤差と乱数の和が処理（３．２）の誤差と乱数の和よりも小さい場合には現在のＣの値に所定のステップｓを加え、更新する。そうでない場合には、現在のＣの値から所定のステップｓ及びステップの最小単位を減じ更新する。
処理（３．４）：処理（３．１）〜（３．３）の操作をＣに換えてＭについて適用する。
処理（３．５）：処理（３．１）〜（３．３）の操作をＣに換えてＹについて適用する。
処理（４）：上記処理（３）の操作を、全ての格子点に適用する。この最適化の操作が１巡した時点で、この色変換装置の誤差を求め、所定の値以下になるか、ほぼ収束する状態、もしくは、所定の回数まで繰り返す。その際、最小の誤差となった場合には、「最適な係数」として係数を記録し、前述の所定の区間を決定するＴに、１よりも大きい所定の値を乗じることによって、Ｔを増加させる。一方、誤差が最適化を１巡行う前に比較して、増加してしまった場合には、Ｔに１よりも小さい所定の値を乗じて、Ｔを減少させる。所定のステップｓについてもＴと同様の操作を行うが、最小ステップ未満の値とはしない。
【０１０７】
以上により、学習が終了した時点で、最終的に記録された「最適な係数」を出力する。
【０１０８】
［実施例４］
つぎに離散的な係数値と誤差との間に想定可能な連続的な関数を導入して係数の最適化を行う実施例４について説明する。図５は実施例４の構成を示しており、この図において図３と対応する箇所には対応する符号を付して詳細な説明をその省略する。図５において、２次関数決定部４１はＥ₀、Ｅ_-、Ｅ₊の誤差に基づいて２次関数を決定し、微係数算出部４２はこの２次関数のＥ₀における微係数を算出する。係数更新部４３は温度（アニーリングにおける温度）および微係数に応じて係数を決定する。これについては後に詳述する。
【０１０９】
つぎにこの実施例における色変換装置２１の係数の最適化について詳細に説明する。色変換装置２１は、本実施単独で最適化を行ってもよいし、また、本実施例に先だって実施例２により適宜回数最適化を行った後に本実施例による最適化を行ってもよい。誤差などの諸定義は実施例２と同じである。
【０１１０】
いま、ｋ個の係数のうち、ｐ番目の係数ｗ_pに着目し、現在の係数値に対する誤差Ｅ₀、すなわち、Ｅ₀＝Ｅ（ｗ₁，ｗ₂，…，ｗ_p，…，ｗ_k）と、現在の係数値より所定のステップｓ₁だけ大きな係数値に対する誤差Ｅ₊、すなわち、Ｅ₊＝Ｅ（ｗ₁，ｗ₂，…，ｗ_p＋ｓ₁，…，ｗ_k）、及び、現在の係数値より所定のステップｓ₂だけ小さな係数値に対する誤差Ｅ、すなわち、Ｅ_-＝Ｅ（ｗ₁，ｗ₂，…，ｗ_p−ｓ₂，…，ｗ_k）の３種類の誤差を算出する。この３点の誤差より、２次関数を推定し、ｗ_pにおける微係数Ｅ’_pを算出する。
【０１１１】
温度ｔに応じて、微係数Ｅ’_pが大きければ高い確率で１（それ以外は０）となる確率変数Ｘ₊（Ｅ’_p；ｔ）と、微係数Ｅ’_pが小さければ高い確率で１（それ以外は０）となる確率変数Ｘ_-（Ｅ’_p；ｔ）によって、係数ｗ_pを、以下の値によって更新する。ここで、確率変数Ｘ₊とＸ_-は、温度が高いほど不確定的に、温度が低いほど確定的に微係数の影響を受けるものとする。
【０１１２】
【数５】
ｗｐ←ｗ_p＋ｓ₁・Ｘ₊（Ｅ’_p；ｔ）−ｓ₂・Ｘ_-（Ｅ’_p；ｔ）
この実施例では加算の場合の所定のステップを異なる値としているが、加算の場合の所定のステップと、減算の場合の所定のステップは必ずしも異なる値とする必要はない。
【０１１３】
この操作を各重みｗ_p（ｐ＝１，２，…，ｋ）について適用する。この最適化の操作が１巡した時点で、この色変換装置の誤差を求め、所定の値以下になるか、ほぼ収束する状態、もしくは、所定の回数まで繰り返す。その際、最小の誤差となった場合には、「最適な係数」として係数を記録し、前述の所定のステップｓ₁、ｓ₂と温度ｔに、１よりも大きい所定の値を乗じることによって、ステップと温度を増加させる。一方、誤差が最適化を１巡行う前に比較して、増加してしまった場合には、ｓ₁、ｓ₂と温度ｔに１よりも小さい所定の値を乗じて、ステップと温度をを減少させる。但し各ステップは、最小ステップ以下未満の値とはしない。
【０１１４】
以上により、学習が終了した時点で、最終的に記録された「最適な係数」を出力する。
【０１１５】
尚、本実施例では３点を取り、２次関数により微係数を算出したが、２点以上の点を取れば適宜の関数によって微係数を定めることができる。
【０１１６】
また、以上では、３点をとっていたが、ｐ種類の適宜の関数ｆ₁（ｗ）、ｆ₂（ｗ）…ｆ_p（ｗ）を用いてｐ種類の係数を算出することができる。
【０１１７】
ここで、例として、ｐ＝４の場合、
【０１１８】
【数６】
ｆ₁（ｗ）＝ｗ＋１
ｆ₂（ｗ）＝ｗ＋２
ｆ₃（ｗ）＝ｗ＋３
ｆ₄（ｗ）＝ｗ＋４
とすることができる。微係数を算出する場合では、現在の係数を含む区間でなくても現在の値の微係数を推定することが可能であるから、関数値が現在の係数を含む区間でなくてもよい。
【０１１９】
また、別の例として、ｐ＝５の場合、
【０１２０】
【数７】
ｆ₁（ｗ）＝ｆｌｏｏｒ（ｗ×０．９８）
ｆ₂（ｗ）＝ｆｌｏｏｒ（ｗ×０．９９）
ｆ₃（ｗ）＝ｗ
ｆ₄（ｗ）＝ｃｅｉｌ（ｗ／０．９９）
ｆ₅（ｗ）＝ｃｅｉｌ（ｗ／０．９８）
としてもよい。ここで、ｆｌｏｏｒは切り捨て、ｃｅｉｌは切り上げによる丸めである。ここでは、係数の取り得る離散値に丸める操作の例として切り捨てや切り上げを用いて例を示したが、丸める操作は任意の方法を取ることができる。
【０１２１】
［適用例］
つぎに本発明の適用例について説明する。
【０１２２】
図６は、本発明のデータ変換装置を利用した電子機器を示しており、この図において、電子機器１００はデータ変換装置１１０を有している。データ変換装置１１０は上述した実施例と同様なものであり、変換用の係数として離散値をとっている。データ変換装置１１０は係数最適化部１１１により上述した実施例と同様な手法で最適化が行われる。
【０１２３】
この場合、基準となるデータ変換装置で予め係数の最適化を行い、これを電子機器１００のデータ変換装置１１０にインストールするようにしてもよい。この後、さらに係数最適化部１１１で最終的な最適化処理を行うようにしてもよい。
【０１２４】
図７は本発明のデータ変換装置を利用したカラー画像形成装置（カラー複写機やカラー印刷機）を示しており、この図において、画像形成装置２００はデータ変換装置からなる２つの色変換装置２１０、２２０を有している。入力部２３０から入力された色データは色変換部２１０、２２０で逐次色変換され、出力部２４０に供給され、印刷出力される。この例では色変換装置２１０、２２０の両方もしくは一方において本発明のデータ変換装置の係数最適化を行える。
【０１２５】
図８は、本発明のデータ変換装置を利用したロボット装置を示しており、この図において、ロボット３００はデータ変換装置３１０を備えており、位置入力部３２０からの位置入力に応じて姿勢等の制御を行うようになっている。誤差検出部３３０は誤差を検出し、これに応じてデータ変換装置の係数の最適化が行われる。
【０１２６】
【発明の効果】
以上説明したように、本発明によれば、離散的な値を取る係数を用いてデータの変換を行う場合であっても、係数の値を簡易かつ安定して学習させることができる。
【図面の簡単な説明】
【図１】 本発明の実施例１の構成を示す図である。
【図２】 上述実施例の詳細を具体的に説明する図である。
【図３】 本発明の実施例２の構成を示す図である。
【図４】 本発明の実施例３の構成を示す図である。
【図５】 本発明の実施例４の構成を示す図である。
【図６】 本発明の適用例を説明する図である。
【図７】 本発明の適用例を説明する図である。
【図８】 本発明の適用例を説明する図である。
【符号の説明】
１１ 入力バッファ
１２ データ変換装置
１３ 出力バッファ
１４ 理想出力メモリ
１５ 誤差算出部
１６ 誤差履歴メモリ
１７ 乱数分布制御部
１８ ステップ制御部
１９ 係数更新部
１００ 電子機器
２００ カラー画像形成装置
３００ ロボット[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method and apparatus for determining a coefficient for obtaining an output with a small error from ideal output data corresponding to predetermined input data in a data conversion apparatus defined by an appropriate number of discrete value coefficients. . The present invention can be applied to, for example, determination of coefficients of a color conversion device using a hierarchical neural network having discrete coefficient values, and determination of representative point values for color conversion using a representative point table and interpolation.
[0002]
[Prior art]
In a data conversion apparatus defined by an appropriate number of discrete-value coefficients, if the range of possible coefficients is limited, the types of values that each coefficient can take are limited. Therefore, if errors are evaluated for all combinations of coefficients, there is at least one optimum coefficient. In addition, according to the method of searching the entire space of coefficients in this way, it is possible to surely obtain an optimum coefficient. However, in general, there are an enormous number of such combinations, and this is not practical as a method for calculating coefficients. Therefore, it is common to calculate the coefficients by a priori method or various approximate methods based on the characteristics of each data converter.
[0003]
In a data conversion device that includes discrete value coefficients, if the optimal coefficient is determined a priori for any given input / output response, the coefficient can be determined by that method, using conventional techniques. But it won't be a problem.
[0004]
On the other hand, even if the coefficient is determined a priori, it may not be a discrete coefficient. For example, in a data conversion device using matrix operations consisting of coefficients of discrete values, each coefficient that minimizes the error can be calculated a priori, but the calculation result is not a discrete value, and this is rounded, rounded up, rounded down, etc. Therefore, an operation of rounding to a discrete value is required. Since each coefficient becomes a value different from the optimum value due to rounding, the error generally increases.
[0005]
Similarly, even in the case of a technique such as matrix operation, when the effective accuracy is limited in the operation process, for example, in the case of finite precision fixed-point product-sum operation, the calculation process is rounded in the operation process of the data converter. Etc., the accuracy further decreases. In such a case, it is necessary to consider characteristics such as rounding of the calculation process in order to calculate the optimum coefficient. However, since the correspondence between the coefficient and the error has a very complicated relationship, it is conventionally considered. There was no. In order to improve accuracy by conventional techniques, techniques such as effective accuracy in calculation processes and finer increments of coefficients have been generally used.
[0006]
In a data conversion apparatus using a representative point table and interpolation, the converted data is recorded in advance in a table at a grid point composed of input representative points of each dimension, and a conversion result is obtained by performing interpolation. As a coefficient recorded in the table in such a data conversion apparatus, data after conversion of representative points is generally used. In general, an interpolation error occurs due to interpolation, but there has been no method for optimizing the coefficients recorded at the grid points in consideration of input conversion errors other than the grid points. In order to improve the accuracy by the conventional technique, generally, a technique of increasing the number of representative points of the input dimension has been used.
[0007]
For a data conversion device in which a coefficient is a continuous value and an error can be partially differentiated by each coefficient, a coefficient determination method by successive approximation of a differential equation is known. In particular, in a neural network, a coefficient calculation method represented by a back propagation method is generally used.
[0008]
However, in the case of including discrete-value coefficients, it is impossible to perform partial differentiation of errors with these coefficients, and the above-described method represented by back-propagation cannot be used.
[0009]
Therefore, conventionally, in the case where a data converter capable of partial differentiation can be configured with the same configuration, a technique has been used in which a coefficient is calculated in advance as a continuous value and the result is rounded to obtain a discrete value coefficient. It was. In this case, as with the above-described determinant, there is a problem that accuracy is reduced by rounding.
[0010]
In learning by hardware, a technique similar to backpropagation in which similar differential equations are approximated with finite precision has been used. This technique has a problem in that learning stops when the error of back propagation falls below the calculation accuracy.
[0011]
Furthermore, in the case of neural networks using finite precision fixed-point operations, as with fixed-point determinants, there is an influence such as rounding of the calculation process, and the relationship between coefficients and errors becomes more complicated, so the optimum optimum is actually achieved. It was difficult to obtain discrete values. In order to improve accuracy by conventional techniques, techniques such as effective accuracy in calculation processes and finer increments of coefficients have been generally used. When the effective accuracy and the coefficient increment are made fine, the configuration of the data conversion apparatus becomes complicated.
[0012]
In addition, this method has a problem that the configuration of the apparatus based on this method becomes complicated because it is necessary to solve the differential equation by successive approximation.
[0013]
As a learning method having a relatively simple configuration when limited to a neural network, a coefficient update difference amount is generated by a random number and updated as disclosed in JP-A-4-282476 (US Pat. No. 5,459,817). There was a method to update the coefficient by the alternative of before and after. This method requires a mechanism that generates random numbers for each synapse. Furthermore, since the update amount itself is not controlled and only the code is controlled by a random number, the update amount is not controlled from the initial stage of learning to the stage where the sequential learning progresses. For this reason, there is a problem in that the speed of learning arises, and there is a problem that convergence will be minimal if the alternative configuration is not properly performed.
[0014]
[Problems to be solved by the invention]
Of the methods described above, except for the method of searching the entire space of the coefficients, the method of calculating the coefficients is different based on the configuration of each data conversion device, and when a device based on these methods is configured, There has been a problem that the configuration of the apparatus becomes complicated. Further, as described above, an apparatus based on a technique for searching the entire space of coefficients is not realistic because it searches a huge space, although the configuration is simple.
[0015]
In order to improve the accuracy of the data conversion apparatus, it is necessary to change the configuration of the apparatus and method.
[0016]
In addition, when updating a coefficient based on a differential coefficient, it is essential to construct a differential equation, and for a non-differentiable correspondence such as a digit loss, a differential equation cannot be constructed and the coefficient cannot be determined. It was.
[0017]
Therefore, the present invention has less errors in a shorter time than the method of searching the entire space of coefficients, regardless of the configuration of each data conversion apparatus, taking into account the influence of the coefficients themselves and the rounding of the calculation process. It is an object to calculate a coefficient.
[0018]
[Means for Solving the Problems]
The present invention is characterized in that a coefficient having a small error is calculated by reducing the error by repeating an operation based on calculation of the error and selection of a probabilistic coefficient depending on the error.
[0019]
That is, according to the present invention, in order to achieve the above-described object, m-dimensional input data is converted into n-dimensional output data according to k coefficients including at least one coefficient that takes discrete values. A coefficient determination device for optimizing a coefficient in a data conversion apparatus, for each coefficient having a discrete value, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and the current Means for calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than the coefficient value by a predetermined step s2, and an output data group calculated for the at least two coefficient values and the predetermined value The probability that the smaller the error from the ideal output data group corresponding to the input data group is, the higher the probability is, and one of the at least two coefficient values is newly set. And it is provided with a coefficient value selecting means for selecting as a number.
[0020]
In this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value having a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0021]
Further, in this configuration, the coefficient value selecting means includes means for adding a random number according to a predetermined distribution to each error in the at least two coefficient values and selecting a coefficient value that gives a minimum value of the sum. Can be.
[0022]
Also, a means for controlling the degree of the gradual decrease of the probability with respect to the magnitude of the error or derivative, or the predetermined steps s1 and s2, or both according to the error history may be provided. Good.
[0023]
The means for controlling the degree of gradual decrease of the probability with respect to the magnitude of the error according to the error history may be a means for controlling the predetermined distribution of random numbers.
[0024]
In addition, at least one coefficient taking the discrete value is recorded in advance as a discrete value corresponding to n outputs for each representative point in the m-dimensional representative point table corresponding to the m-dimensional input data. The value corresponding to the output of the representative point of the data conversion apparatus that obtains the n-dimensional output by interpolating the value corresponding to the output, and defining the error and the ideal output value group for the appropriate input value group Thus, a means for updating the coefficient can be provided.
[0025]
Further, according to the present invention, in order to achieve the above-described object, the data conversion apparatus receives m-dimensional input data according to k coefficients including at least one coefficient taking a discrete value. For each of the data conversion means for converting to output data and the coefficient taking the discrete value, a current coefficient value, a coefficient value larger by a predetermined step s1 than the current coefficient value, and a predetermined value from the current coefficient value Means for calculating an output data group for a predetermined input data group with respect to at least two coefficient values among the coefficient values small by step s2, and the output data group calculated for the at least two coefficient values and the predetermined input data group. A factor for selecting one of the at least two coefficient values as a new coefficient value with a probability that the smaller the error from the corresponding ideal output data group is, the higher the probability is. Are provided and a value selection means.
[0026]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0027]
Further, according to the present invention, in order to achieve the above-described object, the color conversion device receives m-dimensional first color data according to k coefficients including at least one coefficient taking a discrete value. color conversion means for converting to n-dimensional second color data; and for each of the coefficients taking discrete values, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and the above Means for calculating a second color data group for a predetermined first color data group for at least two coefficient values of coefficient values smaller than the current coefficient value by a predetermined step s2, and calculating for the at least two coefficient values; Any one of the at least two coefficient values has a probability of increasing as the error between the second color data group and the ideal second color data group corresponding to the predetermined first color data group decreases. The new A coefficient value selecting means for selecting as a number is provided.
[0028]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0029]
In this configuration, the error can be a color difference.
[0030]
Further, according to the present invention, in order to achieve the above object, the color image forming apparatus (for example, a color copying machine or a color printing machine) receives the m-dimensional first color data, discrete values, and the like. Color conversion means for converting the m-dimensional first color data into n-dimensional second color data in accordance with k coefficients including at least one coefficient taking the above, and the color conversion means output from the color conversion means For each of the output means for performing a predetermined output operation based on the second color data and the coefficient having the discrete value, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, And means for calculating a second color data group for a predetermined first color data group for at least two coefficient values of coefficient values smaller than the current coefficient value by a predetermined step s2, and the at least two coefficient values One of the at least two coefficient values has a probability that it increases as the error between the calculated second color data group and the ideal second color data group corresponding to the predetermined first color data group decreases. Coefficient value selection means for selecting one as a new coefficient value is provided.
[0031]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0032]
In this configuration, the output means may receive the second color data via a subsequent color conversion means.
[0033]
Further, according to the present invention, in order to achieve the above-described object, the electronic device is provided with means for receiving m-dimensional input data and k coefficients including at least one coefficient taking a discrete value. Data conversion means for converting the m-dimensional input data into n-dimensional output data; output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means; For each coefficient that takes a value, at least two coefficient values are selected from the current coefficient value, a coefficient value that is larger than the current coefficient value by a predetermined step s1, and a coefficient value that is smaller than the current coefficient value by a predetermined step s2. Means for calculating an output data group for a predetermined input data group, corresponding to the output data group calculated for the at least two coefficient values and the predetermined input data group That at a probability becomes higher as a small error from the ideal output data group, so that provided the coefficient value selecting means for selecting one of the at least two coefficient values as a new coefficient value.
[0034]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0035]
In addition, according to the present invention, coefficients are optimized in a data conversion apparatus that converts m-dimensional input data into n-dimensional output data according to k coefficients including at least one coefficient taking discrete values. For the coefficient determination device, for each coefficient taking the discrete value, means for calculating an output data group for p kinds of coefficient values in an appropriate section including the current coefficient value, and for the p kinds of coefficient values An error between the calculated output data group and the ideal output data group corresponding to the predetermined input data group is calculated, and a calculation means for obtaining p types of errors, and a differential in the current coefficient value from the p types of errors. Assuming a possible predetermined function from the coefficient value to the error, a differential coefficient calculating means for calculating the differential coefficient at the current coefficient value, and a function for updating the coefficient probabilistically or deterministically based on the above-mentioned differential coefficient Numeric It is to be provided and new means.
[0036]
Here, instead of obtaining p kinds of coefficients from an appropriate section including the current coefficient value, p kinds of coefficient values can be calculated by applying p kinds of predetermined functions to the current coefficient value. . This function can be an arbitrary function. In particular, an appropriate discrete value can be added to the current coefficient value to obtain a function value, and the appropriate value can be changed to the current coefficient value. A value obtained by multiplying and rounding the product of the result to a discrete value can also be used as a function value. Means may be further provided for controlling the number of p and the predetermined p types of functions according to an error history. The predetermined function may be a function value obtained by adding an appropriate discrete value to the current coefficient value. Further, the predetermined function is obtained by multiplying an appropriate value by a current coefficient value or dividing the current coefficient value by an appropriate value and rounding the product or quotient of the result to a discrete value. It may be a function value.
[0037]
In this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0038]
In this configuration, at least one of the current coefficient value, the coefficient value obtained by adding the predetermined step s1 to the current coefficient value, and the coefficient value obtained by subtracting the predetermined step s2 from the current coefficient value is the above-mentioned p types. It can be included in the coefficient.
[0039]
Further, means for controlling the degree of the gradual decrease of the probability with respect to the magnitude of the derivative and one or both of the predetermined steps s1 and s2 according to an error history may be provided.
[0040]
In addition, at least one coefficient taking the discrete value is recorded in advance as a discrete value corresponding to n outputs for each representative point in the m-dimensional representative point table corresponding to the m-dimensional input data. The value corresponding to the output of the representative point of the data conversion apparatus that obtains the n-dimensional output by interpolating the value corresponding to the output, and defining the error and the ideal output value group for the appropriate input value group Thus, means for updating the coefficient may be provided.
[0041]
Further, according to the present invention, in order to achieve the above-described object, the data conversion apparatus receives m-dimensional input data according to k coefficients including at least one coefficient taking a discrete value. Data conversion means for converting to output data; means for calculating an output data group for p types of coefficient values in an appropriate section including the current coefficient value for each of the coefficients having discrete values; An error between the output data group calculated for the type of coefficient value and the ideal output data group corresponding to the predetermined input data group is calculated to obtain p types of errors, and from the p types of errors, the current Assuming a function from an appropriate differentiable count value to an error in the coefficient value of, and a differential coefficient calculation means for calculating a differential coefficient at the current coefficient value, and a coefficient stochastic or deterministically based on the above differential coefficient Update And it is provided with a coefficient value updating means.
[0042]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0043]
Further, according to the present invention, in order to achieve the above-described object, the color conversion device receives m-dimensional first color data according to k coefficients including at least one coefficient taking a discrete value. Color conversion means for converting to n-dimensional second color data, and second color data for p-type coefficient values in an appropriate section including the current coefficient value for each of the coefficients having discrete values. Calculating an error between the means for calculating the group, the second color data group calculated for the p kinds of coefficient values, and the ideal second color data group corresponding to the predetermined first color data group; Assuming a calculation means for obtaining p types of errors and a predetermined function from the coefficient values to the errors that can be differentiated in the current coefficient values from the p types of errors, a differential coefficient in the current coefficient values is calculated. Based on the derivative calculation means and the above derivative, And it is provided with a coefficient value updating means for updating the coefficients Joteki.
[0044]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0045]
In this configuration, the error can be a color difference.
[0046]
Further, according to the present invention, in order to achieve the above-mentioned object, the color image forming apparatus (for example, a color copying machine or a color printing machine) receives the m-dimensional first color data and the discrete values. Color conversion means for converting the m-dimensional first color data into n-dimensional second color data in accordance with k coefficients including at least one coefficient taking the above, and the color conversion means output from the color conversion means The output means for performing a predetermined output operation based on the second color data, and the second of the p types of coefficient values in the appropriate section including the current coefficient value for each of the coefficients having the discrete values. An error between the means for calculating the color data group, the second color data group calculated for the p kinds of coefficient values, and the ideal second color data group corresponding to the predetermined first color data group is calculated. Calculating means for obtaining p types of errors, and the above p types Assuming a predetermined function from the coefficient value to the error, which is differentiable from the error of the current coefficient value, and based on the differential coefficient calculating means for calculating the differential coefficient in the current coefficient value, Coefficient value updating means for updating the coefficient stochastically or deterministically is provided.
[0047]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0048]
In this configuration, the output means may receive the second color data via a subsequent color conversion means.
[0049]
Further, according to the present invention, in order to achieve the above-described object, the electronic device is provided with means for receiving m-dimensional input data and k coefficients including at least one coefficient taking a discrete value. Data conversion means for converting the m-dimensional input data into n-dimensional output data; output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means; For each coefficient that takes a value, means for calculating an output data group for p types of coefficient values in an appropriate section including the current coefficient value, an output data group calculated for the p types of coefficient values, and the predetermined value A calculation means for calculating an error from the ideal output data group corresponding to the input data group and obtaining p types of errors, and from the p types of errors to a coefficient value to an error that can be differentiated in the current coefficient value. Place As a function, a differential coefficient calculation unit that calculates a differential coefficient at the current coefficient value, and a coefficient value update unit that updates the coefficient stochastically or deterministically based on the differential coefficient are provided. .
[0050]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0051]
Further, according to the present invention, in order to achieve the above-described object, the coefficient value is determined in a neural network having k coefficients including at least one of discrete coupling coefficients and / or discrete threshold values. For each of the coefficients that take the discrete values, the coefficient determination device that performs the optimization has a current coefficient value, a coefficient value that is larger than the current coefficient value by a predetermined step s1, and a predetermined value that is greater than the current coefficient value. Means for calculating an output data group for a predetermined input data group for at least two coefficient values of coefficient values smaller by step s2, and corresponding to the output data group calculated for the at least two coefficient values and the predetermined input data group One of the at least two coefficient values is replaced with a new coefficient value with a probability that the smaller the error from the ideal output data group is, the higher the probability is. And it is provided with a coefficient value selecting means for selecting and.
[0052]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0053]
Further, according to the present invention, in order to achieve the above-mentioned object, the data conversion apparatus includes a neural network having k coefficients including at least one of discrete coupling coefficients and / or discrete threshold values. For each of the network and the coefficient taking the discrete value, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and a coefficient value smaller than the current coefficient value by a predetermined step s2. Means for calculating an output data group for a predetermined input data group for at least two coefficient values, an output data group calculated for the at least two coefficient values, and an ideal output data group corresponding to the predetermined input data group, A coefficient value selection that selects one of the at least two coefficient values as a new coefficient value with a probability that the error becomes higher as the error of And it is provided with a means.
[0054]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0055]
Further, according to the present invention, in order to achieve the above-mentioned object, the coefficient value is calculated in a neural network having k coefficients including at least one of discrete coupling coefficients and / or discrete threshold values. A coefficient determination device to be optimized has means for calculating an output data group for p kinds of coefficient values in an appropriate section including a current coefficient value, for each of the coefficients having the discrete values, An error between the output data group calculated for the coefficient value and an ideal output data group corresponding to the predetermined input data group is calculated, and a calculation means for obtaining p types of errors, and the current relation from the p types of errors. Assuming a specific function that can be differentiated numerically from the coefficient value to the error, the derivative calculation means for calculating the derivative at the current coefficient value, and the probability or confirmation based on the derivative And it is provided with a coefficient value updating means for updating the coefficients.
[0056]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0057]
Further, according to the present invention, in order to achieve the above-mentioned object, the data conversion apparatus includes a neural network having k coefficients including at least one of discrete coupling coefficients and / or discrete threshold values. For each of the network and the coefficient taking the discrete value, a means for calculating an output data group for p types of coefficient values in an appropriate section including the current coefficient value, and calculation for the p types of coefficient values An error between the output data group and the ideal output data group corresponding to the predetermined input data group is calculated to obtain p types of errors; from the p types of errors, the current coefficient value can be differentiated. Supposing a predetermined function from the coefficient value to the error, a derivative calculating means for calculating a derivative in the current coefficient value, and a function for updating the coefficient probabilistically or deterministically based on the derivative And it is provided with a value updating means.
[0058]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0059]
According to the present invention, in order to achieve the above-mentioned object, m-dimensional input data is converted into n-dimensional output data according to k coefficients including at least one coefficient taking discrete values. A coefficient determination device for optimizing a coefficient value in a data conversion apparatus, for each coefficient having a discrete value, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and the current Means for calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than the coefficient value by a predetermined step s2, and the output data group calculated for the at least two coefficient values and the predetermined value The probability that the smaller the error from the ideal output data group corresponding to the input data group is, the higher the probability is that it becomes higher, and one of the at least two coefficient values is newly associated Coefficient value selecting means for selecting values, means for calculating an output data group for p kinds of coefficient values in an appropriate section including the current coefficient value, for each of the coefficients having discrete values, and the p An error between the output data group calculated for the type of coefficient value and the ideal output data group corresponding to the predetermined input data group is calculated to obtain p types of errors, and from the p types of errors, the current Assuming a predetermined function from the coefficient value to the error that can be differentiated in the coefficient value, a derivative calculation means for calculating the derivative in the current coefficient value, and based on the derivative, probabilistically or deterministically Coefficient value updating means for updating the coefficient is provided, and after the coefficient value selection by the coefficient value selection means is executed at least once, the coefficient value update by the coefficient value update means is executed at least once. .
[0060]
In this configuration, first, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Thereafter, an error function is assumed based on this error, and a differential coefficient of the error function at the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0061]
According to the present invention, in order to achieve the above-mentioned object, m-dimensional input data is converted into n-dimensional output data according to k coefficients including at least one coefficient taking discrete values. In the method of determining the coefficient value in the data converter, for each coefficient having the discrete value, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and the current coefficient A step of calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than a numerical value by a predetermined step s2, and an output data group calculated for the at least two coefficient values and the predetermined input One of the at least two coefficient values is newly added with a probability that the smaller the error from the ideal output data group corresponding to the data group, the higher the error. And so as to execute and selecting a coefficient value.
[0062]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0063]
According to the present invention, in order to achieve the above-mentioned object, m-dimensional input data is converted into n-dimensional output data according to k coefficients including at least one coefficient taking discrete values. In the method for determining the coefficient value in the data converter, for each coefficient having the discrete value, calculating an output data group for p types of coefficient values in an appropriate section including the current coefficient value; Calculating a difference between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group, and obtaining p kinds of errors; and from the p kinds of errors, Assuming a predetermined function from a coefficient value to an error that is differentiable in the current coefficient value, calculating a derivative in the current coefficient value, and, based on the derivative, probabilistic or It is to be executed and updating the coefficients Joteki.
[0064]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0065]
According to the present invention, in order to achieve the above-mentioned object, m-dimensional input data is converted into n-dimensional output data according to k coefficients including at least one coefficient taking discrete values. In the method of determining the coefficient value in the data converter, for each coefficient having the discrete value, a current coefficient value, a coefficient value larger than the current coefficient value by a predetermined step s1, and the current coefficient A step of calculating an output data group for a predetermined input data group for at least two coefficient values among coefficient values smaller than a numerical value by a predetermined step s2, and an output data group calculated for the at least two coefficient values and the predetermined input One of the at least two coefficient values is newly added with a probability that the smaller the error from the ideal output data group corresponding to the data group, the higher the error. Output data for p types of coefficient values in an appropriate section including the current coefficient value for each of the coefficients taking discrete values after the step of selecting as a coefficient value and the new coefficient value is selected Calculating a group; and calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group, and obtaining p kinds of errors; Assuming a predetermined function from the coefficient value to the error that can be differentiated from the p types of errors from the current coefficient value, calculating a differential coefficient at the current coefficient value, and based on the differential coefficient, The coefficient is updated probabilistically or deterministically, the coefficient value is selected one or more times, and then the coefficient value is updated one or more times.
[0066]
In this configuration, first, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Thereafter, an error function is assumed based on this error, and a differential coefficient of the error function at the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0067]
According to the present invention, in order to achieve the above-mentioned object, m-dimensional input data is converted into n-dimensional output data according to k coefficients including at least one coefficient taking discrete values. In the method of setting the coefficient value in the data converter, in a standard data converter having a function equivalent to that of the main body of the data converter, for each coefficient taking the discrete value, a current coefficient value, the current Calculating an output data group for a predetermined input data group for at least two coefficient values among a coefficient value larger than the coefficient value by a predetermined step s1 and a coefficient value smaller than the current coefficient value by a predetermined step s2; The error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the predetermined input data group is small. The step of selecting any one of the at least two coefficient values as a new coefficient value and the step of setting the selected coefficient as a coefficient of the data conversion device main body are executed with a probability of becoming higher. ing.
[0068]
Also in this configuration, an error is calculated for a candidate coefficient value, and a candidate coefficient value with a smaller error is set to a new coefficient value with a higher probability. Therefore, the coefficient value can be optimized by repeatedly updating the coefficient value.
[0069]
According to the present invention, in order to achieve the above-mentioned object, m-dimensional input data is converted into n-dimensional output data according to k coefficients including at least one coefficient taking discrete values. In the method of setting the coefficient value in the data conversion apparatus, the reference data conversion apparatus having a data conversion function equivalent to that of the data conversion apparatus main body includes a current coefficient value for each of the coefficients taking the discrete values. Calculating an output data group for p types of coefficient values in an appropriate section; and calculating an error between the output data group calculated for the p types of coefficient values and an ideal output data group corresponding to the predetermined input data group. Assuming a calculation means for calculating and obtaining p types of errors, and a predetermined function from coefficient values to errors that can be differentiated from the p types of errors in the current coefficient value, A step of calculating a differential coefficient in the coefficient value, a step of updating the coefficient probabilistically or deterministically based on the differential coefficient, and a step of setting the updated coefficient as a coefficient of the data converter main body I am doing so.
[0070]
Also in this configuration, an error is calculated for the candidate coefficient value, an error function is assumed based on this error, and a differential coefficient of the error function in the current coefficient value is obtained based on this function. Then, a new coefficient value is obtained based on this differential coefficient. By repeatedly updating the coefficient value, the coefficient value can be optimized.
[0071]
BEST MODE FOR CARRYING OUT THE INVENTION
Examples of the present invention will be described below.
[Example 1]
FIG. 1 shows a configuration of a first embodiment of the present invention. In this figure, a coefficient optimization system of a data conversion apparatus includes an input buffer 11, a data conversion apparatus 12, an output buffer 13, an ideal output memory 14, An error calculation unit 15, an error history memory 16, a random number distribution control unit 17, a step control unit 18, and a coefficient update unit 19 are included. The input buffer 11 stores m-dimensional input data given from the outside. The data converter 12 converts m-dimensional input data into n-dimensional output data using coefficients that take discrete values. The output buffer 13 stores n-dimensional output data output from the data converter 12. The error calculation unit 15 calculates an error between the output data and the ideal output data, and sends this error to the coefficient update unit 19 and the error history memory 16. The random number distribution control unit 17 varies the random number distribution according to the error history, and the step control unit 18 also varies the step size according to the error history. Thereby, annealing is performed. The coefficient updating unit 19 sets a coefficient value that minimizes the sum of the error and the random number as a new coefficient value.
[0072]
Next, optimization of coefficients will be described in detail. A case where j sets of m-dimensional input data and corresponding n-dimensional ideal output data are given will be described. That is, the input data x and the ideal output data y are expressed as {x₁, Y₁}, {X₂, Y₂}, ..., {x_i, Y_i} ..., {x_j, Y_j} And each input data x_iIs m-dimensional and x_i= (X_i1, X_i2, ..., x_im) And each ideal output data y_iIs n-dimensional and y_i= (Y_i1, Y_i2, ..., y_in). K coefficients (w₁, W₂, ..., w_p, ..., w_k) Is initialized in advance with an appropriate initial value, for example, a coefficient determined by a conventional method such as rounding, or all zeros. In this data converter, m-dimensional data x_iIs given by f (x_i｜ w₁, W₂, ..., w_p, ..., w_k). Ideal output y at this time_iAnd d (y_i, F (x_i｜ w₁, W₂, ..., w_p, ..., w_k)). Here, d is an appropriate n-dimensional distance, such as the Euclidean distance. In this embodiment, the error of this data conversion apparatus is calculated by adding the error of each data.
[0073]
[Expression 1]
E (w₁, W₂, ..., w_p, ..., w_k)
= Σ_{i = 1 ... j}d (y_i, F (x_i｜ w₁, W₂, ..., w_p, ..., w_k))
And
[0074]
Now, of the k coefficients, the p-th coefficient w_pThe error E with respect to the current coefficient value₀That is, E₀= E (w₁, W₂, ..., w_p, ..., w_k), An error E for a coefficient value larger than the current coefficient value by a predetermined step s.₊That is, E₊= E (w₁, W₂, ..., w_p+ S, ..., w_k) And an error E for a coefficient value smaller than the current coefficient value by a predetermined step s._-That is, E_-= E (w₁, W₂, ..., w_p-S, ..., w_k) Three types of errors are calculated. In this embodiment, the predetermined step in the case of addition and the predetermined step in the case of subtraction are s in both cases, but the predetermined step in the case of addition and the predetermined step in the case of subtraction are not necessarily the same value. It is not necessary to.
[0075]
Next, a random number N based on a uniform distribution in a predetermined section [0, T] is added to each of these errors,
[0076]
[Expression 2]
e₀= E₀+ N
e₊= E₊+ N
e_-= E_-+ N
Get. Where e₀, E₊, E_-E₀If is the smallest, w_pWill not be updated. e₊If is the smallest, w_pS is added to and updated. e_-If is the smallest, w_pSubtract from s and update.
[0077]
This operation is performed for each coefficient w_p(P = 1, 2,..., K). When this optimization operation completes one round, the error of the data conversion apparatus is obtained, and the error is repeated until it reaches a predetermined value or is almost converged, or a predetermined number of times. At that time, if the minimum error occurs, the coefficient is recorded as an “optimum coefficient”, and T is increased by multiplying T, which determines the predetermined section, by a predetermined value greater than 1. Let On the other hand, if the error has increased compared to before performing one round of optimization, T is decreased by multiplying T by a predetermined value smaller than 1. The same operation is performed for the predetermined step s, but the value is not less than the minimum step.
[0078]
As described above, when the learning is finished, the finally recorded “optimum coefficient” is output.
[0079]
Next, a specific procedure for determining the coefficient will be described using the simplest example of this embodiment shown in FIG. 1 input 1 output, 2 integer coefficients w₁And w₂A data conversion apparatus having the following formula will be described.
[0080]
[Equation 3]
y = x · w₁+ W₂
Here, x is an input of the data converter, and y is an output of the data converter. The predetermined step is s₁= S₂= 1, the following values are supplied to the data converter as an input group and a corresponding ideal output group.
[0081]
[Table 1]

By the method of determining the coefficients according to this embodiment, w₁And w₂And the initial value is 0. In this case, the total Euclidean distance is used as the error. First, w₁Is calculated by adding an error and a uniform random number in the interval [0... 2] to the error. As a result, it is calculated as shown in the following table.
[0082]
[Table 2]

Based on this result, w₁Will not be updated. Then w₂Similarly, the error and the error plus the same random number are calculated. As a result, it is calculated as shown in the following table.
[0083]
[Table 3]

Based on this result, w₂Also do not update. This situation is an example of a minimal situation where the error is smaller when neither variable is changed. Since an error is added in the present embodiment, this calculation is continuously repeated, and it is possible to escape from such a minimum with a predetermined probability.
[0084]
At this point, the error is evaluated and 2 is obtained. Since the error is large, w₁For, calculate the error and the error plus a random number. As a result, it is calculated as shown in the following table.
[0085]
[Table 4]

Based on this result, w₁Is updated to 1. In addition, w₂Similarly, an error and a value obtained by adding a random number to the error are calculated. As a result, it is calculated as shown in the following table.
[0086]
[Table 5]

Based on this result, w₂Is updated to -1. At this point, the error is evaluated and 0 is obtained. Since the error is sufficiently small, the coefficient optimization is finished.
[0087]
As described above by way of example, according to this embodiment, the error gradually decreases, and the error is minimized by adding a predetermined random number. Can be obtained.
[0088]
In the simple example shown above, the optimization is completed when the optimization is performed twice, but it is general that a more complex coefficient needs to be determined in the practical coefficient determination. In this case, if optimization is performed while the size of the random number is large, even if the optimization is almost completed, it is difficult to converge to the final coefficient. Therefore, the size of the random number is reduced and the convergence is advanced so that a coefficient with a small error is selected with a higher probability. On the other hand, if the random number is too small, it may be impossible to escape the minimum. In this embodiment, this problem is solved by controlling the probability based on the error history.
[0089]
In the simple example shown above, the predetermined step is s.₁, S₂Although 1 is used for both, a predetermined step is controlled by a history of errors for the purpose of speeding up the processing and for the purpose of being able to escape from the minimum with a higher probability. Also, s₁, S₂Using different values for and substantially smaller steps, ie s₁, S₂, | S₁-S₂Allows optimization by the greatest common divisor of |.
[0090]
Although the operation has been described with a simple example, the same operation is performed even in a complicated data conversion apparatus according to the present embodiment.
[0091]
In this method, the error of the data conversion apparatus is evaluated by an error including rounding and accuracy in the apparatus. Accordingly, it is possible to calculate a coefficient having a smaller error at a higher speed than in the entire search, including such an error.
[0092]
[Example 2]
Next, a second embodiment in which color conversion is performed using a neural network that takes discrete coefficients as a data conversion apparatus will be described. FIG. 3 shows the configuration of the present embodiment. In this figure, portions corresponding to those in FIG. In FIG. 3, the input buffer 11 holds C (Cyan), M (magenta), Y (yellow), and K (black) area ratios for printing as input data. The color conversion device 21 using a neural network calculates C, M, Y, and K area ratios as CIE^*a^*b^*(D50) Conversion into color coordinates. The coefficients of the neural network are discrete and are optimized by the coefficient update unit 19. The converted color coordinate data is stored in the output buffer 13, and the color difference calculation unit 22 calculates the color difference between the output color coordinate data and the ideal color coordinate data. The color difference square average calculation unit 23 calculates the square average of the color differences, and this is regarded as an error.
[0093]
Next, optimization of the coefficients of the color conversion device 21 will be described in detail. As described above, the color conversion device 21 determines the area ratio of C, M, Y, and K for printing as CIE L for printing results.^*a^*b^*(D50) Conversion into color coordinates. In determining the coefficients of the color conversion device 21, 928 sets of CMYK area ratios based on IT8 / 7.3 extended set are used as inputs, and printing is performed based on each area ratio as an ideal output. Color measurement with D50 light source, CIE L^*a^*b^*Use color coordinates. That is, the input data x and the ideal output data y are expressed as {x₁, Y₁}, {X₂, Y₂}, ..., {x_i, Y_i} ..., {x₉₂₈, Y₉₂₈} And each input data x_iIs four-dimensional and x_i= (C_i, M_i, Y_i, K_i) And each ideal output data y_iIs three-dimensional and y_i= (L_i, A_i, B_i). K coefficients (w₁, W₂, ..., w_p, ..., w_k) Are initialized to 0 in advance. In this data converter, data x_iIs given as g (x_i｜ w₁, W₂, ..., w_p, ..., w_k). Ideal output y at this time_iError with ΔE color difference, that is, CIE L^*a^*b * Euclidean distance ΔE (y in color space_i, G (x_i｜ w₁, W₂, ..., w_p, ..., w_k)). In this embodiment, the error of the color conversion device is calculated by calculating the root mean square error of each color, that is,
[0094]
[Expression 4]

And
[0095]
Now, of the k coefficients, the p-th coefficient w_pThe error E with respect to the current coefficient value₀That is, E₀= E (w₁, W₂, ..., w_p, ..., w_k) And a predetermined step s from the current coefficient value₁Error E for large coefficient values₊That is, E₊= E (w₁, W₂, ..., w_p+ S₁, ..., w_k) And a predetermined step s from the current coefficient value₂Error E for small coefficient values, ie E_-= E (w₁, W₂, ..., w_p-S₂, ..., w_k) Three types of errors are calculated. In this embodiment, the predetermined step for addition is a different value, but the predetermined step for addition and the predetermined step for subtraction do not necessarily have to be different values.
[0096]
Next, based on these errors, one of the lower errors is selected by an appropriate function that is selected with a higher probability. E₀If is selected, w_pWill not be updated. E₊If is selected, w_pIn₁Add and update. E_-If is selected, w_pTo s₂Reduce and update.
[0097]
Repeat this operation for each weight w_p(P = 1, 2,..., K). When this optimization operation completes one cycle, the error of this color conversion device is obtained and repeated until it reaches a predetermined value or substantially converges or until a predetermined number of times. At that time, when the error becomes the minimum, the coefficient is recorded as “optimum coefficient”, and s is increased by multiplying the predetermined step s by a predetermined value larger than 1. On the other hand, if the error has increased compared to before performing one round of optimization, s₁And S₂Is multiplied by a predetermined value less than 1, and s₁And S₂Is not reduced below the minimum step.
[0098]
As described above, when the learning is finished, the finally recorded “optimum coefficient” is output.
[0099]
[Example 3]
Next, a description will be given of a third embodiment using a color conversion device using a table in which coefficients take discrete values and interpolation. FIG. 4 shows the configuration of the third embodiment. In this figure, portions corresponding to those in FIG. In FIG. 4, the input buffer 11 receives CIE L as input data.^*a^*b^*  (D50) Color coordinate data is stored. The color conversion device 31 uses a table in which coefficients take discrete values and interpolation, and CIE L^*a^*b^*  (D50) The color coordinates are input, and the C, M, Y, and K area ratios of a predetermined printing apparatus are calculated. In this embodiment, the value stored in each grid point is a discrete value. Details of the conversion device 31 will be described later. The area ratios of C, M, Y, and K are stored in the output buffer 13, and based on this, the printing device 32 is driven to obtain a print output. After this, print output is measured and CIE L^*a^*b^*(D50) Color coordinate data is obtained. This color coordinate data is stored in the measurement value buffer 33. The ideal output data memory 14 stores the input data itself, the color difference between the input data and the color coordinate data of the measurement value buffer 33 is calculated by the color difference calculation unit 22, and the average color difference is calculated by the average color difference calculation unit 34. It is considered an error.
[0100]
Next, optimization of the coefficient of the conversion device 31 will be described in detail. The conversion device 31 has an L on the input space.^*Axis, a^*Axis, b^*The CMYK area ratios after conversion are recorded in advance in a representative point of each axis, for example, a three-dimensional table consisting of 10 points on each axis, and at the time of color conversion, it corresponds to each vertex of a rectangular parallelepiped including the input color coordinates The conversion value of the lattice point is interpolated according to the position in the rectangular parallelepiped to obtain the conversion result. As the interpolation method, tetrahedral interpolation method, prism interpolation method, cubic interpolation method and the like are known. . This embodiment can be applied to any of these interpolation methods.
[0101]
In general, the conversion value stored in each grid point is a value obtained by rounding the conversion value of each representative point according to the accuracy of the table. In any interpolation method, an interpolation error occurs depending on the correspondence between input and output. .
[0102]
The error of the color conversion device in a predetermined coefficient is defined as an average color difference obtained by the following procedure. Color conversion is performed by a predetermined coefficient at a sufficiently fine predetermined interval, for example, an interval of 1/16 of the interval between the representative values of the grid points in each dimension, and each area ratio of CMYK is calculated. Printing is performed based on the calculation result, the color difference between the colorimetric value and the color coordinate before conversion is calculated, and the average color difference over the entire input range is regarded as an error. At this time, instead of actually performing printing and measuring the color, the predicted value after printing may be estimated using a modeled printer.
[0103]
The present embodiment aims to optimize the value of each grid point so that the average color difference after interpolation is minimized, and performs the following optimization.
[0104]
First, for all grid points, the coefficients of discrete values {C (L, A, B), M (L, A, B), Y (L, L) stored in the table of each grid point (L, A, B) are used. A, B), K (L, A, B)} are initialized with values obtained by rounding the corresponding conversion values according to the precision of the table. Let T and s be appropriate initial values. Each grid point is assigned a serial number in order from the lowest saturation within the color reproduction range. Subsequently, a serial number is assigned to the grid points outside the color reproduction range in ascending order of color difference before and after conversion. Next, the following processing steps are performed.
Process (1): The grid point values of K are optimized by the operations of processes (1.1) to (1.3) in ascending order of serial numbers.
Process (1.1): A predetermined step s is added to the current value of K, and the error of the color conversion device is calculated.
Process (1.2): A predetermined step s and a minimum unit of steps are subtracted from the current value of K, and an error of the color conversion device is calculated.
[0105]
At this time, instead of the entire input range, the average of color differences may be obtained only in the range in which this coefficient has an influence. For example, in the tetrahedral interpolation method, the prism interpolation method, and the cubic interpolation method, an average may be obtained only for a portion included in a tetrahedron, a triangular prism, or a rectangular parallelepiped having the lattice point as a vertex.
Process (1.3): Random numbers based on a uniform distribution in the predetermined section [0, T] are added to the error in process (1.1) and the error in process (1.2), respectively, and the process ( If the sum of the error in 1.1) and the random number is smaller than the sum of the error in the process (1.2) and the random number, a predetermined step s is added to the current K value to update it. Otherwise, the current value of K is updated by subtracting the predetermined step s and the minimum unit of steps.
Process (2): The operation of the process (1) is applied to K of all grid points. When this optimization operation completes one cycle, the error of this color conversion device is obtained and repeated until it reaches a predetermined value or substantially converges or until a predetermined number of times. At that time, if the error becomes the smallest, the coefficient is recorded as “K is the optimum coefficient”, and T for determining the predetermined section is multiplied by a predetermined value larger than 1 to calculate T Increase. On the other hand, if the error has increased compared to before performing one round of optimization, T is decreased by multiplying T by a predetermined value smaller than 1. The same operation is performed for the predetermined step s, but the value is not less than the minimum step.
[0106]
Next, the following processing is executed with “K is an optimum coefficient” as an initial value and T and s as appropriate initial values.
Process (3): The CMY grid point values are optimized by the operations of processes (3.1) to (3.5) in ascending order of serial numbers.
Process (3.1): A predetermined step s is added to the current C value to calculate the error of the color conversion apparatus.
Process (3.2): The error of the color conversion device is calculated by subtracting the predetermined step s and the minimum unit of steps from the current C value.
Process (3.3): Random numbers based on a uniform distribution in a predetermined section [0, T] are added to the error of process (3.1) and the error of process (3.2), respectively, and the process ( If the sum of the error in 3.1) and the random number is smaller than the sum of the error in the process (3.2) and the random number, a predetermined step s is added to the current C value to update it. Otherwise, the current value of C is updated by subtracting the predetermined step s and the minimum unit of steps.
Process (3.4): The operations of processes (3.1) to (3.3) are applied to M instead of C.
Process (3.5): The operations of processes (3.1) to (3.3) are changed to C and applied to Y.
Process (4): The operation of the process (3) is applied to all grid points. When this optimization operation completes one cycle, the error of this color conversion device is obtained and repeated until it reaches a predetermined value or substantially converges or until a predetermined number of times. At that time, if the minimum error occurs, the coefficient is recorded as an “optimum coefficient”, and T is increased by multiplying T, which determines the predetermined section, by a predetermined value greater than 1. Let On the other hand, if the error has increased compared to before performing one round of optimization, T is decreased by multiplying T by a predetermined value smaller than 1. The same operation as T is performed for the predetermined step s, but the value is not less than the minimum step.
[0107]
As described above, when the learning is finished, the finally recorded “optimum coefficient” is output.
[0108]
[Example 4]
Next, a description will be given of a fourth embodiment in which the coefficient is optimized by introducing a continuous function that can be assumed between the discrete coefficient value and the error. FIG. 5 shows a configuration of the fourth embodiment. In this figure, portions corresponding to those in FIG. 3 are denoted by corresponding reference numerals, and detailed description thereof is omitted. In FIG. 5, the quadratic function determining unit 41 is E₀, E_-, E₊A quadratic function is determined on the basis of the error of the differential function.₀The derivative at is calculated. The coefficient updating unit 43 determines a coefficient in accordance with the temperature (temperature in annealing) and the differential coefficient. This will be described in detail later.
[0109]
Next, optimization of the coefficients of the color conversion device 21 in this embodiment will be described in detail. The color conversion device 21 may perform the optimization by the present embodiment alone, or may perform the optimization by the present embodiment after performing the number of optimizations according to the second embodiment prior to the present embodiment. Various definitions such as error are the same as those in the second embodiment.
[0110]
Now, of the k coefficients, the p-th coefficient w_pThe error E with respect to the current coefficient value₀That is, E₀= E (w₁, W₂, ..., w_p, ..., w_k) And a predetermined step s from the current coefficient value₁Error E for large coefficient values₊That is, E₊= E (w₁, W₂, ..., w_p+ S₁, ..., w_k) And a predetermined step s from the current coefficient value₂Error E for small coefficient values, ie E_-= E (w₁, W₂, ..., w_p-S₂, ..., w_k) Three types of errors are calculated. From this three-point error, a quadratic function is estimated and w_pDerivative E 'in_pIs calculated.
[0111]
Depending on the temperature t, the derivative E '_pIs a random variable X with a high probability of 1 (otherwise 0)₊(E ’_pT) and the derivative E '_pIs a random variable X with a high probability of 1 (otherwise 0)_-(E ’_p; By t), the coefficient w_pIs updated with the following values: Where the random variable X₊And X_-Is uncertainly affected by higher temperatures and deterministically affected by lower temperatures.
[0112]
[Equation 5]
wp ← w_p+ S₁・ X₊(E ’_pT) -s₂・ X_-(E ’_pT)
In this embodiment, the predetermined step for addition is a different value, but the predetermined step for addition and the predetermined step for subtraction do not necessarily have to be different values.
[0113]
Repeat this operation for each weight w_p(P = 1, 2,..., K). When this optimization operation completes one cycle, the error of this color conversion device is obtained and repeated until it reaches a predetermined value or substantially converges or until a predetermined number of times. At that time, if the minimum error occurs, the coefficient is recorded as “optimum coefficient”, and the predetermined step s described above is performed.₁, S₂And the temperature t are multiplied by a predetermined value greater than 1 to increase the step and temperature. On the other hand, if the error has increased compared to before performing one round of optimization, s₁, S₂And the temperature t are multiplied by a predetermined value less than 1 to reduce the step and temperature. However, each step does not have a value less than the minimum step.
[0114]
As described above, when the learning is finished, the finally recorded “optimum coefficient” is output.
[0115]
In this embodiment, three points are taken and the derivative is calculated by a quadratic function. However, if two or more points are taken, the derivative can be determined by an appropriate function.
[0116]
Also, in the above, three points were taken, but p kinds of appropriate functions f₁(W), f₂(W) ... f_pP types of coefficients can be calculated using (w).
[0117]
Here, as an example, when p = 4,
[0118]
[Formula 6]
f₁(W) = w + 1
f₂(W) = w + 2
f_Three(W) = w + 3
f_Four(W) = w + 4
It can be. In the case of calculating the derivative, it is possible to estimate the derivative of the current value even if it is not a section including the current coefficient. Therefore, the function value may not be a section including the current coefficient.
[0119]
As another example, when p = 5,
[0120]
[Expression 7]
f₁(W) = floor (w × 0.98)
f₂(W) = floor (w × 0.99)
f_Three(W) = w
f_Four(W) = ceil (w / 0.99)
f_Five(W) = ceil (w / 0.98)
It is good. Here, floor is rounded down and ceil is rounded up. Here, as an example of the operation of rounding to a discrete value that can be taken by the coefficient, an example is shown using rounding down or rounding up, but the rounding operation can take any method.
[0121]
[Application example]
Next, application examples of the present invention will be described.
[0122]
FIG. 6 shows an electronic apparatus using the data conversion apparatus of the present invention. In this figure, the electronic apparatus 100 has a data conversion apparatus 110. The data converter 110 is the same as that in the above-described embodiment, and takes discrete values as conversion coefficients. The data conversion apparatus 110 is optimized by the coefficient optimization unit 111 in the same manner as in the above-described embodiment.
[0123]
In this case, the coefficient may be optimized in advance by the reference data conversion device and installed in the data conversion device 110 of the electronic device 100. Thereafter, the coefficient optimization unit 111 may further perform final optimization processing.
[0124]
FIG. 7 shows a color image forming apparatus (a color copying machine or a color printing machine) using the data conversion apparatus of the present invention. In this figure, the image forming apparatus 200 includes two color conversion apparatuses 210 including data conversion apparatuses. , 220. The color data input from the input unit 230 is sequentially color-converted by the color conversion units 210 and 220, supplied to the output unit 240, and printed out. In this example, the coefficient conversion of the data conversion apparatus of the present invention can be optimized in both or one of the color conversion apparatuses 210 and 220.
[0125]
FIG. 8 shows a robot apparatus using the data conversion apparatus of the present invention. In this figure, the robot 300 includes a data conversion apparatus 310, and the posture and the like according to the position input from the position input unit 320. It comes to perform control. The error detection unit 330 detects an error, and the coefficient of the data conversion device is optimized accordingly.
[0126]
【The invention's effect】
As described above, according to the present invention, even when data is converted using a coefficient having a discrete value, the coefficient value can be learned easily and stably.
[Brief description of the drawings]
FIG. 1 is a diagram showing a configuration of a first exemplary embodiment of the present invention.
FIG. 2 is a diagram specifically explaining details of the above-described embodiment.
FIG. 3 is a diagram showing a configuration of a second exemplary embodiment of the present invention.
FIG. 4 is a diagram showing a configuration of Example 3 of the present invention.
FIG. 5 is a diagram illustrating a configuration of a fourth embodiment of the present invention.
FIG. 6 is a diagram illustrating an application example of the present invention.
FIG. 7 is a diagram illustrating an application example of the present invention.
FIG. 8 is a diagram illustrating an application example of the present invention.
[Explanation of symbols]
11 Input buffer
12 Data converter
13 Output buffer
14 Ideal output memory
15 Error calculator
16 Error history memory
17 Random number distribution controller
18 Step controller
19 Coefficient update unit
100 electronic equipment
200 color image forming apparatus
300 robots

Claims (33)

In a data converter for converting m-dimensional input data into n-dimensional output data according to k coefficients (however, including at least one coefficient taking discrete values) ,
For each of the coefficients taking discrete values, the current coefficient value, the coefficient value larger by the step width s1 of addition than the current coefficient value, and the coefficient value smaller by the step width s2 of subtraction than the current coefficient value. Means for calculating an output data group for an input data group for optimization for at least two coefficient values;
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. And a coefficient value selecting means for selecting as a new coefficient value.   The coefficient value selection means includes means for adding a random number in a predetermined range to each error in the at least two coefficient values and selecting a coefficient value that gives a minimum value of the sum. 1 is a coefficient determination device. 3. The device according to claim 2, further comprising means for controlling the degree of gradual decrease of the probability with respect to the magnitude of the error and / or the step widths s1 and s2 in accordance with an error history. Coefficient determination device. 4. The coefficient determination apparatus according to claim 3, wherein a size of a predetermined range of the random number is controlled in order to control the degree of gradual decrease of the probability with respect to the size of the error according to an error history. The at least one coefficient that takes the discrete value records in advance a discrete value corresponding to n outputs for each representative point in the table of m-dimensional representative points corresponding to m-dimensional input data, A value corresponding to the output of the representative point of the data conversion apparatus that obtains an n-dimensional output by interpolating a value corresponding to the output, and defines an error and an ideal output value group for the input data group for optimization. 5. The coefficient determination apparatus according to claim 1, further comprising means for updating the coefficient. data conversion means for converting m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient taking discrete values) ;
For each of the coefficients taking discrete values, the current coefficient value, the coefficient value larger by the step width s1 of addition than the current coefficient value, and the coefficient value smaller by the step width s2 of subtraction than the current coefficient value. Means for calculating an output data group for an input data group for optimization for at least two coefficient values;
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. And a coefficient value selecting means for selecting a new coefficient value. color conversion means for converting m-dimensional first color data into n-dimensional second color data according to k coefficients (including at least one coefficient taking discrete values) ;
For each of the coefficients taking discrete values, the current coefficient value, the coefficient value larger by the step width s1 of addition than the current coefficient value, and the coefficient value smaller by the step width s2 of subtraction than the current coefficient value. Means for calculating a second color data group for the first color data group for optimization for at least two coefficient values;
With the probability that the smaller the error between the second color data group calculated for the at least two coefficient values and the ideal second color data group corresponding to the first color data group for optimization, the higher the value. A color conversion apparatus comprising: coefficient value selection means for selecting any one of at least two coefficient values as a new coefficient value.   8. The color conversion apparatus according to claim 7, wherein the error is a color difference. means for receiving m-dimensional first color data;
color conversion means for converting the m-dimensional first color data into n-dimensional second color data according to k coefficients (including at least one coefficient taking discrete values) ;
Output means for performing a predetermined output operation based on the second color data output from the color conversion means;
For each of the coefficients taking discrete values, the current coefficient value, the coefficient value larger by the step width s1 of addition than the current coefficient value, and the coefficient value smaller by the step width s2 of subtraction than the current coefficient value. Means for calculating a second color data group for the first color data group for optimization for at least two coefficient values;
With the probability that the smaller the error between the second color data group calculated for the at least two coefficient values and the ideal second color data group corresponding to the first color data group for optimization, the higher the value. A color image forming apparatus comprising: coefficient value selection means for selecting any one of at least two coefficient values as a new coefficient value. The color image forming apparatus according to claim 9 , further comprising another color conversion unit that converts the second color data output from the output unit into third color data . means for receiving m-dimensional input data;
data conversion means for converting the m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient taking discrete values) ;
Output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means;
For each of the coefficients taking discrete values, the current coefficient value, the coefficient value larger by the step width s1 of addition than the current coefficient value, and the coefficient value smaller by the step width s2 of subtraction than the current coefficient value. Means for calculating an output data group for an input data group for optimization for at least two coefficient values;
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. And a coefficient value selection means for selecting a new coefficient value. In a data conversion device that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient that takes discrete values) ,
Means for calculating an output data group from an input data group for optimization for p kinds of coefficient values in an appropriate section including a current coefficient value for each of the coefficients taking discrete values;
An error between the output data group calculated for the p types of coefficient values and an ideal output data group corresponding to the optimization input data group is calculated, and a calculation for obtaining p types (p is an integer of 2 or more) is obtained. Means,
A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value assuming a predetermined function from the coefficient value to the error that can be differentiated from the p kinds of errors in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, coefficient determination apparatus characterized by having a larger coefficient value updating means in accordance with the progress of the optimization process are further the probability of a coefficient update. The p-type coefficient includes at least one of a current coefficient value, a coefficient value obtained by adding an addition step width s1 to the current coefficient value, and a coefficient value obtained by subtracting a subtraction step width s2 from the current coefficient value. 13. The coefficient determination apparatus according to claim 12, wherein 14. The method according to claim 12, further comprising means for controlling the degree of gradual decrease of the probability with respect to the magnitude of the derivative and one or both of the step widths s1 and s2 in accordance with an error history. Coefficient determination device. The at least one coefficient that takes the discrete value records in advance a discrete value corresponding to n outputs for each representative point in the table of m-dimensional representative points corresponding to m-dimensional input data, A value corresponding to the output of the representative point of the data conversion apparatus that obtains an n-dimensional output by interpolating a value corresponding to the output, and defines an error and an ideal output value group for the input data group for optimization. 15. A coefficient determination apparatus according to claim 12, 13 or 14, further comprising means for updating the coefficient. data conversion means for converting m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient taking discrete values) ;
Means for calculating an output data group from an input data group for optimization for p kinds of coefficient values in an appropriate section including a current coefficient value for each of the coefficients taking discrete values;
Calculation for calculating the error between the output data group calculated for the coefficient values of p types (p is an integer of 2 or more) and the ideal output data group corresponding to the input data group for optimization to obtain p types of errors Means,
Assuming a function from an appropriate count value that can be differentiated in the current coefficient value from the p types of errors, a differential coefficient calculating means for calculating a differential coefficient in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, the data conversion apparatus characterized by having a coefficient updating means probability of further coefficient update increases with progress of the processing of the optimization. color conversion means for converting m-dimensional first color data into n-dimensional second color data according to k coefficients (including at least one coefficient taking discrete values) ;
Means for calculating a second color data group from the first color data group for optimization with respect to each of the coefficients taking the discrete values for p kinds of coefficient values in an appropriate section including the current coefficient value. When,
An error between the second color data group calculated for the p types of coefficient values and the ideal second color data group corresponding to the first color data group for optimization is calculated, and p types (p is Calculating means for obtaining an error of an integer of 2 or more;
A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value assuming a predetermined function from the coefficient value to the error that can be differentiated from the p kinds of errors in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, the color conversion apparatus characterized by having a larger coefficient value updating means in accordance with the progress of the optimization process are further the probability of a coefficient update.   The color conversion apparatus according to claim 17, wherein the error is a color difference. means for receiving m-dimensional first color data;
color conversion means for converting the m-dimensional first color data into n-dimensional second color data according to k coefficients (including at least one coefficient taking discrete values) ;
Output means for performing a predetermined output operation based on the second color data output from the color conversion means;
For each of the coefficients having the discrete values, the p-type (p is an integer of 2 or more) coefficient values in an appropriate section including the current coefficient value are second to the second color data for optimization . Means for calculating the color data group of
An error between the second color data group calculated for the p kinds of coefficient values and the ideal second color data group corresponding to the first color data group for optimization is calculated, and the p kinds of errors are calculated. Calculating means to obtain;
A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value assuming a predetermined function from the coefficient value to the error that can be differentiated from the p kinds of errors in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, further color image forming apparatus characterized by having a larger coefficient value updating means in accordance with the progress of the probability of the coefficient updating of the optimization process.   20. The color image forming apparatus according to claim 19, wherein the output unit receives the second color data via a subsequent color conversion unit. means for receiving m-dimensional input data;
data conversion means for converting the m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient taking discrete values) ;
Output means for performing a predetermined output operation based on the n-dimensional output data output from the data conversion means;
For each coefficient having a discrete value, an output data group is calculated from the input data group for optimization with respect to p kinds (p is an integer of 2 or more) of coefficient values in an appropriate interval including the current coefficient value. Means to
Calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the optimization input data group, and obtaining p kinds of errors;
A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value assuming a predetermined function from the coefficient value to the error that can be differentiated from the p kinds of errors in the current coefficient value;
Electronic device based on the differential coefficients, stochastically updating the coefficient, the probability of further coefficients update is characterized by having a larger coefficient value updating means in accordance with the progress of the optimization process. In a neural network having k coefficients (including at least one discrete coupling coefficient and / or discrete threshold) ,
For each of the coefficients taking discrete values, the current coefficient value, the coefficient value larger by the step width s1 of addition than the current coefficient value, and the coefficient value smaller by the step width s2 of subtraction than the current coefficient value. Means for calculating an output data group for an input data group for optimization for at least two coefficient values;
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. And a coefficient value selecting means for selecting a coefficient value as a new coefficient value. a neural network having k coefficients (including at least one of discrete coupling coefficients and / or discrete thresholds) and a current coefficient value for each of the coefficients taking the discrete values, Output data for an input data group for optimization with respect to at least two coefficient values among a coefficient value larger than the current coefficient value by an addition step width s1 and a coefficient value smaller than the current coefficient value by a subtraction step width s2. Means for calculating the group;
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. And a coefficient value selecting means for selecting a new coefficient value. In a neural network having k coefficients (including at least one discrete coupling coefficient and / or discrete threshold) ,
Means for calculating an output data group from an input data group for optimization for p kinds of coefficient values in an appropriate section including a current coefficient value for each of the coefficients taking discrete values;
An error between the output data group calculated for the p types of coefficient values and an ideal output data group corresponding to the optimization input data group is calculated, and a calculation for obtaining p types (p is an integer of 2 or more) is obtained. Means,
A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value assuming a predetermined function from the coefficient value to the error that can be differentiated from the p kinds of errors in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, further coefficient determiner neural network and having a larger coefficient value updating means in accordance with the progress of processing of the probability optimization coefficient update. For each of the neural network having k coefficients (including at least one of discrete coupling coefficients and / or discrete thresholds) and the coefficient taking the discrete value, the current coefficient value is Means for calculating an output data group from an input data group for optimization with respect to p kinds (p is an integer of 2 or more) of coefficient values in an appropriate interval including:
Calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the optimization input data group, and obtaining p kinds of errors;
A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value assuming a predetermined function from the coefficient value to the error that can be differentiated from the p kinds of errors in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, coefficient determination device and a neural network characterized by having a larger coefficient value updating means in accordance with further progress of the process of the probability optimization coefficient update Data conversion device using neural network. In a data conversion device that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient that takes discrete values) ,
For each of the coefficients taking the discrete value, a current coefficient value, a coefficient value larger by the addition step width s1 than the current coefficient value, and a coefficient value smaller by the subtraction step width s2 than the current coefficient value. Means for calculating an output data group for an input data group for optimization with respect to at least two coefficient values,
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. Coefficient value selection means for selecting as a new coefficient value;
Means for calculating an output data group for p kinds (p is an integer of 2 or more) of coefficient values in an appropriate section including the current coefficient value for each of the coefficients having discrete values;
Calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the optimization input data group, and obtaining p kinds of errors;
A differential coefficient calculating means for calculating a differential coefficient in the current coefficient value assuming a predetermined function from the coefficient value to the error that can be differentiated from the p kinds of errors in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, and a larger coefficient value updating means in accordance with the progress of the optimization process is further probability coefficient update,
A coefficient determination device that executes coefficient value update by the coefficient value update means once or more after the coefficient value selection means executes the coefficient value selection one or more times. In the method of determining the coefficient value in a data conversion device that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient that takes discrete values) ,
For each of the coefficients taking the discrete value, a current coefficient value, a coefficient value larger by the addition step width s1 than the current coefficient value, and a coefficient value smaller by the subtraction step width s2 than the current coefficient value. Calculating an output data group for an input data group for optimization for at least two coefficient values,
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. Selecting a new coefficient value as a coefficient value. In the method of determining the coefficient value in a data conversion device that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient that takes discrete values) ,
For each of the coefficients having discrete values, an output data group is calculated from the input data group for optimization with respect to p kinds (p is an integer of 2 or more) of coefficient values in an appropriate interval including the current coefficient value. And steps to
Calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the optimization input data group, and obtaining p kinds of errors;
Assuming a predetermined function from the coefficient value to the error that is differentiable from the p kinds of errors in the current coefficient value, and calculating a differential coefficient in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, coefficient determination method characterized by a step of further probability coefficient updating to be larger in accordance with the progress of the optimization process. In the method of determining the coefficient value in a data conversion device that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient that takes discrete values) ,
For each of the coefficients taking the discrete value, a current coefficient value, a coefficient value larger by the addition step width s1 than the current coefficient value, and a coefficient value smaller by the subtraction step width s2 than the current coefficient value. Calculating an output data group for an input data group for optimization for at least two coefficient values,
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. Selecting as a new coefficient value;
Calculating an output data group for p kinds of coefficient values in an appropriate section including a current coefficient value for each of the coefficients taking the discrete values after the new coefficient value is selected;
Calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the predetermined input data group, and obtaining p kinds of errors;
Assuming a predetermined function from the coefficient value to the error that is differentiable from the p kinds of errors in the current coefficient value, and calculating a differential coefficient in the current coefficient value;
Based on the above derivative, stochastically updating the coefficients, and a step to be larger in accordance with the progress of the optimization process is further probability coefficient update,
A coefficient determination method, wherein the coefficient value is updated once or more after the coefficient value is selected one or more times. In a method of setting the coefficient value in a data conversion apparatus that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient taking discrete values) ,
In the standard data converter having the same function as the data converter main body,
For each of the coefficients taking the discrete value, a current coefficient value, a coefficient value larger by the addition step width s1 than the current coefficient value, and a coefficient value smaller by the subtraction step width s2 than the current coefficient value. Calculating an output data group for an input data group for optimization for at least two coefficient values,
Any one of the at least two coefficient values has a probability of increasing as the error between the output data group calculated for the at least two coefficient values and the ideal output data group corresponding to the optimization input data group decreases. Selecting as a new coefficient value;
And a step of setting the selected coefficient as a coefficient of the data converter main body. In a method of setting the coefficient value in a data conversion apparatus that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient taking discrete values) ,
In a reference data converter having a data conversion function equivalent to that of the data converter main body,
For each coefficient having a discrete value, an output data group is calculated from the input data group for optimization with respect to p kinds (p is an integer of 2 or more) of coefficient values in an appropriate interval including the current coefficient value. And steps to
Calculating means for calculating an error between the output data group calculated for the p kinds of coefficient values and an ideal output data group corresponding to the optimization input data group, and obtaining p kinds of errors;
Assuming a predetermined function from the coefficient value to the error that is differentiable from the p kinds of errors in the current coefficient value, and calculating a differential coefficient in the current coefficient value;
A step based on the differential coefficients, stochastically updating the coefficients, further probability coefficient update is set to be larger as the progress of the optimization process,
And a step of setting the updated coefficient as a coefficient of the data converter main body. In a data conversion device that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient that takes discrete values) ,
Coefficient calculation for calculating p-type coefficient values (p is an integer of 2 or more) by applying p-type predetermined functions to the current coefficient value for at least one of the coefficients having discrete values. Means,
Output data calculating means for calculating an output data group from an input data group for optimization with respect to p kinds of coefficient values given by the coefficient calculating means;
An error calculating means for calculating an error between the output data group and an ideal output data group corresponding to the optimization input data group to obtain p types of errors;
From the p types of errors, in the current coefficient value,
A coefficient determination apparatus comprising differential coefficient calculation means for calculating a differential coefficient at a current coefficient value assuming a differentiable predetermined function from a coefficient value to an error. In a data conversion device that converts m-dimensional input data into n-dimensional output data according to k coefficients (including at least one coefficient that takes discrete values) ,
Coefficient calculating means for calculating p kinds of coefficient values by applying p kinds of predetermined functions to the current coefficient values for at least one of the coefficients having discrete values,
Output data calculating means for calculating an output data group from an input data group for optimization with respect to p kinds (p is an integer of 2 or more) of coefficient values given by the coefficient calculating means;
An error calculating means for calculating an error between the output data group and an ideal output data group corresponding to the optimization input data group to obtain p types of errors;
From the p types of errors, in the current coefficient value,
Assuming a differentiable predetermined function from the coefficient value to the error, a derivative calculating means for calculating a derivative at the current coefficient value;
Based on the above factors, stochastically updating the coefficients, coefficient determination apparatus characterized by having a larger coefficient value updating means in accordance with the progress of the optimization process are further the probability of a coefficient update.

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