JP2004253845A - Image forming apparatus - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide an image forming apparatus capable of excellently magnifying an original image with a small memory capacity. <P>SOLUTION: The image forming apparatus is characterized in that image data of two or three lines are stored for original image data and magnification processing is first applied to the original image data in a subscanning direction by a set magnification or an integer magnification greater than the set magnification and also reduction processing is applied to the magnified original image data in the subscanning direction at such magnification that a formed image with the set magnification can be obtained. <P>COPYRIGHT: (C)2004,JPO&NCIPI

Description

【００３１】
表１の「出力処理ライン」は、拡大処理後に時間順に出力されるライン列を表している。各ラインメモリＡ，Ｂの「Ｗｒｉｔｅ（ ）」は、ラインの画像データを読み込む動作を表し、カッコ内の数字は、何番目のラインであるかを表している。「Ｒｅａｄ（ ）」は、ラインの画像データを読み出す動作を表し、カッコ内の数字は、何番目のラインであるかを表している。上向きの矢印は「処理待ち」を表している。
【００３２】
表１の１番上の列に注目すると、ラインメモリＡによって１ライン目の画像データを読み込む。３列目になると、ラインメモリＢによって２ライン目の画像データを読み込むと同時に、ラインメモリＡによって読み込まれた１ライン目の画像データを読み出す。４列目で、ラインメモリＡによって読み込まれた１ライン目の画像データをもう一度読み出す。この２回の読み出しにより２００％拡大をしている。５列目で、ラインメモリＡによって３ライン目の画像データを読み込むと同時に、ラインメモリＢによって読み込まれた２ライン目の画像データを読み出す。６列目では、ラインメモリＢによって読み込まれた２ライン目の画像データをもう一度読み出す。
【００３３】
このように、１本のラインメモリからの読み出しは、表１から分かるように２回行うので、２倍の拡大処理ができていることになる（ステップＲ４）。この後に行う縮小処理（ステップＲ５）は、後述する。
なお、ラインメモリを２本分使っているので、読み出せるラインメモリは１本しかなく、他のラインメモリ１本は書き込みにまわさなければならない。したがって、この拡大処理（ステップＲ４）では、画像データの補間処理を行うことはできない。
【００３４】
次に、ラインメモリ５８が３本ある場合を説明する。それぞれをラインメモリＡ，Ｂ，Ｃとする。
図３を参照して、入力画像処理部５に与えられる画像信号は、副走査方向に拡大・縮小されていない等倍の信号となっている（ステップＳ１）。入力画像処理部５３は、この画像信号をラインごとに、各ラインメモリＡ，Ｂ，Ｃに格納する（ステップＳ２〜Ｓ４）。その格納手順を、表２を参照して説明する。操作部１８で設定された倍率は１００％以上〜２００％未満であるとする。この場合、入力画像処理部５３は、副走査方向に２倍（２００％）に拡大する。
【００３５】
【表２】

【００３６】
表２の各ラインメモリＡ，Ｂ，Ｃの「Ｗｒｉｔｅ（ ）」は、ラインの画像データを読み込む動作を表し、カッコ内の数字は、何番目のラインであるかを表している。「Ｒｅａｄ（ ）」は、ラインの画像データを読み出す動作を表し、カッコ内の数字は、何番目のラインであるかを表している。
表２の１番上の列に注目すると、ラインメモリＡによって１ライン目の画像データを読み込む。そして３列目になると、ラインメモリＢによって１ライン目の画像データを読み込む。５列目になって、ラインメモリＡによって読み込まれた１ライン目の画像データと、ラインメモリＢによって読み込まれた２ライン目の画像データとを読み出し、ラインメモリＣによって３ライン目の画像データを読み込む。６列目では、ラインメモリＡによって読み込まれた１ライン目の画像データと、ラインメモリＢによって読み込まれた２ライン目の画像データとを読み出す。７列目では、ラインメモリＢによって読み込まれた２ライン目の画像データと、ラインメモリＣによって読み込まれた３ライン目の画像データとを読み出し、ラインメモリＡによって４ライン目の画像データを読み込む。８列目では、ラインメモリＢによって読み込まれた２ライン目の画像データと、ラインメモリＣによって読み込まれた３ライン目の画像データとを読み出す。そして、同時に読み出された２ライン分の画像データを用いて、後述する補間処理を行う。
【００３７】
このように、１本のラインメモリからの読み出しは、表２から分かるように４列分の時間を使って４回行うとともに、同時に２ラインを用いて補間処理を行って１ライン分の画像データを得ているので、４×（１／２）＝２、すなわち２倍の拡大処理ができていることになる（ステップＳ５）。
また、ラインメモリを３本分使っているので、ラインメモリ２本で同時に２ライン分を読み出すとともに、他のラインメモリ１本で書き込みができる。したがって、同時に読み出された２ライン分の画像データを用いて、補間処理を行うことができる。
【００３８】
この補間処理は、拡大処理の倍率が２倍であれば、表１に示すように、２ライン分の画像データ（Ｒｅａｄ（１） とＲｅａｄ（２））を使って、出力処理ラインの１ライン目を作り、同じ２ライン分の画像データを使って、出力処理ラインの２ライン目を作る。そして１ラインずらして、次の２ライン分の画像データ（Ｒｅａｄ（２） とＲｅａｄ（３））を使って、出力処理ラインの３ライン目を作り、出力処理ラインの４ライン目を作る。以下、同様にして出力処理ラインを作っていく。
【００３９】
出力処理ラインの作り方は、補間に用いる原稿画像データの２ライン分をそれぞれ「注目ラインＡ」「注目ラインＢ」と表すと、
「出力処理ライン」＝α「注目ラインＡ」＋β「注目ラインＢ」
（０≦α≦１，０≦β≦１，α＋β＝１）
と表されるように重み付け平均をとる。
重みα，βの決め方は、「出力処理ライン」が奇数番目のときは、α＝１，β＝０とし、「出力処理ライン」が偶数番目のときは、α＝１／２，β＝１／２とする。これにより、原稿から読み込んだ２ラインの間に、等分に補間されたラインを１ライン挿入することができる。
【００４０】
拡大処理の倍率が３倍のときは、表には示していないが、２ライン分の画像データ（Ｒｅａｄ（１） とＲｅａｄ（２））を使って、出力処理ラインの１ライン目を作り、同じ２ライン分の画像データを使って、出力処理ラインの２ライン目と３ライン目を作る。そして１ラインずらして、次の２ライン分の画像データ（Ｒｅａｄ（２） とＲｅａｄ（３））を使って、出力処理ラインの４，５，６ライン目を作る。以下、同様にして出力処理ラインを作っていく。この場合、重みα，βの決め方は、「出力処理ライン」が３ｎ番目（ｎは整数）のときは、α＝１，β＝０とし、（３ｎ＋１）番目のときは、α＝２／３，β＝１／３とし、（３ｎ＋２）番目のときは、α＝１／３，β＝２／３とする。
【００４１】
図５は、拡大処理の倍率が３倍のときの補間の様子を表す図解図である。例えば注目ラインＡ，Ｂとすると、その間に「出力処理ライン」▲１▼、▲２▼が入る。「出力処理ライン」▲１▼は、通して数えると（３ｎ＋１）番目であるから、
「出力処理ライン」▲１▼＝（２／３）「注目ラインＡ」＋（１／３）「注目ラインＢ」
で表され、「出力処理ライン」▲２▼は、（３ｎ＋２）番目であるから、
「出力処理ライン」▲２▼＝（１／３）「注目ラインＡ」＋（２／３）「注目ラインＢ」
で表される。かりに、「注目ラインＡ」の値を２０、「注目ラインＢ」の値を１４０とすると、
「出力処理ライン」▲１▼＝（２／３）２０＋（１／３）１４０＝１８０／３＝６０
「出力処理ライン」▲２▼＝（１／３）２０＋（２／３）１４０＝３００／３＝１００
となる。
【００４２】
拡大処理の倍率が４倍、５倍と増えていっても、重みα，βは、同じ考え方で、２ライン分の画像データの差を４等分、５等分するように決めていくことができる。
このようにして、原稿のラインを整数倍に拡大しながら、補間処理された滑らかな出力処理ラインが得られる。
なお、以上の拡大処理では、操作部１８で設定された倍率は１００％以上〜２００％未満であるとすると、入力画像処理部５３は、副走査方向に２倍（２００％）に拡大していた。しかし、操作部１８で設定された倍率よりも大きな倍率で副走査方向に拡大処理を行えばよいので、２倍に限定されるものではない。例えば、ラインメモリからの読み出し速度を一律に最大（例えば８倍）にして、次の縮小処理で、所望の変倍率を得ることも可能である。
【００４３】
次に、拡大された画像を、操作部１８によって設定された倍率に戻す必要があるので、副走査方向の縮小処理を行う（ステップＲ５，Ｓ６）。縮小処理は、主走査同期信号を縮小倍率に応じて間引くことによって行う。数式で説明すると次のようになる。次のような変数を設定する。
ｍ： 主走査同期信号ごとの演算回数（初期値は０）
ＳＵＭｍ： 演算回ｍにおける加算値パラメータ。この加算値にＰＡＲＭ１を足していって、ＰＡＲＭ２進数で桁上がりが生じたときに、ライン出力をする。ＳＵＭｍの初期値ＳＵＭ０は、０≦ＳＵＭ０＜ＰＡＲＭ２の範囲でなら、どのような値に決めてもよいが、例えば０とする。
【００４４】
ＰＡＲＭ１：縮小倍率（単位は千分率）
ＰＡＲＭ２：１倍（単位は千分率）
計算方法は次のとおりである。加算値ＳＵＭｍ に、ＰＡＲＭ１を加算してＳＵＭ１とする。
ＳＵＭ１＝ＳＵＭｍ ＋ＰＡＲＭ１
ＳＵＭ１からＰＡＲＭ２を引いて、これをＳＵＭ２とする。
ＳＵＭ２＝ＳＵＭ１−ＰＡＲＭ２
ＳＵＭ２＜０のときは、ＰＡＲＭ２進数の桁上がりが生じていないので、ＳＵＭ１をそのまま次の演算回（ｍ＋１）おける加算値ＳＵＭｍ＋１とする。
【００４５】
ＳＵＭｍ＋１＝ＳＵＭ１
ＳＵＭ２≧０のときは、ＰＡＲＭ２進数の桁上がりが生じたので、ライン出力をして、ＳＵＭ２を次の演算回（ｍ＋１）の加算値ＳＵＭｍ＋１とする。
ＳＵＭｍ＋１＝ＳＵＭ２
縮小倍率を４２．３％（ＰＡＲＭ１＝４２３）としたときの具体的な数値例を表３に示す。
【００４６】
【表３】

【００４７】
表３によれば、演算回ｍにおける加算値ＳＵＭｍは３７となっている。これに、ＰＡＲＭ１（＝４２３）を足せばＳＵＭ１は４６０となり、ここからＰＡＲＭ２（＝１０００）を引いてＳＵＭ２を求めると、−５４０となる。桁上がりは、生じていないので、ライン非出力とし、ＳＵＭ１＝４６０をそのままＳＵＭｍ＋１とする。
演算回ｍ＋２に注目すると、加算値ＳＵＭｍ＋２は８８３となっている。これに、ＰＡＲＭ１（＝４２３）を足せばＳＵＭ１は１３０６となり、ここからＰＡＲＭ２（＝１０００）を引いてＳＵＭ２を求めると、３０６となる。ＳＵＭ２≧０なので桁上がりが生じている。そこで、ライン出力として、ＳＵＭ２＝３０６を次のＳＵＭｍ＋３とする。
【００４８】
以上のようにして、副走査方向の縮小処理を行うことができる。
副走査方向の縮小処理似より、間引きした画像データの情報が使えなくなるので、画質劣化のおそれがある。そこで、縮小時の画質劣化を抑制するための補正処理として、平均化補正処理を行えるようにする。この補正処理には、ラインメモリ５８の中の、拡大時の補正処理に用いたラインメモリＡ，Ｂ，Ｃと同一のフォーマットのラインメモリを使用することができる。
【００４９】
出力しようとするラインをＩＤｍとし、間引かれるラインをＩＤｍ−ｋ，ＩＤｍ−ｋ＋１，ＩＤｍ−ｋ＋２，．．．，ＩＤｍ−１とする。ｋは、間引かれるライン数を表す。
補正の結果出力するラインをＲＤｍと表す。補正式は、次のように表される。
ＲＤｍ＝（ＩＤｍ−ｋ＋ＩＤｍ−ｋ＋１＋．．．＋ＩＤｍ−１＋ＩＤｍ）／（ｋ＋１）
例えば間引かれるラインが２（ｋ＝２）の場合、補正式は、
ＲＤｍ＝（ＩＤｍ−２＋ＩＤｍ−１＋ＩＤｍ）／３
となる。
【００５０】
図６は、副走査方向の縮小処理の具体例を示した図解図である。入力される画像データをＩＤｍ，ＩＤｍ＋１，．．．で表し、縮小後出力される画像データをＲＤｎ，ＲＤｎ＋１，．．．で表している。図６では、ＩＤｍ＋２の時点で、ＲＤｎが出力され、ＩＤｍ＋４の時点で、ＲＤ２が出力される。そして、ＲＤｎは、ＲＤｎ出力以前の画像データＩＤｍ，ＩＤｍ＋１及びＩＤｍ＋２を用いて補正されたデータであり、ＲＤｎ＋１は、ＲＤｎの出力後ＲＤｎ＋１出力以前の画像データＩＤｍ＋３及びＩＤｍ＋４を用いて補正されたデータであることが示されている。
【００５１】
いままで説明してきた、副走査方向の拡大処理、縮小処理をまとめて図解すると、図７、図８のようになる。いずれの図も、２００％の拡大を行い、その後８５％の縮小を行うので、あわせて、１７０％の画像が得られる。左のブロックが、原稿画像データを表し、中央のブロックが拡大された画像データを表し、右のブロックが縮小後の画像データを表している。白、黒、網掛けは、それぞれ階調を大雑把に示したものである。
【００５２】
図７は、拡大処理に用いるラインメモリが２本ある場合を示している。この場合、拡大時に読み出すことができるラインメモリが１本になるため、補間処理はできない。そのため、拡大処理では、単に同一内容の画像データを２本ずつ出力することになる。縮小処理時に、前述した間引かれた画像データの情報を取り込む補正処理を行っている。
図８は、拡大処理に用いるラインメモリが３本ある場合を示している。この場合、拡大時に読み出すことができるラインメモリが２本になるため、前述した、補間される画像データを滑らかにつなぐ補間処理ができる。縮小処理時には、前述した間引かれた画像データの情報を取り込む補正処理を行う。従って、拡大時と縮小時に補正処理ができるので、得られた画像は、副走査方向に滑らかにつながった良好な画質の画像となる。
【００５３】
なお、以上の副走査方向の拡大・縮小処理にあわせて、主走査方向にも拡大・縮小処理を行うが、その方法は公知であり、詳細な説明は省略する。
なお、この発明は、以上の実施形態の内容に限定されるものではなく、発明の範囲内において種々の変更が可能である。
例えば、画像形成部の構成は、１つの感光体７１に対して４色分の現像装置７３Ｃ，７３Ｍ，７３Ｙ，７３ＢＫが配置された構成に限らず、たとえば、４つの感光体と、それぞれの感光体表面に各色トナー像を形成するための４つの現像装置とを含み、直線搬送路に沿って搬送される用紙に対して、各感光体で順次トナー像を形成していく、いわゆるタンデム型の構成であってもよい。
【００５４】
コンタクトガラス３上に１枚ずつ原稿をセットすることができるだけでなく、原稿読取部２に向けて１枚ずつ原稿を自動的に供給して読み取らせる（いわゆる流し読み）ための自動原稿供給装置が備えられていてもよい。
原稿読取部２における原稿の読み取りは、光源２１および反射鏡２３１〜２３３の移動のみによって行われる構成に限らず、たとえば、ＣＣＤイメージセンサ２２も移動するような構成であってもよい。
【００５５】
このデジタルカラー複写機は、スキャナ機能を備えていてもよい。すなわち、メモリ５１に記憶されたデジタル画像データは、出力画像処理部５５における出力画像処理後にレーザ走査ユニット６へと送られる構成に限らず、たとえばメモリ制御部５６を介して、当該デジタルカラー複写機１に接続された外部機器（たとえば、パーソナルコンピュータなど）へと送られるようになっていてもよい。
【００５６】
【発明の効果】
以上のように本発明によれば、原稿画像データ全体を記憶して拡大するのではなく、同時に２本又は３本のライン分の画像データを用いて、拡大処理を行うので、従来よりも少ないメモリ容量で原稿画像を良好に変倍できる画像形成装置を実現することができる。
【図面の簡単な説明】
【図１】この発明の一実施形態に係るデジタルカラー複写機の内部構成を示す概略断面図である。
【図２】画像処理の流れを説明するためのブロック図である。
【図３】ラインメモリが２本の場合の、副走査方向の拡大処理、縮小処理を説明するための処理の流れ図である。
【図４】ラインメモリが３本の場合の、副走査方向の拡大処理、縮小処理を説明するための処理の流れ図である。
【図５】拡大処理の倍率が３倍のときの補間の様子を表す図解図である。
【図６】副走査方向の縮小処理の具体例を示し図解図である。
【図７】拡大処理に用いるラインメモリが２本ある場合の、副走査方向の拡大処理、縮小処理をまとめて図解した図である。
【図８】拡大処理に用いるラインメモリが３本ある場合の、副走査方向の拡大処理、縮小処理をまとめて図解した図である。
【符号の説明】
１ デジタルカラー複写機
２ 原稿読取部
５ 制御部
１８ 操作部
２２Ｒ，２２Ｇ，２２Ｂ 読取ライン
２６ ステッピングモータ
５２ ライン補正部
５３ 入力画像処理部
５８ ラインメモリ[0001]
TECHNICAL FIELD OF THE INVENTION
The present invention relates to an image forming apparatus that forms an image on a sheet based on image data of a document read by a document reading unit.
[0002]
[Prior art]
An ordinary digital copying machine has a light source for illuminating a document, a CCD image sensor for detecting reflected light from the document and converting it into an electric signal, and a light reflected from the document on a detection surface of the CCD image sensor. The main scanning of the original is achieved by, for example, electrical scanning in a CCD image sensor, and the sub-scanning of the original is achieved by moving the light source and the reflecting mirror. ing. The movement of the light source and the reflecting mirror is performed, for example, by rotating a stepping motor.
[0003]
In addition, there is a method in which the document reading speed is varied to perform enlargement / reduction (see Patent Document 1). Also in this case, a stepping motor is used to change the document reading speed.
Also, instead of changing the moving speed of the light source or the reflecting mirror according to the set magnification, a method of temporarily storing image data in a memory and scaling the image data to the set magnification when forming an image is generally adopted. Have been.
[0004]
[Patent Document 1]
JP-A-8-251395
[Problems to be solved by the invention]
However, the method of changing the rotation speed of the stepping motor has a problem in that the mechanical configuration is complicated, and a high-precision stepping motor capable of changing the rotation speed in multiple stages is expensive, which increases the production cost. Was.
Further, the method of storing image data in a memory has a problem that a large amount of memory capacity is required.
[0006]
SUMMARY OF THE INVENTION It is an object of the present invention to provide an image forming apparatus capable of satisfactorily scaling an original image with a small memory capacity.
[0007]
[Means for Solving the Problems]
According to another aspect of the present invention, there is provided an image forming apparatus, comprising: a magnification setting unit capable of setting a magnification at the time of image formation with respect to a document size; And a capacity for two or three lines capable of storing and reading image data along the main scanning direction for use in the magnification processing in the sub-scanning direction. A line memory, and reduction processing means for performing reduction processing in the sub-scanning direction on the original image data enlarged by the enlargement processing means at a magnification at which a formed image having a magnification set by the magnification setting means is obtained. The enlargement processing means performs enlargement processing using the image data stored in the line memory at the magnification set by the magnification setting means or a magnification larger than the magnification. That.
[0008]
For example, the image forming apparatus has a line sensor extending in the main scanning direction, and reads an original by changing the positional relationship between the line sensor and the original in the sub-scanning direction while repeating electrical main scanning. Things.
According to this configuration, two or three lines of image data are simultaneously stored with respect to the document image data, and the enlargement processing is first performed in the sub-scanning direction at a set magnification or a magnification larger than that. I do. Then, the enlarged document image data is reduced in the sub-scanning direction at such a magnification that a formed image with the set magnification can be obtained. Therefore, instead of storing and enlarging the entire original image data, the enlarging process is performed using image data for two or three lines at the same time, so that a smaller memory capacity than in the related art is required. If two line memories are used, one line can be used for writing image data and the other line can be used for reading image data. If used, one can be used for writing image data and the other two can be used for reading image data.
[0009]
The enlargement processing means performs enlargement processing using the line memory at the magnification set by the magnification setting means or an integer magnification larger than the magnification (claim 2). The “integer magnification” is, for example, a magnification of 200% or 300%. With this configuration, the enlargement process can be performed only by reading the same image data for one line a plurality of times, so that the process is simplified.
The number of lines that can be stored in the line memory at the same time is three, and the enlargement processing means performs interpolation processing of the line to be enlarged when performing the enlargement processing. By using two image data which can be used for reading at the same time, interpolation processing can be performed simultaneously with enlargement.
[0010]
The reduction processing means may reduce the image data of the document in the sub-scanning direction by thinning out image data for a predetermined line from the enlarged document image data. According to this configuration, the image data of the document can be easily reduced without performing a complicated operation only by thinning out the line image data of a plurality of lines subjected to the enlargement processing. Therefore, an error due to the calculation hardly occurs, and the original image can be scaled better.
[0011]
The image processing apparatus further includes a second line memory capable of storing image data corresponding to the thinned lines, wherein the reduction processing unit performs reduction by using the thinned image data when performing the reduction processing. The image data may be subjected to a correction process (claim 5). If the image to be decimated is stored in the second line memory and the image data to be reduced is corrected, a final image with better image quality can be obtained.
[0012]
BEST MODE FOR CARRYING OUT THE INVENTION
Hereinafter, embodiments of the present invention will be specifically described with reference to the drawings.
FIG. 1 is a schematic sectional view showing the internal configuration of a digital color copying machine 1 according to one embodiment of the present invention.
The digital color copying machine 1 uses, for example, single-color toners of cyan (C), magenta (M), yellow (Y), and black (B) based on color image data of a document read by the document reading unit 2. By superimposing on paper, a full-color image can be formed by a so-called electrophotographic method.
[0013]
A document to be read by the document reading unit 2 is set on a contact glass 3 arranged on the upper surface of the digital color copying machine 1 so that the image faces downward. A cover 4 that can be opened and closed is disposed above the contact glass 3 so that the cover 4 can be opened and closed so that documents can be set one by one on the contact glass 3. I have.
The original reading unit 2 includes a light source 21 for illuminating the original set on the contact glass 3 from below, a CCD image sensor 22 for detecting reflected light from the original and converting the reflected light into an electric signal, First, second and third reflecting mirrors 231 to 233 for guiding the reflected light to the detection surface of the CCD image sensor 22, and a lens for forming an optical image of the document on the detection surface of the CCD image sensor 22 24. Main scanning of the document is achieved by electrical scanning in the CCD image sensor 22.
[0014]
The light source 21 and the first reflecting mirror 231 are held by a first holding member 251, and the second and third reflecting mirrors 232 and 233 are held by a second holding member 252. The two holding members 251 and 252 are movable along the lower surface of the contact glass 3 in the left-right direction (sub-scanning direction) in FIG. The first and second holding members 251 and 252 are driven in the same direction by the rotation of the stepping motor 26 (see FIG. 2) so that the speed of the second holding member 252 becomes half the speed of the first holding member 251. To move to. The sub-scanning of the original set on the contact glass 3 is achieved by the movement of the light source 21 and the reflecting mirrors 231 to 233 accompanying the movement of the first and second holding members 251, 252.
[0015]
On the detection surface of the CCD image sensor 22, reading lines 22R, 22G, and 22B (see FIG. 2) for detecting respective colors of red (R), green (G), and blue (B) are respectively provided along the main scanning direction. And extend at a predetermined interval (for example, a distance of four lines) from each other.
The CCD image sensor 22 outputs an analog electric signal based on each color component (RGB) detected on each of the reading lines 22R to 22B, and the output analog electric signal is used as a control signal provided in the digital color copying machine 1. It is input to the unit 5 (see FIG. 2). The control unit 5 generates cyan (C), magenta (M), yellow (Y), and black (BK) digital image data based on the input analog electric signal, and outputs the digital image data. To the laser scanning unit 6 (LSU). The laser scanning unit 6 separately irradiates the irradiation light based on the given digital image data toward the surface of the substantially cylindrical photoconductor 71 provided in the image forming unit 7.
[0016]
The image forming section 7 contains a main charger 72 for charging the surface of the photoreceptor 71 and toners of cyan, magenta, yellow and black in addition to the photoreceptor 71. The image forming apparatus includes developing devices 73C, 73M, 73Y, and 73BK for forming toner images of respective colors, and a cleaning device 73 for removing toner remaining on the surface of the photoconductor 71 after the transfer of the toner image.
The surface of the substantially cylindrical transfer drum 75 contacts the surface of the photoconductor 71. The transfer drum 75 is formed such that its outer peripheral length is longer than the length of a sheet to be used. A transfer device 76 is provided in the transfer drum 75 at a position facing the photoconductor 71. In the digital color copying machine 1, the paper is wound around the transfer drum 75 rotating clockwise in FIG. 1, and passes through the transfer position (between the photoconductor 71 and the transfer drum 75) a plurality of times (for example, four times). Thus, the color toner images sequentially formed on the surface of the photoconductor 71 can be transferred one by one to the paper by the operation of the transfer device 76.
[0017]
More specifically, during image formation, first, the surface of the photoconductor 71 rotating counterclockwise in FIG. 1 is uniformly charged by the discharge of the main charger 72. Irradiation light based on digital image data of a document read by the document reading unit 2 is radiated from the laser scanning unit 6 onto the charged surface of the photoconductor 71, so that the surface of the photoconductor 71 is selectively provided. Upon exposure, an electrostatic latent image corresponding to any one of cyan, magenta, yellow, and black is formed on the surface of the photoconductor 71. Then, on the surface of the photoreceptor 71 on which the electrostatic latent image is formed, toner is adhered by a developing device corresponding to the one-color toner, and a one-color toner image to be transferred to paper is formed.
[0018]
The paper to be used can be set in, for example, a paper cassette 8 or a manual tray 9. In the digital color copying machine 1, the paper is guided from each of the paper cassette 8 and the manual tray 9 to the image forming unit 7. A branched paper transport path 10 is arranged so as to be able to perform the operation.
The paper cassette 8 can store a plurality of papers, for example, and can feed out the stored papers one by one to the paper transport path 10 by a pickup roller 81. On the other hand, the sheets set one by one on the manual feed tray 9 are sent out to a sheet transport path 10 by a sheet feeding roller 91.
[0019]
The sheet sent from the sheet cassette 8 or the manual feed tray 9 to the image forming unit 7 through the sheet conveyance path 10 is temporarily stopped when the leading end thereof reaches the registration roller 11. Then, the rotation of the registration roller 11 is adjusted such that the timing at which the one-color toner image formed on the surface of the photoreceptor 71 comes to a position facing the transfer drum 75 and the timing at which the paper reaches the transfer position coincide. Will be resumed. At this time, static electricity is applied to the surface of the transfer drum 75 by the discharge of the discharge device 12 arranged opposite to the surface of the transfer drum 75, and the paper sent from the registration roller 11 is transferred to the transfer drum 75 by the electrostatic force. It can be wound around. The sheet sent from the registration roller 11 is wound around the transfer roller 75 and moves to the transfer position, and the one-color toner image formed on the surface of the photoconductor 71 is transferred to the sheet.
[0020]
After the toner remaining on the surface of the photoreceptor 71 after the transfer of the toner image is collected by the cleaning device 73, the photoreceptor 71 is uniformly charged again by the main charger 72. An electrostatic latent image corresponding to a toner image to be formed next (other than the one-color toner image) is formed on the charged surface of the photoconductor 71 by irradiation light from the laser scanning unit 6. Toner is attached to the surface of the photoreceptor 71 on which the electrostatic latent image is formed by a developing device corresponding to the color to form a one-color toner image to be transferred to paper. Then, the toner image formed on the surface of the photoconductor 71 is wrapped around the transfer drum 75 and is again transferred to the sheet that has reached the transfer position.
[0021]
In this way, the paper is wound around the transfer drum 75 and passes through the transfer position four times, and each time the paper passes through the transfer position, a different color toner image is sequentially transferred to the paper, whereby cyan, magenta, yellow And black toner images of four colors are superimposedly transferred onto a sheet.
When the four color toner images are transferred to the sheet, the discharge device 12 discharges the static electricity on the surface of the transfer drum 75, and the sheet is separated from the transfer drum 75. Then, the toner adhered to the surface of the transfer drum 75 after the paper is separated is collected by the cleaning brush device 77.
[0022]
The toner image-transferred sheet separated from the transfer drum 75 is transported to the fixing device 14 on the surface of the rotating endless transport belt 13. Then, the sheet subjected to a predetermined fixing process by the fixing device 14 is discharged to a sheet discharge unit 17 disposed outside the apparatus via a conveying roller 15 and a discharge roller 16.
FIG. 2 is a block diagram for explaining the flow of image processing.
The digital color copying machine 1 is provided with a control unit 5 composed of, for example, a microcomputer. The control unit 5 includes, for example, a memory 51 that can store digital image data, a line memory 58 that stores image data for each line along the main scanning direction, a line correction unit 52, an input image processing unit 53, and a compression process. It functionally includes a unit 54, an output image processing unit 55, a memory control unit 56, and the like.
[0023]
The control unit 5 receives a signal from an operation unit 18 disposed on the upper surface of the digital color copying machine 1, for example. By operating the operation unit 18, the operator can start an image forming operation in the digital color copying machine 1 or set a magnification (enlargement / reduction rate) of digital image data with respect to a document size. it can.
Light emitted from the light source 21 is reflected on the original, and the reflected light is reflected by the reflecting mirrors 231 to 233 and is incident on the detection surface of the CCD image sensor 22. Then, an analog electric signal based on each color component (RGB) detected on each reading line (red reading line 22R, green reading line 22G, blue reading line 22B) of the CCD image sensor 22 is transmitted from the CCD image sensor 22 to the control unit 5 by the control unit 5. Is entered.
[0024]
When an analog electric signal is input from the CCD image sensor 22, the control unit 5 performs various processes in the processing units 52 to 56 using, for example, program software stored in advance.
Specifically, first, the line correction unit 52 performs a line correction for correcting a shift of the input analog electric signal of each color. In other words, each analog electric signal has a shift corresponding to the distance between the read lines 22R, 22G, and 22B (the distance for four lines), and the line correction unit 52 stores the lines stored in the memory 51. The correction data is read via the memory control unit 56, and a process for eliminating the deviation of each analog electric signal is performed. For example, a green (G) analog electric signal is delayed by 4 lines with respect to a red (R) analog electric signal, and a blue (B) analog electric signal is delayed with respect to a green (G) analog electric signal. If the signal is delayed by four lines (delayed by eight lines with respect to the red (R) analog electric signal), the line correction unit 52 converts the green (G) analog electric signal by four lines. By delaying the red (R) analog electric signal by eight lines, it is possible to eliminate the deviation of each analog electric signal.
[0025]
In this embodiment, since the line correction data is stored in the memory 51, the production cost can be reduced as compared with a configuration in which a dedicated buffer memory is separately provided.
Each analog electric signal after the line correction is provided to the input image processing unit 53. The input image processing unit 53 first quantizes each of the red, green and blue analog electric signals into cyan, magenta and yellow digital image data (for example, 256 gradations). For the digital image data generated in this way, for example, the optical system such as the light source 21 has different light distribution characteristics between the center and the end in the main scanning direction (the luminance at both ends in the main scanning direction is reduced). Correction processing for correcting variations in sensitivity of the read lines 22R, 22G, and 22B for each read pixel due to the presence of the read lines 22R, 22G, and 22B, and gamma correction processing for providing a gradation characteristic proportional to the density of the document. In addition, processing for enlarging or reducing digital image data in the sub-scanning direction, processing for enlarging or reducing in the main scanning direction, and the like are performed.
[0026]
The digital image data after the input image processing is subjected to data compression processing by the compression processing unit 54 and then stored in the memory 51 via the memory control unit 56. The compressed digital image data stored in the memory 51 is read out and decompressed by the memory control unit 56 at a predetermined timing, and then output image processing is performed by the output image processing unit 55. It is sent to the scanning unit 6. However, the digital image data after the input image processing may be stored in the memory 51 without being subjected to the compression processing, or may be provided to the output image processing unit 55 without being subjected to the compression processing. After the output image processing, the image data may be sent to the laser scanning unit 6.
[0027]
The output image processing includes, for example, filter processing (so-called edge enhancement processing and smoothing processing) and intermediate value processing (so-called error diffusion processing and dither processing). At the time of output image processing, black generation processing is performed by, for example, extracting only the same component (level) from cyan, magenta, and yellow and replacing it with a black component. Thereby, black (BK) digital image data is added to the digital image data supplied to the laser scanning unit 6.
[0028]
FIGS. 3 and 4 are flowcharts of processing for explaining the enlargement processing and reduction processing in the sub-scanning direction of the input image processing unit 53.
In this processing, the content differs depending on the number of lines that can be stored in the line memory 58 at the same time. Therefore, the case where there are two line memories 58 (FIG. 3) will be described first, and the case where there are three line memories 58 (FIG. 4). Will be described. Note that the line memory 58 is constituted by, for example, an SRAM.
[0029]
Referring to FIG. 3, the image signal provided to input image processing unit 5 is a signal of the same size that has not been enlarged or reduced in the sub-scanning direction (step R1). These are line memories A and B, respectively. The input image processing section 53 stores this image signal in each line memory A, B for each line (steps R2, R3). The storage procedure will be described with reference to Table 1. The input image processing unit 53 performs enlargement processing in the sub-scanning direction at a magnification larger than the magnification set by the operation unit 18. For example, assuming that the magnification set by the operation unit 18 is 100% or more and less than 200%, in this case, the input image processing unit 53 enlarges in the sub-scanning direction by a factor of 2 (200%).
[0030]
[Table 1]

[0031]
“Output processing line” in Table 1 represents a line sequence output in chronological order after the enlargement processing. “Write ()” in each of the line memories A and B indicates an operation of reading image data of a line, and the number in parentheses indicates the number of the line. “Read ()” indicates an operation of reading image data of a line, and the number in parentheses indicates the number of the line. The upward arrow indicates "waiting for processing".
[0032]
Paying attention to the top row of Table 1, the line memory A reads the image data of the first line. In the third column, the image data of the second line is read by the line memory B, and at the same time, the image data of the first line read by the line memory A is read. In the fourth column, the image data of the first line read by the line memory A is read again. By these two readings, the magnification is increased by 200%. In the fifth column, the image data of the third line is read by the line memory A and the image data of the second line read by the line memory B at the same time. In the sixth column, the image data of the second line read by the line memory B is read again.
[0033]
As described above, since reading from one line memory is performed twice, as can be seen from Table 1, double enlargement processing is performed (step R4). Subsequent reduction processing (step R5) will be described later.
Since two line memories are used, only one line memory can be read, and the other line memory must be used for writing. Therefore, in this enlargement processing (step R4), interpolation processing of image data cannot be performed.
[0034]
Next, a case where there are three line memories 58 will be described. These are assumed to be line memories A, B, and C, respectively.
Referring to FIG. 3, the image signal provided to input image processing unit 5 is a signal of the same size that has not been enlarged or reduced in the sub-scanning direction (step S1). The input image processing unit 53 stores this image signal in each of the line memories A, B, and C for each line (steps S2 to S4). The storage procedure will be described with reference to Table 2. It is assumed that the magnification set by the operation unit 18 is 100% or more and less than 200%. In this case, the input image processing unit 53 enlarges the image twice (200%) in the sub-scanning direction.
[0035]
[Table 2]

[0036]
“Write ()” in each of the line memories A, B, and C in Table 2 represents an operation of reading image data of a line, and the number in parentheses represents the number of the line. “Read ()” indicates an operation of reading image data of a line, and the number in parentheses indicates the number of the line.
Paying attention to the top row of Table 2, the image data of the first line is read by the line memory A. Then, in the third column, the image data of the first line is read by the line memory B. In the fifth column, the first line of image data read by the line memory A and the second line of image data read by the line memory B are read, and the third line of image data is read by the line memory C. Read. In the sixth column, the image data of the first line read by the line memory A and the image data of the second line read by the line memory B are read. In the seventh column, the image data of the second line read by the line memory B and the image data of the third line read by the line memory C are read, and the image data of the fourth line is read by the line memory A. In the eighth column, the image data of the second line read by the line memory B and the image data of the third line read by the line memory C are read. Then, an interpolation process described later is performed by using the image data of the two lines read simultaneously.
[0037]
As can be seen from Table 2, reading from one line memory is performed four times using the time for four columns, and at the same time, interpolation processing is performed using two lines to read one line of image data. Is obtained, 4 × (）) = 2, that is, double enlargement processing has been performed (step S5).
In addition, since three line memories are used, two line memories can simultaneously read two lines, and one other line memory can write. Therefore, the interpolation processing can be performed using the image data of two lines read simultaneously.
[0038]
In the interpolation processing, if the magnification of the enlargement processing is twice, as shown in Table 1, two lines of image data (Read (1) and Read (2)) are used to output one line of the output processing line. An eye is created, and a second output processing line is created using the same two lines of image data. Then, one line is shifted, the third line of the output processing line is created, and the fourth line of the output processing line is created using the image data of the next two lines (Read (2) and Read (3)). Hereinafter, an output processing line is similarly created.
[0039]
The output processing line is formed by expressing two lines of the document image data used for the interpolation as “line of interest A” and “line of interest B”, respectively.
“Output processing line” = α “attention line A” + β “attention line B”
(0 ≦ α ≦ 1, 0 ≦ β ≦ 1, α + β = 1)
And take the weighted average as
The weights α and β are determined by setting α = 1 and β = 0 when the “output processing line” is odd-numbered, and α = 1/2 and β = 1 when the “output processing line” is even-numbered. / 2. This makes it possible to insert one equally interpolated line between the two lines read from the document.
[0040]
When the magnification of the enlargement process is three times, although not shown in the table, the first line of the output processing line is created using the image data of two lines (Read (1) and Read (2)). The second and third output processing lines are created using the same two lines of image data. Then, by shifting one line, the fourth, fifth, and sixth output processing lines are created using the image data (Read (2) and Read (3)) for the next two lines. Hereinafter, an output processing line is similarly created. In this case, the weights α and β are determined by setting α = 1 and β = 0 when the “output processing line” is the 3n-th (n is an integer), and α = ２ when the “output processing line” is the (3n + 1) -th. , Β = 1/3, and for the (3n + 2) th, α = 1/3, β = ２.
[0041]
FIG. 5 is an illustrative view showing a state of interpolation when the magnification of the enlargement processing is three times. For example, assuming lines of interest A and B, "output processing lines" (1) and (2) are inserted therebetween. Since the “output processing line” (1) is the (3n + 1) th when counted through,
“Output processing line” (1) = (2/3) “attention line A” + (1/3) “attention line B”
Since the “output processing line” (2) is the (3n + 2) th,
“Output processing line” (2) = (1/3) “line of interest A” + (2/3) “line of interest B”
Is represented by By the way, if the value of “line of interest A” is 20 and the value of “line of interest B” is 140,
"Output processing line" {circle around (1)} = (2/3) 20+ (1/3) 140 = 180/3 = 60
"Output processing line" (2) = (1/3) 20+ (2/3) 140 = 300/3 = 100
It becomes.
[0042]
Even if the magnification of the enlargement processing is increased to four times or five times, the weights α and β are determined so as to divide the difference of the image data of two lines into four equal parts and five equal parts based on the same concept. Can be.
In this way, a smooth output processing line interpolated is obtained while enlarging the original line to an integral multiple.
In the above-described enlargement processing, assuming that the magnification set by the operation unit 18 is 100% or more and less than 200%, the input image processing unit 53 enlarges the image twice (200%) in the sub-scanning direction. Was. However, the enlargement process may be performed in the sub-scanning direction at a magnification larger than the magnification set by the operation unit 18, so that the magnification is not limited to two. For example, the reading speed from the line memory can be uniformly maximized (for example, 8 times), and a desired magnification can be obtained in the next reduction processing.
[0043]
Next, since it is necessary to return the enlarged image to the magnification set by the operation unit 18, reduction processing in the sub-scanning direction is performed (steps R5 and S6). The reduction processing is performed by thinning out the main scanning synchronization signal according to the reduction magnification. The following is a description of mathematical expressions. Set the following variables.
m: Number of operations for each main scanning synchronization signal (initial value is 0)
SUMm: Addition value parameter in the calculation number m. PARM1 is added to this added value, and a line is output when a carry occurs in a PARM binary number. The initial value SUM0 of SUMm may be set to any value within a range of 0 ≦ SUM0 <PARM2, but is set to 0, for example.
[0044]
PARM1: Reduction ratio (unit: per thousand)
PARM2: 1 time (unit is per thousand)
The calculation method is as follows. PARM1 is added to the sum SUMm to obtain SUM1.
SUM1 = SUMm + PARM1
PARM2 is subtracted from SUM1, which is referred to as SUM2.
SUM2 = SUM1-PARM2
When SUM2 <0, since the carry of the PARM binary number has not occurred, SUM1 is used as it is as the sum SUMm + 1 in the next operation (m + 1).
[0045]
SUMm + 1 = SUM1
When SUM2 ≧ 0, since a carry of a PARM binary number has occurred, a line is output, and SUM2 is set as an addition value SUMm + 1 of the next operation (m + 1).
SUMm + 1 = SUM2
Table 3 shows specific numerical examples when the reduction ratio is 42.3% (PARM1 = 423).
[0046]
[Table 3]

[0047]
According to Table 3, the added value SUMm in the calculation number m is 37. By adding PARM1 (= 423) to this, SUM1 becomes 460, and when SARM2 is obtained by subtracting PARM2 (= 1000) therefrom, it becomes -540. Since no carry has occurred, the line is not output, and SUM1 = 460 is directly used as SUMm + 1.
Paying attention to the calculation times m + 2, the added value SUMm + 2 is 883. If PARM1 (= 423) is added to this, SUM1 becomes 1306, and SUM2 is obtained by subtracting PARM2 (= 1000) from this. Since SUM2 ≧ 0, a carry has occurred. Therefore, SUM2 = 306 is set as the next SUMm + 3 as the line output.
[0048]
As described above, the reduction processing in the sub-scanning direction can be performed.
Since the information of the thinned image data cannot be used due to the reduction processing in the sub-scanning direction, the image quality may be deteriorated. Therefore, averaging correction processing can be performed as correction processing for suppressing image quality deterioration at the time of reduction. For this correction processing, a line memory of the same format as the line memories A, B, and C used for the correction processing at the time of enlargement in the line memory 58 can be used.
[0049]
The line to be output is IDm, and the lines to be thinned out are IDm-k, IDm-k + 1, IDm-k + 2,. . . , IDm-1. k represents the number of lines to be thinned.
The line output as a result of the correction is denoted by RDm. The correction formula is expressed as follows.
RDm = (IDm-k + IDm-k + 1 + ... + IDm-1 + IDm) / (k + 1)
For example, if the number of lines to be thinned is 2 (k = 2), the correction formula is
RDm = (IDm-2 + IDm-1 + IDm) / 3
It becomes.
[0050]
FIG. 6 is an illustrative view showing a specific example of the reduction processing in the sub-scanning direction. The input image data is represented by IDm, IDm + 1,. . . , And the image data output after reduction is represented by RDn, RDn + 1,. . . It is represented by In FIG. 6, RDn is output at the time of IDm + 2, and RD2 is output at the time of IDm + 4. RDn is data corrected using the image data IDm, IDm + 1 and IDm + 2 before RDn output, and RDn + 1 is data corrected using image data IDm + 3 and IDm + 4 before RDn + 1 output after RDn output. It is shown that there is.
[0051]
FIG. 7 and FIG. 8 illustrate the enlargement processing and reduction processing in the sub-scanning direction which have been described so far. In each of the figures, the image is enlarged by 200% and then reduced by 85%, so that an image of 170% is obtained in total. The left block represents the original image data, the central block represents the enlarged image data, and the right block represents the reduced image data. The white, black, and shaded areas roughly indicate the gradation.
[0052]
FIG. 7 shows a case where there are two line memories used for the enlargement processing. In this case, interpolation processing cannot be performed because only one line memory can be read at the time of enlargement. Therefore, in the enlargement processing, image data having the same content is simply output two by two. At the time of reduction processing, the above-described correction processing for taking in the information of the thinned image data is performed.
FIG. 8 shows a case where there are three line memories used for the enlargement processing. In this case, since two line memories can be read at the time of enlargement, the above-described interpolation processing for smoothly connecting the image data to be interpolated can be performed. At the time of the reduction processing, the above-described correction processing for capturing the information of the thinned image data is performed. Therefore, since the correction processing can be performed at the time of enlargement and reduction, the obtained image is an image of good quality smoothly connected in the sub-scanning direction.
[0053]
The enlargement / reduction processing is also performed in the main scanning direction in accordance with the above-described enlargement / reduction processing in the sub-scanning direction, but the method is publicly known and detailed description is omitted.
It should be noted that the present invention is not limited to the contents of the above embodiments, and various changes can be made within the scope of the invention.
For example, the configuration of the image forming unit is not limited to the configuration in which the developing devices 73C, 73M, 73Y, and 73BK for four colors are arranged for one photoconductor 71. For example, four photoconductors and respective photoconductors are provided. A so-called tandem type in which four photoconductors are sequentially formed on a sheet conveyed along a linear conveyance path, including four developing devices for forming respective color toner images on the body surface. It may be a configuration.
[0054]
An automatic document feeder for not only setting originals one by one on the contact glass 3 but also automatically feeding and reading originals one by one toward the original reading unit 2 (so-called flow reading) is provided. It may be provided.
The reading of the document by the document reading unit 2 is not limited to the configuration in which the light source 21 and the reflecting mirrors 231 to 233 are moved alone, and for example, the CCD image sensor 22 may also be moved.
[0055]
This digital color copying machine may have a scanner function. That is, the digital image data stored in the memory 51 is not limited to the configuration in which the digital image data is sent to the laser scanning unit 6 after the output image processing in the output image processing unit 55. 1 may be sent to an external device (for example, a personal computer or the like) connected to 1.
[0056]
【The invention's effect】
As described above, according to the present invention, enlargement processing is performed using image data for two or three lines at the same time, instead of storing and enlarging the entire original image data. An image forming apparatus that can satisfactorily scale an original image with a memory capacity can be realized.
[Brief description of the drawings]
FIG. 1 is a schematic sectional view showing an internal configuration of a digital color copying machine according to an embodiment of the present invention.
FIG. 2 is a block diagram illustrating a flow of image processing.
FIG. 3 is a flowchart of a process for explaining an enlargement process and a reduction process in the sub-scanning direction when there are two line memories.
FIG. 4 is a flowchart of a process for explaining an enlargement process and a reduction process in the sub-scanning direction when there are three line memories.
FIG. 5 is an illustrative view showing a state of interpolation when a magnification of an enlargement process is three times;
FIG. 6 is an illustrative view showing a specific example of a reduction process in the sub-scanning direction;
FIG. 7 is a diagram collectively illustrating enlargement processing and reduction processing in the sub-scanning direction when there are two line memories used for enlargement processing.
FIG. 8 is a diagram collectively illustrating enlargement processing and reduction processing in the sub-scanning direction when there are three line memories used for enlargement processing.
[Explanation of symbols]
REFERENCE SIGNS LIST 1 digital color copier 2 document reading unit 5 control unit 18 operation unit 22R, 22G, 22B reading line 26 stepping motor 52 line correction unit 53 input image processing unit 58 line memory

Claims (5)

An image forming apparatus capable of forming an image on a sheet based on image data read by main scanning and sub scanning of a document in a document reading unit,
Magnification setting means for setting a magnification at the time of image formation with respect to the document size;
Enlargement processing means for performing enlargement processing on the document image data in the sub-scanning direction;
A line memory having a capacity of two or three lines capable of storing and reading image data along the main scanning direction for use in the enlargement processing in the sub-scanning direction;
Reduction processing means for performing reduction processing in the sub-scanning direction on the original image data enlarged by the enlargement processing means at a magnification at which a formed image having a magnification set by the magnification setting means is obtained;
The image processing apparatus according to claim 1, wherein the enlargement processing unit performs the enlargement processing using the image data stored in the line memory at the magnification set by the magnification setting unit or a magnification larger than the magnification. Forming equipment. 2. The image according to claim 1, wherein the enlargement processing means performs the enlargement processing using the line memory at a magnification set by the magnification setting means or an integer magnification larger than the magnification. Forming equipment. The number of lines that the line memory can store at the same time is three,
The image forming apparatus according to claim 1, wherein the enlargement processing unit performs an interpolation process on a line to be enlarged when performing the enlargement process. 2. An image according to claim 1, wherein said reduction processing means reduces the image data of the document in the sub-scanning direction by thinning out image data for a predetermined line from the enlarged document image data. Forming equipment. A second line memory capable of storing image data of the thinned lines,
5. The image forming apparatus according to claim 4, wherein said reduction processing means performs a correction process of the reduced image data using the thinned image data when performing the reduction process.

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