JP2005045438A - Color conversion matrix calculation method and color correction method - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a color conversion matrix capable of approximating a reproduced color with respect to a hue to an original color with high accuracy. <P>SOLUTION: A color conversion matrix calculation method obtains RGB signals of input colors Cin corresponding to a plurality of color patches by photographing a color chart and obtains RGB signals of target colors Cme from photometry values of each color patch, obtains a hue optimum matrix A_huew whereby the hue of the input colors Cin is coincident with the hue of the target colors Cme, obtains a saturation optimum matrix A_satw whereby the saturation of the input colors Cin is coincident with the saturation of the target colors Cme, and decides the product of the both to be a color conversion matrix A. The color conversion matrix calculation method obtains correction colors Ces by acting the color conversion matrix A on the input colors Cin, obtains a hue angle difference (θme-θes) between the correction colors Ces and the target colors Cme, and recognizes the color conversion matrix A to be effective when a square sum of the hue angle differences of all the color patches does not exceed a permissible value. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

【００２３】
なお、本実施形態では正確な色再現を行うことを目的としているため、色変換マトリクスＡを算出する際に設定される目標値はカラーパッチＰ_１〜Ｐ_２４の測色信号であるが、人物の肌色や青空の色等のよく使われる特定色を、正確な色ではなく使用者の望む色に再現する場合には、特定色に関して測色信号を修正した値を目標値に設定してもよい。なお、測色によるＲＧＢ信号は、色彩計でＲ、ＧおよびＢの信号レベルを直接測定して得る他、例えば分光光度計によって分光反射率を測定する、または色彩計によってＲＧＢ表色系と異なる表色系で表現されたＸＹＺ信号やＬ^＊ａ^＊ｂ^＊信号を測定して、分光反射率、ＸＹＺ信号またはＬ^＊ａ^＊ｂ^＊信号をＲＧＢ信号に変換して得てもよい。
【００２４】
マクベスカラーチャート４０は、市販の既製品であるため手に入れ易く、各カラーパッチＰ_１〜Ｐ_２４の測色信号が既知であり測色の手間が省ける。例えば、標準光の照明環境下のもとでの第１番のカラーパッチＰ_１（色名；暗い肌色）の測色信号は、ｘ＝０．４００２、ｙ＝０．３５０４およびＹ＝１０．０５であり、これら測色信号ｘ、ｙおよびＹを公知の変換式によってＲＧＢ信号に変換することができる。ただし、ｘ＝Ｘ／（Ｘ＋Ｙ＋Ｚ）、ｙ＝Ｙ／（Ｘ＋Ｙ＋Ｚ）であり、Ｘ、ＹおよびＺはＸＹＺ表色系における三刺激値である。第１〜１８番のカラーパッチＰ_１〜Ｐ_１８は有彩色であり、最終列の第１９〜２４番のカラーパッチＰ_１９〜Ｐ_２４は無彩色である。
【００２５】
なお、カラーチャートとしては本実施形態のマクベスカラーチャートに限らず、複数のカラーパッチが均等色空間上に一様に分布するものであればよく、例えばＪＩＳ標準色標でもよい。マクベスカラーチャート４０に基づいて得た色変換マトリクスは、各カラーパッチＰ_１〜Ｐ_２４の色については精度良く色再現できるが、他の色については保障されない。従って、良く使用される特定色（人物の肌色、青空の色、緑など）をカラーパッチにした独自のカラーチャートを作成しておけば、特定色について特に忠実に色再現できることになる。
【００２６】
図２および図３を参照して、色変換マトリクス算出方法について説明する。図２には、色温度が６５０４Ｋの昼光を代表する標準の光ＣＩＥ−Ｄ_６５を照明用光源とするＣＩＥ−Ｌ^＊ａ^＊ｂ^＊色空間（以下、Ｌａｂ色空間と記載する）が示され、このＬａｂ色空間において、所定の１色に関する入力色Ｃｉｎと、補正すべき目標の色Ｃｍｅ（以下、目標色と記載する）とがそれぞれ点で示されている。目標色ＣｍｅのＬ^＊ａ^＊ｂ^＊信号は測色で得られた値に設定される。図３は、色変換マトリクス算出処理の処理流れおよび各種色信号の関係を模式的に示すブロック図である。
【００２７】
マトリクス演算では色はＲＧＢ信号で扱われるが、色の一致度の評価ではＬ^＊ａ^＊ｂ^＊信号で扱われる。これは、Ｌａｂ色空間が人間の色知覚と座標上の距離との相関性が良好な均等色空間であることによる。図２に示すＬａｂ色空間においては、明度を表すＬ^＊、色相および彩度を示すａ^＊、ｂ^＊の座標により任意の色を表すことができる。明度指数Ｌ^＊は任意の色の相対的な明るさや暗さを示し、黒の０％から白の１００％の範囲である。色相はａ^＊ｂ^＊平面における座標原点周りの角度で示され、０°から３６０°の範囲である。ａ^＊軸において正の数字が大きくなる程赤が強くなり、負の数字が大きくなるほど緑が強くなる。ｂ^＊軸において正の数字が大きくなる程黄が強くなり、負の数字が大きくなるほど青が強くなる。また、座標原点からの距離が大きくなるほど彩度が高く、鮮やかな色になる。座標原点は無彩色である。
【００２８】
ＲＧＢ信号からＬ^＊ａ^＊ｂ^＊信号への変換は下記に示す公知の（３）式および（４）式により行う。（３）式はＲＧＢ信号をＸＹＺ信号に変換するための変換式であり、（４）式はＸＹＺ信号をＬ^＊ａ^＊ｂ^＊信号に変換するための変換式である。色の一致度の評価時にはＲＧＢ信号はＲＧＢ→ＸＹＺ→Ｌ^＊ａ^＊ｂ^＊変換によりＬ^＊ａ^＊ｂ^＊信号に変換され、マトリクス演算の時にはＬ^＊ａ^＊ｂ^＊信号はＬ^＊ａ^＊ｂ^＊→ＸＹＺ→ＲＧＢ変換によりＲＧＢ信号に戻される。Ｌ^＊ａ^＊ｂ^＊→ＸＹＺ→ＲＧＢ変換は（３）式および（４）式を変形した変換式により行われ、ここではその式は省略する。
【００２９】
【数２】

【００３０】
【数３】

【００３１】
本実施形態では、カラーパッチＰ_１〜Ｐ_１８の１８色について入力色Ｃｉｎから予測した補正色Ｃｅｓがそれぞれ対応する目標色Ｃｍｅに色相が一致するように色変換マトリクスＡを最適化した後、彩度が一致するように最適化する。補正色Ｃｅｓと目標色Ｃｍｅとの一致の度合いは、Ｌａｂ色空間における両者の色相角θｅｓおよびθｍｅの差によって評価する。色相角θ（θｅｓおよびθｍｅ）はａ^＊ｂ^＊面に下ろした点のａ^＊軸からの原点周りの回転角であり、下記の（５）式により定義される。色相角θｅｓおよびθｍｅはそれぞれのａ^＊座標およびｂ^＊座標を（５）式に代入して求められる。人間の知覚では、色相が異なる方が彩度が異なる場合に比べて別の色として認識され易いので、本実施形態では色相を優先的に一致させている。
【００３２】
【数４】

【００３３】
まず、色相を合わせるために、Ｌａｂ色空間において座標原点と目標色Ｃｍｅとを結ぶ直線Ｌ上に入力色Ｃｉｎを正射影した点の色を色相最適化目標色Ｃｍｅ’に設定し、その色相最適化目標色Ｃｍｅ’のＬ^＊ａ^＊ｂ^＊信号をＬ^＊ａ^＊ｂ^＊→ＸＹＺ→ＲＧＢ変換してＲＧＢ信号を求める処理を１８色についてそれぞれ行い、１８色の入力色Ｃｉｎをそれぞれ対応する色相最適化目標色Ｃｍｅ’に一致させるための色相最適化マトリクスＡ₋ｈｕｅｗ（第１マトリクス）を重回帰分析により求める。色相最適化目標色Ｃｍｅ’のＲＧＢ信号は色相に関する第１目標色信号である。直線Ｌは目標色Ｃｍｅと色相が同じ色の点の集合であり、入力色Ｃｉｎを直線Ｌ上に正射影した点の色Ｃｍｅ’（以下、色相最適化目標色と記載する）は、目標色Ｃｍｅと色相が同じであってなおかつ入力色Ｃｉｎに対してＬａｂ空間での距離が最も近い色である。即ち目標色を色相最適化目標色Ｃｍｅ’にすれば、Ｌａｂ色空間において最短移動距離で色相を合わせることができる。なお、図２には１色のみが代表して示される。個々の入力色Ｃｉｎに色相最適化マトリクスＡ₋ｈｕｅｗを作用させて得られる色相補正色Ｃｅｓ’は、対応する色相最適化目標色Ｃｍｅ’に略一致する。
【００３４】
次に、彩度を合わせるために、１８色の色相補正色Ｃｅｓ’をそれぞれ対応する目標色Ｃｍｅに一致させるための彩度最適化マトリクスＡ₋ｓａｔｗ（第２マトリクス）を重回帰分析により求める。目標色ＣｍｅのＲＧＢ信号は彩度に関する第２目標色信号である。個々の色相補正色Ｃｅｓ’に彩度最適化マトリクスＡ₋ｓａｔｗを作用させて得られる補正色Ｃｅｓは、対応する目標色Ｃｍｅに略一致する。
【００３５】
入力色Ｃｉｎを補正色Ｃｅｓに変換するための色変換マトリクスＡは、下記の（６）式に示すように、目標色Ｃｍｅに色相を近似させるための色相最適化マトリクスＡ₋ｈｕｅｗと、目標色Ｃｍｅに彩度を近似させるための彩度最適化マトリクスＡ₋ｓａｔｗとの積により求められる。（６）式と等価なマトリクス要素による表現式を（７）式に示す。（７）式におけるａ’_１〜ａ’_９は色相最適化マトリクスＡ₋ｈｕｅｗのマトリクス要素であり、ａ”_１〜ａ”_９は彩度最適化マトリクスＡ₋ｓａｔｗのマトリクス要素である。
【００３６】
【数５】

【００３７】
従って、入力色Ｃｉｎを色変換マトリクスＡによって補正色Ｃｅｓに変換するということは、入力色Ｃｉｎを補正色Ｃｅｓに対して色相を一致させた後に彩度を一致させるということと同等である（（８）式を参照）。
【数６】

【００３８】
次に、図４〜図６のフローチャートを参照して、色変換マトリクス算出処理について詳細に説明する。
【００３９】
まずステップＳ１０２において、２４色のカラーパッチＰ_１〜Ｐ_２４を有するマクベスカラーチャート４０を用意し、これら２４個のカラーパッチＰ_１〜Ｐ_２４をＣＩＥ−Ｄ_６５の照明光源下でデジタルカメラ１０により撮影し、得られたＲＡＷデータを色変換マトリクス算出装置３４に転送する。
【００４０】
色変換マトリクス算出装置３４は、ＲＡＷデータに基づいて１８個の有彩色カラーパッチＰ_１〜Ｐ_１８に対応する入力色ＣｉｎのＲＧＢ信号を得る（ステップＳ１０４）。ここで、個々の有彩色カラーパッチＰ_１〜Ｐ_１８に対応する色データを区別するために、有彩色カラーパッチＰ_１〜Ｐ_１８の順番を示すパラメータｋ（ｋ＝１、２、…、１８）を設定し、ｋ番目のカラーパッチＰ_ｋに対応する入力色をＣｉｎ（ｋ）、そのＲＧＢ信号を（Ｒｉｎ（ｋ），Ｇｉｎ（ｋ），Ｂｉｎ（ｋ））で表す。入力色Ｃｉｎ（ｋ）のＲＧＢ信号（Ｒｉｎ（ｋ），Ｇｉｎ（ｋ），Ｂｉｎ（ｋ））は、カラーパッチＰ_ｋに相当する撮像領域から抽出された３０×３０画素のＲ、ＧおよびＢの信号レベルのそれぞれの平均値（以下、ＲＧＢ平均値と記載する）であり、８ビットデータである。ＲＧＢ平均値の信頼性を高めるために、３０×３０画素のうち欠陥画素などは取り除かれる。なお、ＲＧＢ信号（Ｒｉｎ（ｋ），Ｇｉｎ（ｋ），Ｂｉｎ（ｋ））は１０ビットデータまたは１２ビットデータであってもよい。
【００４１】
マクベスカラーチャート４０の第１９〜２４番のカラーパッチＰ_１９〜Ｐ_２４は６段階の無彩色カラーパッチであり、詳しくは第１９番のカラーパッチＰ_１９（色名；白色）、第２０番のカラーパッチＰ_２０（色名；グレイ８）、第２１番のカラーパッチＰ_２１（色名；グレイ６．５）、第２２番のカラーパッチＰ_２２（色名；グレイ５）、第２３番のカラーパッチＰ_２３（色名；グレイ３．５）、第２４番のカラーパッチＰ_２４（色名；黒色）から成る。
【００４２】
これら無彩色の６個のカラーパッチＰ_１９〜Ｐ_２４はグレー階調の補正に用いられる。具体的には、各カラーパッチＰ_１９〜Ｐ_２４にそれぞれ相当する撮像領域から抽出された３０×３０画素のＲＧＢ平均値が求められ、６つの無彩色カラーパッチＰ_１９〜Ｐ_２４のＲＧＢ平均値とそれぞれの目標値（例えば測色信号）との誤差が最小となるようなオフセット値がＲ、ＧおよびＢのそれぞれについて求められる。ステップＳ１０４で有彩色カラーパッチＰ_ｋ（ｋ＝１、２、…、１８）の入力色Ｃｉｎ（ｋ）のＲＧＢ信号（Ｒｉｎ（ｋ），Ｇｉｎ（ｋ），Ｂｉｎ（ｋ））を得る前に、ＲＡＷデータのＲ、ＧおよびＢ信号からそれぞれオフセット値が差し引かれ、これにより画像の白基準レベルおよび黒基準レベルが補正されるとともに、グレー階調、即ち色の濃さが適切なレベルに補正される。なお、階調はγ＝１．０で正規化されたものである。
【００４３】
また、６個の無彩色カラーパッチＰ_１９〜Ｐ_２４は、ホワイトバランス補正にも用いられ、ＲＡＷデータから得られる各無彩色カラーパッチＰ_１９〜Ｐ_２４のＲＧＢ平均値に基づいて、Ｒ、ＧおよびＢのゲインがそれぞれ決定され、１８個の有彩色カラーパッチＰ_１〜Ｐ_１８のＲＧＢ平均値がゲイン調整される。
【００４４】
従って、ステップＳ１０４で得られる１８色の有彩色カラーパッチＰ_ｋ（ｋ＝１、２、…、１８）の入力色Ｃｉｎ（ｋ）のＲＧＢ信号（Ｒｉｎ（ｋ），Ｇｉｎ（ｋ），Ｂｉｎ（ｋ））は、グレー階調補正およびホワイトバランス補正が施され、γ＝１．０で正規化されたものである。
【００４５】
また、ステップＳ１０６において既知である１８個のカラーパッチＰ_１〜Ｐ_１８の測色信号（ＲＧＢ信号）を色変換マトリクス算出装置３４に入力する。なお、入力したデータが、ＲＧＢ信号でない場合、例えばＸＹＺ信号、Ｌ^＊ａ^＊ｂ^＊信号、分光反射率等の場合には公知の変換式によりＲＧＢ信号に変換しておく。また、測色信号の値が未知の場合には、ステップＳ１０６の前に撮影と同じ照明環境下でカラーパッチＰ_１〜Ｐ_１８を測色する。
【００４６】
そして次のステップＳ１０８において、ｋ番目（ｋ＝１、２、…、１８）のカラーパッチＰ_ｋの目標色をＣｍｅ（ｋ）、そのＲＧＢ信号を（Ｒｍｅ（ｋ），Ｇｍｅ（ｋ），Ｂｍｅ（ｋ））と定義し、ステップＳ１０６で得られた測色信号を目標色Ｃｍｅ（ｋ）のＲＧＢ信号（Ｒｍｅ（ｋ），Ｇｍｅ（ｋ），Ｂｍｅ（ｋ））に設定する。本実施形態では正確な色再現を行うことを目的としているので、測色信号を目標色Ｃｍｅ（ｋ）のＲＧＢ信号（Ｒｍｅ（ｋ），Ｇｍｅ（ｋ），Ｂｍｅ（ｋ））としているが、特定色を好ましい色に再現することを目的とする場合などでは、目的に応じて任意にＲｍｅ（ｋ）、Ｇｍｅ（ｋ）、Ｂｍｅ（ｋ）の値を変更する。なお、ステップＳ１０６およびＳ１０８は次のステップＳ１１０の前であればいつ行ってもよい。
【００４７】
ステップＳ１１０では、ステップＳ１０４で得られた１８色の入力色Ｃｉｎ（ｋ）のＲＧＢ信号（Ｒｉｎ（ｋ），Ｇｉｎ（ｋ），Ｂｉｎ（ｋ））（ｋ＝１、２、…、１８）を、ＲＧＢ→ＸＹＺ→Ｌ^＊ａ^＊ｂ^＊変換（（３）式および（４）式）によりＬ^＊ａ^＊ｂ^＊信号に変換する。同様に、ステップＳ１０８で得られた１８色の目標色Ｃｍｅ（ｋ）のＲＧＢ信号（Ｒｍｅ（ｋ），Ｇｍｅ（ｋ），Ｂｍｅ（ｋ））（ｋ＝１、２、…、１８）をＬ^＊ａ^＊ｂ^＊信号に変換する。
【００４８】
ステップＳ１１２では、１８色についてそれぞれ色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）を設定し、それらのＬ^＊ａ^＊ｂ^＊信号を求める。即ち、Ｌａｂ色空間においてｋ番目（ｋ＝１、２、…、１８）の目標色Ｃｍｅ（ｋ）と座標原点とを結ぶ直線上に入力色Ｃｉｎ（ｋ）を正射影した点を色相最適化目標色Ｃｍｅ’（ｋ）に設定し、そのＬ^＊ａ^＊ｂ^＊座標を求める。そして、ステップＳ１１４において、色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）のＬ^＊ａ^＊ｂ^＊信号をそれぞれＬ^＊ａ^＊ｂ^＊→ＸＹＺ→ＲＧＢ変換し、ＲＧＢ信号（Ｒｍｅ’（１），Ｇｍｅ’（１），Ｂｍｅ’（１））〜（Ｒｍｅ’（１８），Ｇｍｅ’（１８），Ｂｍｅ’（１８））を求める。
【００４９】
ステップＳ１２０では、１８色の入力色Ｃｉｎ（１）〜Ｃｉｎ（１８）のＲＧＢ信号を説明変数群とし、１８色の色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）のＲＧＢ信号を目的変数群とし、色相最適化マトリクスＡ₋ｈｕｅｗのマトリクス要素ａ’_１〜ａ’_９を偏回帰係数とする重回帰モデルを構築して重回帰分析を行い、ステップＳ１２２において色相最適化マトリクスＡ₋ｈｕｅｗのマトリクス要素ａ’_１〜ａ’_９を求める。
【００５０】
この重回帰モデルでは、入力色Ｃｉｎ（１）〜Ｃｉｎ（１８）のＲＧＢ信号および色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）のＲＧＢ信号を各々列ベクトルとするマトリクスＢｉｎ、Ｂｍｅ’と、偏回帰係数から成る色相最適化マトリクスＡ₋ｈｕｅｗとの間で、１８色について（９）式に示す線形１次式が成立するものと仮定する。（９）式と等価なマトリクス要素による表現式を（１０）式に示す。
【００５１】
【数７】

【００５２】
色相最適化マトリクスＡ₋ｈｕｅｗは公知の最小二乗法などの最適化により求める。即ち、上述の重回帰モデル式において左辺（色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）のＲＧＢ値）と、右辺（入力色Ｃｉｎ（１）〜Ｃｉｎ（１８）に色相最適化マトリクスＡ₋ｈｕｅｗさせて得られるＲＧＢ値）とは、実際には一致せず、誤差が存在する。そこで、右辺と左辺の誤差の２乗和を最小にすることを条件として（９）式を（１１）式に変形し、（１１）式を解いて偏回帰係数Ａ₋ｈｕｅｗを求める。「（ ）^ｔ」は転置行列を示し、「（ ）^−１」は逆行列を示す。
【数８】

【００５３】
重回帰分析が終了し色相最適化マトリクスＡ₋ｈｕｅｗが得られると、続くステップＳ１２４〜Ｓ１３０において得られた色相最適化マトリクスＡ₋ｈｕｅｗの有効性が評価される。
【００５４】
ステップＳ１２４において、入力色Ｃｉｎ（１）〜Ｃｉｎ（１８）のＲＧＢ信号をそれぞれ色相最適化マトリクスＡ₋ｈｕｅｗで変換することにより色相補正色Ｃｅｓ’（１）〜Ｃｅｓ’（１８）のＲＧＢ信号（Ｒｅｓ（１），Ｇｅｓ（１），Ｂｅｓ（１））〜（Ｒｅｓ（１８），Ｇｅｓ（１８），Ｂｅｓ（１８））をそれぞれ求め（（１２）式を参照）、ステップＳ１２６において（３）式および（４）式のＲＧＢ→ＸＹＺ→Ｌ^＊ａ^＊ｂ^＊変換により、色相補正色Ｃｅｓ’（１）〜Ｃｅｓ’（１８）のＬ^＊ａ^＊ｂ^＊信号を求める。
【数９】

【００５５】
ステップＳ１２８では、ステップＳ１１２で設定された色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）のＬ^＊ａ^＊ｂ^＊信号と、ステップＳ１２６で得られた色相補正色Ｃｅｓ’（１）〜Ｃｅｓ’（１８）のＬ^＊ａ^＊ｂ^＊信号とに基づいて、色相誤差θｒｍｓを求める。詳述すると、ｋ番目の色について色相最適化目標色Ｃｍｅ’（ｋ）のＬ^＊ａ^＊ｂ^＊信号から（５）式により色相角θｍｅ’（ｋ）を求めるとともに色相補正色Ｃｅｓ’（ｋ）のＬ^＊ａ^＊ｂ^＊信号から（５）式により色相角θｅｓ’（ｋ）を求める処理を、ｋ＝１、２、…、１８について行い、１８色の色相角θｍｅ’（ｋ）およびθｅｓ’（ｋ）の差の２乗和を求め、これを色相誤差θｒｍｓとする（（１３）式を参照）。
【００５６】
【数１０】

【００５７】
ステップＳ１３０では、色相誤差θｒｍｓが許容値α以下であるか否かが判定され、色相誤差θｒｍｓが許容値αを超えた場合はステップＳ１０８に戻り、目標色Ｃｍｅ（１）〜Ｃｍｅ（１８）のＲＧＢ信号のいずれかを変更して新たに色相最適化マトリクスＡ₋ｈｕｅｗを求める。なお、ステップＳ１０８に戻って目標色Ｃｍｅ（１）〜Ｃｍｅ（１８）のＲＧＢ信号を再設定する際は、色相の変化が僅かとなるように、即ちモニタ装置３０における再現色の色味が被写体本来の色と変わらないように、各値が定められることが必要である。
【００５８】
ステップＳ１３０において色相誤差θｒｍｓが許容値α以下であると判定された場合には、入力色Ｃｉｎを目標色Ｃｍｅに対して色相に関して高精度に近似できる色相最適化マトリクスＡ₋ｈｕｅｗが得られたと見做され、彩度最適化マトリクスＡ₋ｓａｔｗを求めるためのステップＳ１４０〜Ｓ１４４が実行される。
【００５９】
ステップＳ１４０では色相だけでなく彩度を合わせるための重回帰モデルを構築し、重回帰分析を行う。この重回帰モデルは（１４）式に示されるように、ステップＳ１２４で求められた１８色の色相補正色Ｃｅｓ’（１）〜Ｃｅｓ’（１８）のＲＧＢ信号が説明変数群であり、ステップＳ１０８で設定された１８色の彩度最適化目標色Ｃｍｅ（１）〜Ｃｍｅ（１８）が目的変数群である。（１４）式のＢｉｎは色相補正色Ｃｅｓ’（１）〜Ｃｅｓ’（１８）を各々列ベクトルとするマトリクスであり、Ｂｍｅは彩度最適化目標色Ｃｍｅ（１）〜Ｃｍｅ（１８）を各々列ベクトルとするマトリクスである。ステップＳ１４２では求められた偏回帰係数ａ”_１〜ａ”_９を彩度最適化マトリクスＡ₋ｓａｔｗのマトリクス要素に定める。彩度最適化マトリクスＡ₋ｓａｔｗの求め方はステップＳ１２０〜Ｓ１２２の色相最適化マトリクスＡ₋ｈｕｅｗの求め方と同じであり、詳述しない。
【数１１】

【００６０】
ステップＳ１４２で彩度最適化マトリクスＡ₋ｓａｔｗが得られると、ステップＳ１４４において前述の（６）式（（７）式）により色変換マトリクスＡを算出する。そして、ステップＳ１４６において入力色Ｃｉｎ（１）〜Ｃｉｎ（１８）のＲＧＢ信号をそれぞれ色変換マトリクスＡで変換することにより補正色Ｃｅｓ（１）〜Ｃｅｓ（１８）のＲＧＢ信号（Ｒｅｓ（１），Ｇｅｓ（１），Ｂｅｓ（１））〜（Ｒｅｓ（１８），Ｇｅｓ（１８），Ｂｅｓ（１８））を求め（上述の（１）式および（２）式を参照）、ステップＳ１４８において（３）式および（４）式のＲＧＢ→ＸＹＺ→Ｌ^＊ａ^＊ｂ^＊変換により、補正色Ｃｅｓ（１）〜Ｃｅｓ（１８）のＬ^＊ａ^＊ｂ^＊信号を求め、ステップＳ１５０において補正色Ｃｅｓ（１）〜Ｃｅｓ（１８）と目標色Ｃｍｅ（１）〜Ｃｍｅ（１８）との色相誤差θｒｍｓを求める。ステップＳ１５０の色相誤差θｒｍｓの求め方はステップＳ１２８の色相誤差θｒｍｓの求め方と同じであり、説明を省略する。
【００６１】
次のステップＳ１５２では、色相誤差θｒｍｓが許容値α以下であるか否かが判定され、色相誤差θｒｍｓが許容値αを超えた場合はステップＳ１０８に戻り、色相誤差θｒｍｓが許容値α以下であると判定された場合には、入力色Ｃｉｎを目標色Ｃｍｅに対して色相および彩度に関して高精度に近似できる色変換マトリクスＡが得られたと見做され、ステップＳ１５４において色変換マトリクスＡの係数が現在の値に確定し、ステップＳ１５６において色変換マトリクス算出装置３４からデジタルカメラ１０へ色変換マトリクスＡの係数データを転送してメモリ２２に書き込んで終了する。
【００６２】
以上のように求められた色変換マトリクスＡをデジタルカメラ１０の色補正処理で用いると、特に色相について測色信号に忠実な色再現ができるｓＲＧＢ信号を得ることができ、モニタ装置３０の画面に被写体本来の色に極めて近い色味で被写体像を表示できる。
【００６３】
このように、本実施形態では色相差を色味の違いとして捕らえ易い人間の視覚特性を考慮した色補正処理を行うことができる。即ち、色補正に用いる色変換マトリクスＡを２つのマトリクス、即ち色相を目標色Ｃｍｅに一致させる色相最適化マトリクスＡ₋ｈｕｅｗと彩度を目標色Ｃｍｅに一致させるＡ₋ｓａｔｗとの積により求め、それぞれのマトリクスを個別に重回帰分析によって求めている。これにより、補正色Ｃｅｓを目標色Ｃｍｅに対して色相を優先的に一致させることができ、モニタ装置３０において被写体本来の色に極めて近い色味を再現することができる。
【００６４】
上記の重回帰モデルでは各色について補正色Ｃｅｓと目標色Ｃｍｅとの色相角差がほぼ均等にばらつくが、肌色等の特定色に限定して色相一致の精度を向上させたい場合には、ステップＳ１２０およびステップＳ１４０の重回帰分析を行う前に、目的変数群となる色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）および目標色Ｃｍｅ（１）〜Ｃｍｅ（１８）に重み付けをする。即ち、１８色についてそれぞれ設定した重みＷ（ｋ）（ｋ＝１，２，…１８）と色相最適化目標色Ｃｍｅ’（ｋ）との積、および重みＷ（ｋ）と目標色Ｃｍｅ（ｋ）との積を目的変数群として重回帰分析を行う。（１５）式には色相最適化目標色Ｃｍｅ’（１）〜Ｃｍｅ’（１８）に重み付けをして色相を一致させるための重回帰モデル式が示され、（１６）式には目標色Ｃｍｅ（１）〜Ｃｍｅ（１８）に重み付けをして彩度を一致させるための重回帰モデル式が示される。Ｗは１８色の重みＷ（ｋ）を要素とするマトリクスであり、重みＷ（１）〜Ｗ（１８）の総和は１である。この重み付けにより、重みを大きくした特定色ほど、より忠実な色再現を行うことができる。
【数１２】

【００６５】
なお、画像入力装置としては本実施形態のデジタルカメラ１０の他、デジタルビデオカメラ、スキャナであってもよい。また、本実施形態では色変換マトリクス算出装置３４をデジタルカメラ１０と別体にしているが、デジタルカメラ１０に色変換マトリクス算出機能を搭載してもよい。またさらに、色変換マトリクスを算出するとともに色補正できる画像処理ソフトウェアとしてパーソナルコンピュータにインストールし、デジタルカメラ１０から出力されたＲＡＷデータをパーソナルコンピュータで色補正できるように構成してもよい。
【００６６】
本実施形態では、撮像系で得られたＲＧＢ信号をｓＲＧＢ規格に合わせて色補正する色変換マトリクスを求めているが、本発明のマトリクス算出方法は特に色補正を目的とする色変換マトリクスの算出に限定されない。例えば異なる色空間の色信号を相互変換する（ＲＧＢ信号をＸＹＺ信号や印刷のためのｃｍｙ信号に変換する等）ための色変換マトリクスの算出にも適用できる。
【００６７】
【発明の効果】
以上説明したように、本発明によると、色相に関して再現色を本来の色に高精度に近似できる色変換マトリクスを得ることができる。
【図面の簡単な説明】
【図１】本発明の色変換マトリクス算出方法および色変換方法の実施形態を示す図であって、色変換を行うデジタルカメラと、色変換マトリクスを算出する色変換マトリクス算出装置とを示すブロック図である。
【図２】色変換マトリクス算出の原理を示す図であって、所定の色に関してＬａｂ色空間における変換前の入力色と変換すべき目標色との位置を示す図である。
【図３】色変換マトリクス算出処理の処理流れおよび各種色信号の関係を模式的に示すブロック図である。
【図４】色変換マトリクス算出処理を示すフローチャートの第１の部分である。
【図５】色変換マトリクス算出処理を示すフローチャートの第２の部分である。
【図６】色変換マトリクス算出処理を示すフローチャートの最後の部分である。
【符号の説明】
１０ デジタルカメラ
２０ デジタル信号処理回路
３０ モニタ装置
３４ 色変換マトリクス算出装置
４０ カラーチャート[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a color correction method for correcting a color signal to improve the color reproducibility of a reproduced color image for a subject, and a color conversion matrix calculation method for calculating a color conversion matrix used for color correction.
[0002]
[Prior art]
In recent years, image color information is often digitized in order to accurately transmit it between different media. For example, an image input device such as a digital camera or a scanner converts a captured subject's color image into three primary colors of light. An RGB signal is converted and output to an image output device such as a monitor or printer, and the image output device reproduces a color image based on the RGB signal (for example, displayed on a monitor screen or printed on paper). Generally done. The RGB signal obtained by the image input device depends on the imaging characteristics of the optical system such as the photographic lens, the light receiving sensor such as the color filter and the image sensor, and the image output device also reproduces even if the same RGB signal is input depending on the reproduction method In addition to the differences in the colors to be reproduced, there are inherent individual differences in the characteristics of the image input device and the image output device. Therefore, the reproduced color image based on the RGB signal has poor color reproducibility with respect to the subject, that is, an accurate color. Cannot reproduce.
[0003]
Therefore, in recent years, color signals conforming to the sRGB standard commonly used between the image input device and the image output device are often used. In the image input device, the RGB signal obtained by the imaging system is used in accordance with the sRGB standard. Color correction is performed and this is output. As a result, an accurate color reproduction can be performed with an image output device compliant with the sRGB standard, that is, an approximate color can be reproduced if the same RGB values are given. There are various color correction methods. For example, the optical color provided in the imaging system approximates the reproduced color to the original color by optical correction that matches the spectral characteristics of the optical filter to the sRGB standard, or electronic correction that performs matrix operation on the RGB signal. I am letting.
[0004]
Conventionally, a multiple regression analysis method has been proposed as a technique for improving the color conversion accuracy of a color conversion matrix used in electronic color correction. Multiple regression analysis optimizes matrix elements by statistical analysis that captures the relationship between the original color and reproduced color as the cause and result, that is, predicts by applying a color conversion matrix to the RGB signal obtained in the imaging system This is a technique for obtaining a matrix element such that the signal level difference between the reproduced color and the original color is less than an allowable value. For example, Patent Document 1 converts RGB signals of three primary colors into XYZ signals of different color systems. The technique which calculates | requires the matrix for this by multiple regression analysis is shown.
[0005]
[Patent Document 1]
Japanese Patent Laid-Open No. 10-164381
[0006]
In general, the degree of coincidence between the reproduced color and the original color is evaluated by three factors of hue, saturation, and brightness according to human physiological color sense. In particular, the difference in hue is easily recognized as a difference in color by humans. However, since the RGB signal does not have a linear relationship with the hue, there is a problem that it is difficult to evaluate the accuracy of the multiple regression analysis described above. That is, even if the signal level difference of the RGB signals is within the allowable value range, a difference in hue that can be recognized as a different color by human eyes may occur.
[0007]
[Problems to be solved by the invention]
The present invention has been made in view of the above problems, and it is an object of the present invention to obtain a color conversion matrix capable of approximating a reproduced color to an original color with high accuracy, particularly with respect to hue.
[0008]
[Means for Solving the Problems]
The color conversion matrix calculation method of the present invention is a method for calculating a color conversion matrix for converting an arbitrary color signal in the first color space into a color signal in the second color space, and the color conversion matrix is the first matrix. And the second matrix, and color signals in the first color space corresponding to a plurality of color patches whose saturation and hue change stepwise are defined as a first explanatory variable group and correspond to each of the color patches. A multiple regression model is constructed in which the first target color signal relating to the hue of the second color space is the first objective variable group, and the elements of the first matrix are the partial regression coefficients, and the first explanatory variable group, the first objective variable group, The element of the first matrix is obtained by the multiple regression analysis based on the color correction, and the hue correction color signal obtained by applying the first matrix to the color signal of the first color space corresponding to each color patch is used as the second explanatory variable group. And A multiple regression model is constructed in which the second target color signal relating to the saturation of the second color space corresponding to each of the patches is the second objective variable group, and the elements of the second matrix are the partial regression coefficients, and the second explanatory variable group And an element of the second matrix is obtained by multiple regression analysis based on the second objective variable group.
[0009]
In the color conversion matrix calculation method, the color signal of the first color space, the hue correction color signal, the first target color signal, and the second target color signal corresponding to the color patch are converted into CIE- L ^* a ^* b ^* It is preferable that the color signal is converted into a color signal in a uniform color space. Further, for example, the target color signal related to saturation is a colorimetric signal of a color patch, and the first target color signal is CIE-L. ^* a ^* b ^* It may be a color signal indicated by a point obtained by orthogonally projecting the first target color signal with respect to a straight line connecting the coordinate origin and the point of the second target color signal in the color space.
[0010]
The color patches used in the color conversion matrix calculation method are, for example, 18 chromatic color patches of the Macbeth color checker. In this case, the color signal of the first color space corresponding to the 18 chromatic color patches is the Macbeth color patch. It is preferable that the white balance correction is performed based on the color signal of the first color space corresponding to the six achromatic color patches of the color checker.
[0011]
In the color conversion matrix calculation method, for example, the color signal in the first color space is an RGB signal of three primary colors obtained by an image sensor provided with a color filter, and the color signal in the second color space is sRGB (standard red green).・ Blue) Signal.
[0012]
The color correction method according to the present invention is a color correction method for converting a color signal of an arbitrary color in the first color space of an image into a color signal in the second color space using a color conversion matrix, The conversion matrix is a product of the first matrix and the second matrix, and color signals in the first color space respectively corresponding to a plurality of color patches whose chroma and hue change stepwise are defined as a first explanatory variable group. A multiple regression model is constructed in which the first target color signal relating to the hue of the second color space corresponding to each of the color patches is the first objective variable group, and the elements of the first matrix are the partial regression coefficients. Hue correction color obtained by applying the first matrix to the color signal of the first color space corresponding to each color patch, the elements of the first matrix being obtained by multiple regression analysis based on the first objective variable group and the first objective variable group Signal A multiple regression model is constructed in which an explanatory variable group, a second target color signal relating to the saturation of the second color space corresponding to each of the color patches is a second objective variable group, and an element of the second matrix is a partial regression coefficient. The elements of the second matrix are obtained by multiple regression analysis based on the second explanatory variable group and the second objective variable group.
[0013]
DETAILED DESCRIPTION OF THE INVENTION
Embodiments of the present invention will be described below with reference to the accompanying drawings.
[0014]
FIG. 1 is a schematic diagram showing an embodiment of a color conversion matrix calculation method and a color conversion method according to the present invention.
[0015]
The digital camera 10 is an image input device that obtains a full-color image of a subject using an image sensor, and includes a photographing optical system 12 and a single-plate CCD 14 in which an image sensor, for example, a color chip filter 16 of RGB three primary colors is provided on the imaging surface. Is provided. The optical object image formed on the image sensor by the photographing optical system 12 is photoelectrically converted by the CCD 14, read out from the CCD 14, subjected to analog signal processing, A / D converted, and RAW data for one frame. It is sent to the digital signal processing circuit 20.
[0016]
The digital signal processing circuit 20 performs color separation processing for generating RGB signals for each pixel from RAW data, white balance correction processing for adjusting R, G, and B gains according to white reference values, and color signals in the first color space. The color correction processing for bringing the reproduced color closer to the target color (for example, the original color of the subject) by converting the color gamut of the primary color RGB signal as described above into the color gamut defined by the sRGB standard, and the γ characteristic of the monitor device 30 A gradation correction process for adjusting the gradation so as to cancel out is sequentially performed to generate an sRGB signal that is a color signal of the second color space. The digital signal processing circuit 20 converts the sRGB signal into an external device such as a personal computer via an interface (not shown) such as a USB cable, a monitor device 30 (CRT display monitor or LCD monitor), a printer, etc. (not shown). To the image output device.
[0017]
The sRGB signal is a signal conforming to the IEC-stipulated international color reproduction standard, and the sRGB standard defines color reproducibility and color gamut according to a standard CRT display monitor device. In this case, in the white balance correction process, the white reference value is CIE-D. ₆₅ In the color correction process, the color gamut of the RGB signal is corrected to the defined color gamut, and in the gradation correction process, the γ value is set to 2.2.
[0018]
The digital signal processing circuit 20 processes signals according to the sRGB standard, but an element having a characteristic value conforming to the sRGB standard is used for the imaging system (the photographing optical system 12, the CCD 14, the RGB color chip filter 16, etc.). For this reason, the color information of the subject cannot be accurately taken in accordance with the sRGB standard, and the reproduced color does not match the original color. In order to avoid this phenomenon, optical correction for matching the sensitivity characteristic of the image pickup system to the sRGB standard has been performed, but it is not sufficient, and it is substantially difficult to make it completely match. For this reason, the signal level of the RGB signal obtained by the imaging system is adjusted and electronically corrected. However, the sensitivity characteristics of the imaging system vary depending on the individual digital camera 10 and are obtained by the original color information of the subject and the digital camera 10. Since there is no regularity in the relationship with the color information to be obtained, it is difficult to theoretically define the relationship between the two, and different signal processing must be performed for each color. When the R, G, and B signals are 8-bit data, the number of colors is (2 ⁸ ) ³ = 167777216, and it is not realistic to perform color correction processing optimal for all colors.
[0019]
Therefore, a color chart composed of a plurality of color samples whose saturation and hue change stepwise, for example, a 24-color patch P of the Macbeth Color Chart (registered trademark) 40 shown in FIG. ₁ ~ P ₂₄ (In FIG. 1, only a part of the 24 color patches are provided with reference numerals), the color is accurately measured by a colorimeter or the like, and the individual digital cameras 10 are photographed in the same lighting environment as the color measurement. A color conversion matrix that matches the obtained RGB signal with the colorimetric RGB signal is obtained and set in the digital camera 10. When the subject is photographed, the digital signal processing circuit 20 performs color correction processing using this color conversion matrix. Thereby, color reproduction faithful to the colorimetric value can be performed.
[0020]
The color conversion matrix is calculated by an external color conversion matrix calculation device 34, for example, a personal computer, and is stored in the memory 22 of the digital camera 10 in advance. On the other hand, the digital camera 10 outputs RAW data obtained by photographing the Macbeth color chart 40 to calculate the color conversion matrix from the digital signal processing circuit 20 to the color conversion matrix calculation device 34. The color conversion matrix is a 3 × 3 matrix obtained in cooperation with the color conversion matrix calculation device 34 at the final stage of the manufacturing process of the digital camera 10, and corresponds to the color sensitivity characteristics of the imaging system of each digital camera 10. Nine matrix element values are determined.
[0021]
When a predetermined color obtained from RAW data is defined as an input color Cin, a color conversion matrix A is defined as a color, and a color after color correction processing by the color conversion matrix A is defined as a corrected color Ces, the respective RGB signals Cin (Rin, Gin, Bin) As for Ces (Res, Ges, Bes), the linear linear expression shown in the following expression (1) holds. An expression using a matrix element equivalent to the expression (1) is shown in an expression (2). a ₁ ~ A ₉ Are matrix elements of the color conversion matrix A.
[0022]
[Expression 1]

[0023]
In this embodiment, since the purpose is to perform accurate color reproduction, the target value set when calculating the color conversion matrix A is the color patch P. ₁ ~ P ₂₄ The colorimetric signal was corrected for the specific color when reproducing the frequently used specific color such as human skin color or blue sky color instead of the exact color. The value may be set as a target value. Note that RGB signals obtained by colorimetry are obtained by directly measuring R, G, and B signal levels with a colorimeter, for example, measuring spectral reflectance with a spectrophotometer, or different from the RGB color system with a colorimeter. XYZ signal and L expressed in color system ^* a ^* b ^* Measure signal, spectral reflectance, XYZ signal or L ^* a ^* b ^* The signal may be obtained by converting it into an RGB signal.
[0024]
The Macbeth color chart 40 is a commercially available off-the-shelf product that is easy to obtain. ₁ ~ P ₂₄ The colorimetric signal is already known and the colorimetry is saved. For example, the first color patch P under a standard light illumination environment ₁ The colorimetric signals of (color name; dark skin color) are x = 0.4002, y = 0.3504, and Y = 10.05, and these colorimetric signals x, y, and Y are converted into RGB signals by a known conversion formula. Can be converted to However, x = X / (X + Y + Z), y = Y / (X + Y + Z), and X, Y, and Z are tristimulus values in the XYZ color system. 1st to 18th color patch P ₁ ~ P ₁₈ Is a chromatic color and the 19th-24th color patch P in the last row ₁₉ ~ P ₂₄ Is achromatic.
[0025]
The color chart is not limited to the Macbeth color chart of the present embodiment, and may be any color chart in which a plurality of color patches are uniformly distributed in a uniform color space. For example, a JIS standard color standard may be used. The color conversion matrix obtained on the basis of the Macbeth color chart 40 represents each color patch P ₁ ~ P ₂₄ The colors of can be accurately reproduced, but other colors are not guaranteed. Therefore, if a unique color chart using specific colors (such as human skin color, blue sky color, and green) that are often used as color patches is created, the specific colors can be reproduced particularly faithfully.
[0026]
The color conversion matrix calculation method will be described with reference to FIGS. FIG. 2 shows a standard light CIE-D representing daylight with a color temperature of 6504K. ₆₅ CIE-L with light source for illumination ^* a ^* b ^* A color space (hereinafter referred to as “Lab color space”) is shown. In this Lab color space, an input color Cin relating to a predetermined color and a target color Cme (hereinafter referred to as “target color”) to be corrected are displayed. Each is indicated by a dot. L of target color Cme ^* a ^* b ^* The signal is set to a value obtained by colorimetry. FIG. 3 is a block diagram schematically showing the flow of the color conversion matrix calculation process and the relationship between various color signals.
[0027]
In matrix operation, colors are handled as RGB signals, but in the evaluation of color matching, L ^* a ^* b ^* Treated with a signal. This is because the Lab color space is a uniform color space in which the correlation between human color perception and coordinate distance is good. In the Lab color space shown in FIG. ^* A, indicating hue and saturation ^* , B ^* Any color can be expressed by the coordinates of. Lightness index L ^* Indicates the relative brightness or darkness of an arbitrary color, and ranges from 0% black to 100% white. Hue is a ^* b ^* It is indicated by an angle around the coordinate origin in the plane, and is in the range of 0 ° to 360 °. a ^* The larger the positive number on the axis, the stronger red, and the larger the negative number, the stronger green. b ^* The larger the positive number on the axis, the stronger yellow, and the larger the negative number, the stronger blue. Further, the greater the distance from the coordinate origin, the higher the saturation and the brighter the color. The coordinate origin is achromatic.
[0028]
RGB signal to L ^* a ^* b ^* Conversion to a signal is performed by the following known equations (3) and (4). Equation (3) is a conversion equation for converting RGB signals to XYZ signals, and Equation (4) is an XYZ signal converted to L ^* a ^* b ^* It is a conversion formula for converting into a signal. When evaluating the degree of color matching, RGB signals are RGB → XYZ → L ^* a ^* b ^* L by conversion ^* a ^* b ^* Converted to a signal and L for matrix operation ^* a ^* b ^* The signal is L ^* a ^* b ^* → XYZ → RGB signals are converted back to RGB signals. L ^* a ^* b ^* → XYZ → RGB conversion is performed by a conversion expression obtained by modifying Expressions (3) and (4), and the expression is omitted here.
[0029]
[Expression 2]

[0030]
[Equation 3]

[0031]
In this embodiment, the color patch P ₁ ~ P ₁₈ The color conversion matrix A is optimized so that the hues of the correction colors Ces predicted from the input color Cin for the 18 colors correspond to the corresponding target colors Cme, and then the saturation is optimized. The degree of coincidence between the correction color Ces and the target color Cme is evaluated by the difference between the hue angles θes and θme in the Lab color space. Hue angle θ (θes and θme) is a ^* b ^* A on the surface ^* The rotation angle around the origin from the axis, which is defined by the following equation (5). The hue angles θes and θme are respectively a ^* Coordinates and b ^* It is obtained by substituting the coordinates into equation (5). In human perception, a different hue is more easily recognized as a different color than a case where the saturation is different, and therefore the hue is preferentially matched in this embodiment.
[0032]
[Expression 4]

[0033]
First, in order to match the hue, the color of the point obtained by orthogonally projecting the input color Cin on the straight line L connecting the coordinate origin and the target color Cme in the Lab color space is set as the hue optimization target color Cme ′, and the hue optimization is performed. L of target color Cme ' ^* a ^* b ^* L signal ^* a ^* b ^* → XYZ → RGB conversion to obtain RGB signals for each of the 18 colors, and a hue optimization matrix A for matching the 18 input colors Cin with the corresponding hue optimization target colors Cme ′ ₋ A hue (first matrix) is obtained by multiple regression analysis. The RGB signal of the hue optimization target color Cme ′ is the first target color signal related to the hue. A straight line L is a set of points having the same hue as the target color Cme, and a color Cme ′ (hereinafter referred to as a hue optimization target color) obtained by orthogonally projecting the input color Cin onto the straight line L is a target color. It is a color having the same hue as Cme and the closest distance in the Lab space with respect to the input color Cin. That is, if the target color is set to the hue optimization target color Cme ′, the hue can be matched with the shortest moving distance in the Lab color space. FIG. 2 shows only one color as a representative. Hue optimization matrix A for each input color Cin ₋ The hue correction color Ces ′ obtained by applying hue substantially matches the corresponding hue optimization target color Cme ′.
[0034]
Next, a saturation optimization matrix A for matching the 18 hue correction colors Ces ′ with the corresponding target color Cme in order to match the saturation. ₋ The satw (second matrix) is obtained by multiple regression analysis. The RGB signal of the target color Cme is a second target color signal related to saturation. Saturation optimization matrix A for each hue correction color Ces' ₋ The correction color Ces obtained by applying satw substantially matches the corresponding target color Cme.
[0035]
The color conversion matrix A for converting the input color Cin to the correction color Ces is a hue optimization matrix A for approximating the hue to the target color Cme as shown in the following equation (6). ₋ Saturation optimization matrix A for approximating saturation to hue and target color Cme ₋ It is obtained by product with satw. An expression using matrix elements equivalent to Expression (6) is shown in Expression (7). A ′ in the formula (7) ₁ ~ A ' ₉ Is a hue optimization matrix A ₋ a matrix element of hue, a " ₁ ~ A " ₉ Is saturation optimization matrix A ₋ It is a matrix element of satw.
[0036]
[Equation 5]

[0037]
Therefore, converting the input color Cin to the correction color Ces by the color conversion matrix A is equivalent to matching the saturation after the hue of the input color Cin is matched to the correction color Ces (( (See 8)).
[Formula 6]

[0038]
Next, the color conversion matrix calculation process will be described in detail with reference to the flowcharts of FIGS.
[0039]
First, in step S102, the 24-color patch P ₁ ~ P ₂₄ The Macbeth color chart 40 having the above is prepared, and these 24 color patches P are prepared. ₁ ~ P ₂₄ CIE-D ₆₅ Then, the RAW data obtained by the digital camera 10 is transferred to the color conversion matrix calculation device 34.
[0040]
The color conversion matrix calculation device 34 calculates 18 chromatic color patches P based on the RAW data. ₁ ~ P ₁₈ RGB signals of the input color Cin corresponding to are obtained (step S104). Here, each chromatic color patch P ₁ ~ P ₁₈ In order to distinguish the color data corresponding to the chromatic color patch P ₁ ~ P ₁₈ Is set to a parameter k (k = 1, 2,..., 18) indicating the order of the kth color patch P _k The input color corresponding to is represented by Cin (k), and the RGB signal is represented by (Rin (k), Gin (k), Bin (k)). The RGB signal (Rin (k), Gin (k), Bin (k)) of the input color Cin (k) is the color patch P _k Is an average value (hereinafter referred to as RGB average value) of R, G, and B signal levels of 30 × 30 pixels extracted from the imaging region corresponding to the 8-bit data. In order to increase the reliability of the RGB average value, defective pixels are removed from 30 × 30 pixels. The RGB signals (Rin (k), Gin (k), Bin (k)) may be 10-bit data or 12-bit data.
[0041]
19th-24th color patch P of Macbeth color chart 40 ₁₉ ~ P ₂₄ Is a 6-stage achromatic color patch. For details, refer to the 19th color patch P ₁₉ (Color name: White), 20th color patch P ₂₀ (Color name: Gray 8), 21st color patch P ₂₁ (Color name: Gray 6.5), 22nd color patch P ₂₂ (Color name: Gray 5), 23rd color patch P ₂₃ (Color name: Gray 3.5), 24th color patch P ₂₄ (Color name; black).
[0042]
These six achromatic color patches P ₁₉ ~ P ₂₄ Is used for correction of gray gradation. Specifically, each color patch P ₁₉ ~ P ₂₄ The RGB average values of 30 × 30 pixels extracted from the imaging regions corresponding to each of the six achromatic color patches P are obtained. ₁₉ ~ P ₂₄ An offset value that minimizes an error between the RGB average value and each target value (for example, a colorimetric signal) is obtained for each of R, G, and B. In step S104, the chromatic color patch P _k Before obtaining RGB signals (Rin (k), Gin (k), Bin (k)) of the input color Cin (k) of (k = 1, 2,..., 18), R, G, and B of the RAW data are obtained. The offset value is subtracted from each signal, thereby correcting the white reference level and the black reference level of the image, and correcting the gray gradation, that is, the color density to an appropriate level. The gradation is normalized by γ = 1.0.
[0043]
Six achromatic color patches P ₁₉ ~ P ₂₄ Is also used for white balance correction, and each achromatic color patch P obtained from RAW data ₁₉ ~ P ₂₄ R, G, and B gains are determined based on the RGB average values of the eighteen chromatic color patches P. ₁ ~ P ₁₈ The RGB average values are adjusted for gain.
[0044]
Accordingly, the 18 chromatic color patches P obtained in step S104. _k The RGB signals (Rin (k), Gin (k), Bin (k)) of the input color Cin (k) of (k = 1, 2,..., 18) are subjected to gray gradation correction and white balance correction. , Γ = 1.0.
[0045]
In addition, the 18 color patches P known in step S106. ₁ ~ P ₁₈ These colorimetric signals (RGB signals) are input to the color conversion matrix calculation device 34. If the input data is not an RGB signal, for example, an XYZ signal, L ^* a ^* b ^* In the case of a signal, spectral reflectance, etc., it is converted into an RGB signal by a known conversion formula. If the value of the colorimetric signal is unknown, the color patch P is used in the same lighting environment as that for photographing before step S106. ₁ ~ P ₁₈ Measure the color.
[0046]
In the next step S108, the kth (k = 1, 2,..., 18) color patch P _k Is defined as Cme (k), and its RGB signals are defined as (Rme (k), Gme (k), Bme (k)), and the colorimetric signal obtained in step S106 is the target color Cme (k). Set to RGB signals (Rme (k), Gme (k), Bme (k)). Since the present embodiment aims to perform accurate color reproduction, the colorimetric signal is an RGB signal (Rme (k), Gme (k), Bme (k)) of the target color Cme (k). When the purpose is to reproduce a specific color as a preferable color, the values of Rme (k), Gme (k), and Bme (k) are arbitrarily changed according to the purpose. Steps S106 and S108 may be performed at any time before the next step S110.
[0047]
In step S110, the RGB signals (Rin (k), Gin (k), Bin (k)) (k = 1, 2,..., 18) of the 18 input colors Cin (k) obtained in step S104 are obtained. , RGB → XYZ → L ^* a ^* b ^* L by transformation (equations (3) and (4)) ^* a ^* b ^* Convert to signal. Similarly, the RGB signals (Rme (k), Gme (k), Bme (k)) (k = 1, 2,..., 18) of the 18 target colors Cme (k) obtained in step S108 are set to L. ^* a ^* b ^* Convert to signal.
[0048]
In step S112, hue optimization target colors Cme ′ (1) to Cme ′ (18) are set for 18 colors, and their L values are set. ^* a ^* b ^* Find the signal. That is, the hue optimization is performed at a point obtained by orthogonally projecting the input color Cin (k) on the straight line connecting the kth (k = 1, 2,..., 18) target color Cme (k) and the coordinate origin in the Lab color space. Set to target color Cme '(k) ^* a ^* b ^* Find the coordinates. In step S114, the hue optimization target colors Cme ′ (1) to Cme ′ (18) L ^* a ^* b ^* Each signal is L ^* a ^* b ^* → XYZ → RGB conversion to obtain RGB signals (Rme ′ (1), Gme ′ (1), Bme ′ (1)) to (Rme ′ (18), Gme ′ (18), Bme ′ (18)) .
[0049]
In step S120, the RGB signals of the 18 input colors Cin (1) to Cin (18) are used as explanatory variable groups, and the RGB signals of the 18 hue optimization target colors Cme ′ (1) to Cme ′ (18) are obtained. Hue optimization matrix A as objective variable group ₋ hue matrix element a ' ₁ ~ A ' ₉ A multiple regression model having a partial regression coefficient is constructed and a multiple regression analysis is performed. In step S122, the hue optimization matrix A is calculated. ₋ hue matrix element a ' ₁ ~ A ' ₉ Ask for.
[0050]
In this multiple regression model, matrices Bin and Bme each having column signals of RGB signals of input colors Cin (1) to Cin (18) and RGB signals of hue optimization target colors Cme ′ (1) to Cme ′ (18), respectively. 'And a hue optimization matrix A consisting of partial regression coefficients ₋ It is assumed that the linear linear expression shown in Expression (9) is established for 18 colors with respect to hue. Expression (10) is an expression using matrix elements equivalent to expression (9).
[0051]
[Expression 7]

[0052]
Hue optimization matrix A ₋ The hue is obtained by optimization such as a known least square method. That is, hue optimization is performed on the left side (RGB values of hue optimization target colors Cme ′ (1) to Cme ′ (18)) and the right side (input colors Cin (1) to Cin (18)) in the multiple regression model equation described above. Matrix A ₋ (RGB values obtained by doing hue) do not actually match, and there is an error. Therefore, on the condition that the square sum of the error between the right side and the left side is minimized, the formula (9) is transformed into the formula (11), and the partial regression coefficient A is solved by solving the formula (11). ₋ Find hue. "() ^t ”Indicates a transposed matrix, and“ () ^-1 "Indicates an inverse matrix.
[Equation 8]

[0053]
Multiple regression analysis is completed and hue optimization matrix A ₋ When hue is obtained, the hue optimization matrix A obtained in subsequent steps S124 to S130. ₋ The effectiveness of hue is evaluated.
[0054]
In step S124, the RGB signals of the input colors Cin (1) to Cin (18) are converted into the hue optimization matrix A, respectively. ₋ RGB signals (Res (1), Ges (1), Bes (1)) to (Res (18), Ges (18) of hue correction colors Ces ′ (1) to Ces ′ (18) by converting with hue. , Bes (18)) (see equation (12)), and in step S126, RGB → XYZ → L of equations (3) and (4) ^* a ^* b ^* By conversion, the hue correction colors Ces ′ (1) to Ces ′ (18) L ^* a ^* b ^* Find the signal.
[Equation 9]

[0055]
In step S128, L of the hue optimization target colors Cme ′ (1) to Cme ′ (18) set in step S112. ^* a ^* b ^* Signal and L of the hue correction colors Ces ′ (1) to Ces ′ (18) obtained in step S126. ^* a ^* b ^* The hue error θrms is obtained based on the signal. More specifically, for the kth color, the hue optimization target color Cme ′ (k) L ^* a ^* b ^* The hue angle θme ′ (k) is obtained from the signal by the equation (5) and the hue correction color Ces ′ (k) L ^* a ^* b ^* The process of obtaining the hue angle θes ′ (k) from the signal by the equation (5) is performed for k = 1, 2,..., 18 and the difference between the hue angles θme ′ (k) and θes ′ (k) of the 18 colors is calculated. The sum of squares is obtained, and this is set as the hue error θrms (see equation (13)).
[0056]
[Expression 10]

[0057]
In step S130, it is determined whether or not the hue error θrms is less than or equal to the allowable value α. If the hue error θrms exceeds the allowable value α, the process returns to step S108, and the target colors Cme (1) to Cme (18) Change one of the RGB signals to create a new hue optimization matrix A ₋ Find hue. Note that when returning to step S108 and resetting the RGB signals of the target colors Cme (1) to Cme (18), the hue of the reproduced color in the monitor device 30 is set to be the subject so that the change in hue is small. Each value needs to be determined so that it does not change from the original color.
[0058]
If it is determined in step S130 that the hue error θrms is less than or equal to the allowable value α, the hue optimization matrix A that can approximate the input color Cin with respect to the target color Cme with high accuracy. ₋ It is assumed that hue has been obtained, and saturation optimization matrix A ₋ Steps S140 to S144 for obtaining satw are executed.
[0059]
In step S140, a multiple regression model for adjusting not only the hue but also the saturation is constructed, and a multiple regression analysis is performed. In this multiple regression model, as shown in the equation (14), the RGB signals of the 18 hue correction colors Ces ′ (1) to Ces ′ (18) obtained in step S124 are explanatory variable groups, and step S108. The 18 color saturation optimization target colors Cme (1) to Cme (18) set in (1) are the objective variable group. Bin in the equation (14) is a matrix having hue correction colors Ces ′ (1) to Ces ′ (18) as column vectors, and Bme is a saturation optimization target color Cme (1) to Cme (18). It is a matrix that is a column vector. In step S142, the obtained partial regression coefficient a " ₁ ~ A " ₉ Saturation optimization matrix A ₋ It is determined in the matrix element of satw. Saturation optimization matrix A ₋ The method for obtaining satw is the hue optimization matrix A in steps S120 to S122. ₋ This is the same as how to obtain hue and will not be described in detail.
[Expression 11]

[0060]
Saturation optimization matrix A in step S142 ₋ When satw is obtained, the color conversion matrix A is calculated in accordance with the above-described expression (6) (expression (7)) in step S144. In step S146, the RGB signals (Res (1), Cin (18)) of the correction colors Ces (1) to Ces (18) are converted by converting the RGB signals of the input colors Cin (1) to Cin (18) using the color conversion matrix A, respectively. Ges (1), Bes (1)) to (Res (18), Ges (18), Bes (18)) are obtained (refer to the above-described equations (1) and (2)), and in step S148 (3 ) Formula and (4) Formula RGB → XYZ → L ^* a ^* b ^* By conversion, L of the correction colors Ces (1) to Ces (18) ^* a ^* b ^* In step S150, a hue error θrms between the correction colors Ces (1) to Ces (18) and the target colors Cme (1) to Cme (18) is obtained. The method for obtaining the hue error θrms in step S150 is the same as the method for obtaining the hue error θrms in step S128, and a description thereof will be omitted.
[0061]
In the next step S152, it is determined whether or not the hue error θrms is less than or equal to the allowable value α. If the hue error θrms exceeds the allowable value α, the process returns to step S108, and the hue error θrms is less than or equal to the allowable value α. If it is determined that the color conversion matrix A can be obtained that can approximate the input color Cin with respect to the target color Cme with high accuracy in terms of hue and saturation, the coefficients of the color conversion matrix A are determined in step S154. In step S156, the coefficient data of the color conversion matrix A is transferred from the color conversion matrix calculation device 34 to the digital camera 10 and written in the memory 22, and the process ends.
[0062]
When the color conversion matrix A obtained as described above is used in the color correction processing of the digital camera 10, it is possible to obtain an sRGB signal that can reproduce a color faithful to the colorimetric signal, particularly with respect to the hue, and display it on the screen of the monitor device 30. The subject image can be displayed with a color very close to the original color of the subject.
[0063]
As described above, in this embodiment, it is possible to perform color correction processing in consideration of human visual characteristics in which a hue difference is easily captured as a color difference. In other words, the color conversion matrix A used for color correction is divided into two matrices, that is, a hue optimization matrix A that matches the hue with the target color Cme. ₋ A to match hue and saturation to the target color Cme ₋ The matrix is obtained by product with satw, and each matrix is individually obtained by multiple regression analysis. Accordingly, the hue of the correction color Ces can be preferentially matched with the target color Cme, and the monitor device 30 can reproduce a color very close to the original color of the subject.
[0064]
In the above-described multiple regression model, the hue angle difference between the correction color Ces and the target color Cme varies approximately equally for each color. Before performing the multiple regression analysis in step S140, the hue optimization target colors Cme ′ (1) to Cme ′ (18) and the target colors Cme (1) to Cme (18), which are target variable groups, are weighted. That is, the product of the weight W (k) (k = 1, 2,... 18) set for each of the 18 colors and the hue optimization target color Cme ′ (k), and the weight W (k) and the target color Cme (k ) And the multiple regression analysis using the objective variable group. The equation (15) shows a multiple regression model equation for weighting the hue-optimized target colors Cme ′ (1) to Cme ′ (18) to match the hues, and the equation (16) shows the target color Cme. A multiple regression model formula for weighting (1) to Cme (18) to match the saturation is shown. W is a matrix having 18 color weights W (k) as elements, and the sum of the weights W (1) to W (18) is 1. By this weighting, a more specific color reproduction can be performed for a specific color with a larger weight.
[Expression 12]

[0065]
The image input device may be a digital video camera or a scanner in addition to the digital camera 10 of the present embodiment. In this embodiment, the color conversion matrix calculation device 34 is separated from the digital camera 10, but the digital camera 10 may be equipped with a color conversion matrix calculation function. Furthermore, it may be configured such that the color conversion matrix is calculated and installed in a personal computer as image processing software capable of color correction, and the RAW data output from the digital camera 10 can be color corrected by the personal computer.
[0066]
In the present embodiment, a color conversion matrix that performs color correction on RGB signals obtained by the imaging system in accordance with the sRGB standard is obtained. However, the matrix calculation method of the present invention calculates a color conversion matrix particularly for color correction purposes. It is not limited to. For example, the present invention can be applied to calculation of a color conversion matrix for mutually converting color signals in different color spaces (converting RGB signals into XYZ signals or cmy signals for printing).
[0067]
【The invention's effect】
As described above, according to the present invention, it is possible to obtain a color conversion matrix capable of approximating the reproduced color with respect to the hue to the original color with high accuracy.
[Brief description of the drawings]
FIG. 1 is a diagram illustrating an embodiment of a color conversion matrix calculation method and a color conversion method according to the present invention, and is a block diagram illustrating a digital camera that performs color conversion and a color conversion matrix calculation device that calculates a color conversion matrix. It is.
FIG. 2 is a diagram illustrating the principle of color conversion matrix calculation, and is a diagram illustrating positions of an input color before conversion and a target color to be converted in a Lab color space with respect to a predetermined color.
FIG. 3 is a block diagram schematically showing the processing flow of color conversion matrix calculation processing and the relationship between various color signals.
FIG. 4 is a first part of a flowchart showing a color conversion matrix calculation process.
FIG. 5 is a second part of a flowchart showing a color conversion matrix calculation process.
FIG. 6 is a final part of a flowchart showing a color conversion matrix calculation process.
[Explanation of symbols]
10 Digital camera
20 Digital signal processing circuit
30 Monitor device
34 color conversion matrix calculation device
40 color chart

Claims (7)

A color conversion matrix calculation method for calculating a color conversion matrix for converting an arbitrary color signal in a first color space into a color signal in a second color space,
The color conversion matrix is a product of a first matrix and a second matrix;
A color signal in the first color space corresponding to each of a plurality of color patches whose saturation and hue change stepwise is defined as a first explanatory variable group, and a first color related to the hue in the second color space corresponding to each of the color patches. A multiple regression model having a target color signal as a first objective variable group and an element of the first matrix as a partial regression coefficient is constructed, and a multiple regression analysis based on the first explanatory variable group and the first objective variable group is performed. Elements of the first matrix are determined;
The hue correction color signal obtained by applying the first matrix to the color signal of the first color space corresponding to each of the color patches is set as a second explanatory variable group, and the second color corresponding to each of the color patches is set. A multiple regression model is constructed in which the second target color signal relating to the saturation of the space is the second objective variable group, and the elements of the second matrix are the partial regression coefficients, and the second explanatory variable group and the second objective variable group A method for calculating a color conversion matrix, wherein elements of the second matrix are obtained by multiple regression analysis based on the above. The color signal of the first color space corresponding to the color patch, the hue correction color signal, the first target color signal, and the second target color signal are CIE-L ^* a when the color matching degree is evaluated. ^* b ^* color conversion matrix calculation method according to claim 1, characterized in that it is converted to a color signal in the uniform color space. The target color signal related to the saturation is a colorimetric signal of the color patch, and the first target color signal connects the coordinate origin and the point of the second target color signal in the CIE-L ^* a ^* b ^* color space. 2. The color conversion matrix calculation method according to claim 1, wherein the color signal is a color signal indicated by a point obtained by orthogonally projecting the first target color signal with respect to a straight line. The color conversion matrix calculation method according to claim 1, wherein the color patches are 18 chromatic color patches of a Macbeth color chart. The color signal of the first color space corresponding to the 18 chromatic color patches is subjected to white balance correction based on the color signal of the first color space corresponding to the six achromatic color patches of the Macbeth color chart. The color conversion matrix calculation method according to claim 4, wherein: The color signal of the first color space is an RGB signal of three primary colors obtained by an image sensor provided with a color filter, and the color signal of the second color space is an sRGB (Standard Red Green Blue) signal. The color conversion matrix calculation method according to claim 1. A color correction method for converting a color signal of an arbitrary color in a first color space of an image into a color signal in a second color space using a color conversion matrix,
The color conversion matrix is a product of a first matrix and a second matrix;
A color signal in the first color space corresponding to each of a plurality of color patches whose saturation and hue change stepwise is defined as a first explanatory variable group, and a first color related to the hue in the second color space corresponding to each of the color patches. A multiple regression model having a target color signal as a first objective variable group and an element of the first matrix as a partial regression coefficient is constructed, and a multiple regression analysis based on the first explanatory variable group and the first objective variable group is performed. Elements of the first matrix are determined;
The hue correction color signal obtained by applying the first matrix to the color signal of the first color space corresponding to each of the color patches is set as a second explanatory variable group, and the second color corresponding to each of the color patches is set. A multiple regression model is constructed in which the second target color signal relating to the saturation of the space is the second objective variable group, and the elements of the second matrix are the partial regression coefficients, and the second explanatory variable group and the second objective variable group A color correction method, wherein the elements of the second matrix are obtained by a multiple regression analysis based on:

Images