TW201804456A - 用於渲染彩色影像的方法 - Google Patents

用於渲染彩色影像的方法 Download PDF

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TW201804456A
TW201804456A TW106116878A TW106116878A TW201804456A TW 201804456 A TW201804456 A TW 201804456A TW 106116878 A TW106116878 A TW 106116878A TW 106116878 A TW106116878 A TW 106116878A TW 201804456 A TW201804456 A TW 201804456A
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肯尼士Ｒ 柯羅斯
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電子墨水股份有限公司
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/40—Picture signal circuits
    • H04N1/405—Halftoning, i.e. converting the picture signal of a continuous-tone original into a corresponding signal showing only two levels
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09G—ARRANGEMENTS OR CIRCUITS FOR CONTROL OF INDICATING DEVICES USING STATIC MEANS TO PRESENT VARIABLE INFORMATION
    • G09G3/00—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes
    • G09G3/20—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes for presentation of an assembly of a number of characters, e.g. a page, by composing the assembly by combination of individual elements arranged in a matrix no fixed position being assigned to or needed to be assigned to the individual characters or partial characters
    • G09G3/2007—Display of intermediate tones
    • G09G3/2044—Display of intermediate tones using dithering
    • G09G3/2051—Display of intermediate tones using dithering with use of a spatial dither pattern
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09G—ARRANGEMENTS OR CIRCUITS FOR CONTROL OF INDICATING DEVICES USING STATIC MEANS TO PRESENT VARIABLE INFORMATION
    • G09G3/00—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes
    • G09G3/20—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes for presentation of an assembly of a number of characters, e.g. a page, by composing the assembly by combination of individual elements arranged in a matrix no fixed position being assigned to or needed to be assigned to the individual characters or partial characters
    • G09G3/2007—Display of intermediate tones
    • G09G3/2059—Display of intermediate tones using error diffusion
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/46—Colour picture communication systems
    • H04N1/52—Circuits or arrangements for halftone screening
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
    • H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
    • H04N1/46—Colour picture communication systems
    • H04N1/56—Processing of colour picture signals
    • H04N1/60—Colour correction or control
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09G—ARRANGEMENTS OR CIRCUITS FOR CONTROL OF INDICATING DEVICES USING STATIC MEANS TO PRESENT VARIABLE INFORMATION
    • G09G2340/00—Aspects of display data processing
    • G09G2340/06—Colour space transformation
    • G—PHYSICS
    • G09—EDUCATION; CRYPTOGRAPHY; DISPLAY; ADVERTISING; SEALS
    • G09G—ARRANGEMENTS OR CIRCUITS FOR CONTROL OF INDICATING DEVICES USING STATIC MEANS TO PRESENT VARIABLE INFORMATION
    • G09G3/00—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes
    • G09G3/20—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes for presentation of an assembly of a number of characters, e.g. a page, by composing the assembly by combination of individual elements arranged in a matrix no fixed position being assigned to or needed to be assigned to the individual characters or partial characters
    • G09G3/34—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes for presentation of an assembly of a number of characters, e.g. a page, by composing the assembly by combination of individual elements arranged in a matrix no fixed position being assigned to or needed to be assigned to the individual characters or partial characters by control of light from an independent source
    • G09G3/3433—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes for presentation of an assembly of a number of characters, e.g. a page, by composing the assembly by combination of individual elements arranged in a matrix no fixed position being assigned to or needed to be assigned to the individual characters or partial characters by control of light from an independent source using light modulating elements actuated by an electric field and being other than liquid crystal devices and electrochromic devices
    • G09G3/344—Control arrangements or circuits, of interest only in connection with visual indicators other than cathode-ray tubes for presentation of an assembly of a number of characters, e.g. a page, by composing the assembly by combination of individual elements arranged in a matrix no fixed position being assigned to or needed to be assigned to the individual characters or partial characters by control of light from an independent source using light modulating elements actuated by an electric field and being other than liquid crystal devices and electrochromic devices based on particles moving in a fluid or in a gas, e.g. electrophoretic devices

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Abstract

藉由下列步驟在具有有限數目的原色之顯示器上渲染影像：結合(104)表示待渲染像素之顏色的輸入資料與誤差資料，以形成經修改輸入資料；在色空間中判定包含經修改輸入資料之單形體(208-通常是四面體)及與單形體相關聯之原色；根據與單形體相關聯之原色將經修改影像資料轉換(210)成重心坐標且設定(212)輸出資料為具有最大重心坐標之原色；計算(214)像素之經修改輸入資料與輸出資料間的差異，因而產生誤差資料；應用(106)此誤差資料至至少一後面待渲染像素；以及應用輸出資料至顯示器及因而在顯示器上渲染影像。亦提供用以實施此程序之設備及電腦儲存媒體。

Description

用於渲染彩色影像的方法
本申請案係有關於美國專利公開第2014/0340430號；美國專利公開第2016/0091770號；以及美國專利第9,383,623及9,170,468號。下面將論述其它相關申請案及專利。
本發明係有關於一種用於渲染彩色影像之方法。更具體地，本發明係有關於一種用於在一組有限原色可用的情況下使彩色圖像進行半色調(half-toning)處理的方法，以及此有限原色組可能不具有良好結構。本發明之方法特別但不是專門意欲用於彩色電泳顯示器。
半色調技術在印刷行業中已經使用了數十年，其藉由以黑色墨水覆蓋白紙之每個像素的不同部分來表示灰色色調。類似的半色調方案可使用於CMY或CMYK彩色印刷系統，且色頻可彼此獨立地變化。
然而，有許多的彩色系統，它們的色頻無法彼此獨立地變化，因為每一個像素可顯示一組有限原色中之任一者(這樣的系統可以在下文中被稱為「有限調色顯示器(limited palette displays)」或「LPD’s」)；ECD 專利彩色顯示器屬於這種類型。為了建立其它顏色，必須對原色在空間上進行抖動處理，以產生正確色感。已知對於任何期望顏色藉由只使用在包含此期望顏色之四面體的頂點處之原色來進行這樣的空間抖動；參見，例如：Arad, N., Shaked, D., Baharav, Z., & Lin, Q. (1999). Barycentric Screening and Ostromoukhov, Victor；以及Roger D. Hersch. "Multi-color and artistic dithering." Proceedings of the 26th annual conferen ce on Computer graphics and interactive techniques. ACM Press/Addison-Wesley Publishing Co., 1999。
這兩件文獻藉由門限陣列基篩選方法(threshold-array based screening method)來進行抖動，此方法是一種被發現無法在ECD專利顯示器中給出良好結果之簡單抖動方法。
像誤差擴散演算法(在此演算法中，藉由以不同於一個像素理論上所需之顏色的特定顏色列印那個像素所引進的「誤差」分佈在相鄰像素間，以致於在整體上產生正確色感)之標準抖動演算法可以使用於有限調色顯示器。然而，就原色在適當色空間中之間的距離實質上是固定的意義而言，這樣的標準演算法通常意欲使用於具有「良好結構」之有限調色板。有相當多關於設計具有良好誤差擴散表現之最佳調色板的問題之文獻：參見，例如： Kolpatzik, Bernd W., and Charles A. Bouman. "Optimized Universal Color Palette Design for Error Diffusion." Journal of Electronic Imaging 4.2 (1995)：131-143。
然而，在ECD及類似有限調色顯示器中，有限調色板係由能被系統產生之顏色來定義，有限調色板可能不具有良好結構，亦即，在色空間中之各種原色間的距離可能彼此會有很大的不同。
所附圖式之第1圖係習知技藝調色板基誤差擴散法之示意流程圖，其大體上以100來表示。在輸入端102處，將顏色值xi,j饋送至處理器104，其中它們被添加至誤差濾波器106(將描述於下)之輸出，以產生經修改輸入ui,j。將經修改輸入ui,j饋送至量化器108，量化器108亦接收輸出裝置之調色板{Pk}的細節。量化器108判定所考量之像素的適當顏色，其藉由下列式子來算出：
Figure TW201804456AD00001
且將適當顏色饋送至裝置控制器(或儲存顏色值，以供稍後傳輸至裝置控制器)。將經修改輸入ui,j與輸出yi,j饋送至處理器110，處理器110計算誤差值ei,j，其中：e i,j =u i,j -y i,j
然後，將誤差值ei,j饋送至誤差濾波器106，誤差濾波器106用以將誤差值分配在一個以上被選像素上。例如，如果在每一列之從左至右及影像之從上至下的像素上 實施誤差擴散，則誤差濾波器106可以將誤差分配在被處理之列中的下一個像素及下一列中被處理之像素的三個最近相鄰像素上。或者，誤差濾波器106可以將誤差分配在被處理之列中的接下來兩個像素及接下來兩列中被處理之像素的最近相鄰像素上。將理解到，誤差濾波器不需要將相同比例的誤差應用至被分配誤差之每一像素；例如，當誤差濾波器106將誤差分配在被處理之列中的下一個像素及接下來兩列中被處理之像素的三個最近相鄰像素上時，將更多的誤差分配至被處理之列中的下一個像素及緊接在被處理之像素下面的像素上以及將較少的誤差分配在被處理之像素的兩個對角相鄰像素上可能是適當的。
不幸地，已發現到，如果試圖使用像第1圖所示之傳統誤差擴散法於ECD及類似有限調色顯示器，則產生可能將結果影像渲染成不能使用之嚴重偽影。例如，在一種類型的偽影(以下，稱為「瞬態」偽影)中，當從一個輸入顏色進入下一個非常不同的顏色時，空間瞬變可能會很長，以致於即使跨越所要渲染之對象的大小，輸出決對不會達到正確的平均值。在另一類型的偽影(以下，稱為「模式跳躍(pattern jumping)」偽影)中，對於一個固定顏色輸入影像，輸出在影像中之一個看似隨機位置處的兩組不同原色間跳躍。雖然兩組原色理想上應該產生接近所需要之顏色的輸出，但是結果輸出係不穩定的，因為系統的變化會促使這些在兩組間作切換且這樣跳躍的結構變化(texture change)亦是顯著且令人不 愉悅的。
本發明尋求提供一種在不產生會容易影響標準誤差擴散法之瞬態及模式跳躍偽影下可用於不具有良好結構且可能是大的調色板之渲染彩色影像的方法。
在一態樣中，本發明提供一種在顯示器上渲染影像之方法，該方法包括：接收表示一待渲染像素之顏色的輸入資料；結合該輸入資料與由先前被渲染之至少一像素所產生的誤差資料，以形成經修改輸入資料；在一色空間中判定包含該經修改輸入資料之單形體(simplex)及與該單形體相關聯之顯示原色；根據該單形體轉換該經修改影像資料成重心坐標且設定輸出資料為具有最大重心坐標之原色；計算該像素之該經修改輸入資料與該輸出資料間的差異及藉以產生該像素之誤差資料；應用因此產生的誤差資料至至少一後面待渲染像素；以及提供複數個像素之輸出資料至該顯示器及藉以在該顯示器上渲染影像。
在此過程之一個形式中，測試該經修改輸入資料，以判定它是否是在該顯示器之色域內，以及如果該經修改輸入資料係在此色域外，則藉由將該經修改輸入資料投影至該色域來進一步修改該經修改輸入資料。此投影可以朝該色域之中性軸沿著固定亮度及色相之線 條來進行。或者，該投影可以朝該像素之輸入資料所表示的顏色來進行，直到達到該色域邊界為止。通常，所使用的色空間將是三維的，以致於該單形體會是四面體。該誤差資料可以且通常將分佈在超過一個像素上。例如，如果使用從上到下且從左到右的像素處理順序來實施本發明之方法，則該誤差資料通常至少分佈在被渲染像素之右側的像素及下面的像素上。或者，該誤差資料可以分佈在被渲染像素之右側的像素及其下面且與其相鄰的三個像素上。特別地，在後者的情況下，沒有必要將同等比例之誤差資料分佈在其所分佈之所有像素上；例如，當誤差分佈在下一列之像素右側的像素及與其相鄰之三個像素上時，有利的是，相較於僅共用一個頂點的兩個像素，將更多的誤差資料分配給與被渲染像素共用一個邊緣的兩個像素。
本發明提供一種設備，該設備包括一顯示裝置，其具有複數個像素，該等像素之每一者係配置成顯示複數個原色中之任一者；以及一計算裝置，其能實施本發明之方法且提供其輸出資料至該顯示裝置，藉以促使該顯示裝置顯示影像。
本發明亦提供一種非暫態電腦儲存媒體，該非暫態電腦儲存媒體包括指令，當該等指令被一處理器執行時，該等指令使該處理器實施本發明之方法。
100‧‧‧習知技藝調色板基誤差擴散法
102‧‧‧輸入端
104‧‧‧處理器
106‧‧‧誤差濾波器
108‧‧‧量化器
110‧‧‧處理器
206‧‧‧色域投影機
208‧‧‧單形體
210‧‧‧處理器
212‧‧‧量化器
ei,j‧‧‧誤差值
xi,j‧‧‧顏色值
ui,j‧‧‧經修改輸入
u’i,j‧‧‧投影輸入
yi,j‧‧‧輸出
λ‧‧‧輸出
如上所述，所附圖式之第1圖係一種用於渲染顏色影像之習知技藝方法的流程圖。
第2圖係說明本發明之方法的類似流程圖。
本發明以下列認知作為基礎：上述瞬態及模式跳躍偽影係由量化器(在第1圖中之108)具有欠約束的可用原色列表所造成。在三維色空間中，可藉由只抖動四個原色來渲染裝置色域中的任何顏色，以及本發明係以適當方式限制原色之選擇作為基礎，以確保在量化期間只使用一組受限原色。
可用於抖動模式來表示給定顏色的原色子集不是唯一的；例如，在三維色空間中，可使用在色空間中定義一個包圍給定顏色之體積的任一組四個以上原色於抖動模式中。即使限制原色子集為只有四個，可使用定義一個包圍給定顏色之四面體的任一組四個原色。然而，為了避免模式跳躍偽影，應該以下列這樣的方式將原色子集分配給特定顏色：任何通過色空間之參數路徑導致相對於參數所使用之各種原色的比例之平滑變化。這可以藉由將系統的總色域(所有原色的凸包(convex hull))分解為具有原色作為頂點的四面體及接著將對應於其包圍四面體之頂點的原色子集分配給待渲染之每個顏色來達成。這可以由Delaunay三角形化來實現，Delaunay三角形化原色之凸包分解成一組四面體，四面體的外接球沒有包圍另一個四面體的任何頂點。這是很方便的，但是色域的其它分解也可能是有益的；例如，為了減少半色調顆粒度，可以選擇具有低亮度變化之原色子集。將理解到，取代在三維空間中使用四面體，分 解方法可以藉由使用任何數量的維度用之適當單形體來推廣至任何數量的維度之色空間。
在所附圖式之第2圖中說明本發明之程序的一個較佳實施例，第2圖係大體上相似於第1圖之示意流程圖。如同第1圖所述之習知技藝方法，第2圖所述之方法從輸入端102開始，其中，將顏色值xi,j饋送至處理器104，其中，將它們添加至誤差濾波器106之輸出，以產生經修改輸入ui,j。(同樣地，敘述假設輸入值xi,j使得經修改輸入ui,j是在裝置之色域內。)如果不是這種情況，可能需要對輸入或經修改輸入進行一些初步修改，以確保它們位於適當的色域內。然而，將經修改輸入ui,j饋送至色域投影機206。
色域投影機206被提供用以處理下面這樣的可能性：即使輸入值xi,j係在系統的色域內，經修改輸入ui,j可能不是在系統的色域內，亦即，由誤差濾波器106所引入的誤差校正可能將經修改後輸入ui,j置於系統的色域之外。在這樣的情況下，不可能為經修改輸入ui,j選擇一個原色子集，因為它位於所有定義的四面體之外。雖然可以想到這個問題的其他方法，但是已經發現可給出穩定結果的唯一方法是在進一步處理前將經修改值ui,j投影至系統的色域。投影可以以許多方式來進行；例如，可以沿著固定亮度及色相朝中性軸進行投影。然而，較佳投影方法係朝輸入顏色投影，直到達到色域邊界為止。
投影輸入u’i,j值被饋送到單形體尋找器 (simplex finder)，單形體尋找器將適當的原色子集{Pks}返回至處理器210，處理器210亦接收投影輸入u’i,j值且將它們轉換成由原色子集{Pks}所定義之四面體(或其他單形體)的重心坐標。雖然可能看起來，原色子集{Pks}應該是基於被分配給輸入像素顏色xi,j的那些子集，但這是不行的；原色子集必須基於投影輸入u’i,j值。處理器210的輸出λ被提供至量化器212，量化器212的功能係非常不同於第1圖所示之量化器108的功能。量化器212選擇與最大重心坐標相關聯之原色，而不是執行傳統的誤差擴散。這是相當於具有臨界值(1/3,1/3,1/3)的重心臨界值(見前述文件Arad et al.)，而其係不等於藉由第1圖中之量化器108所進行的最小距離確定。然後，量化器212的輸出yi,j以通常方式被傳送至裝置控制器或被儲存。
輸出yi,j值以及經修改輸入值ui,j或投影輸入值u’i,j(如第2圖之虛線所示)被提供至處理器214，處理器214藉由下列式子來計算誤差值ei,j：ei,j=u’i,j-yi,j或ei,j=ui,j-yi,j
(取決於正在使用哪一組輸入值而定)，以及以相同於上面第1圖所述之方式將誤差信號傳遞至誤差濾波器106。
在理論上，似乎應該使用原始經修改輸入值ui,j而不是投影輸入值u’i,j來計算誤差值ei,j，因為是前者精確地表示像素之期望與實際顏色間的差異；實際上，使用後面數值，「拋掉」由投影步驟所引入的誤差。依 據經驗，已經發現使用哪一組輸入值對顏色表示的準確性沒有重大影響。此外，在誤差計算中決定在投影前或後使用輸入值時，需要考慮由色域投影機206所進行的投影之種類。一些類型的投影，例如，沿著固定色相和亮度線的投影，提供量化器域邊界至色域外積體(out-of-gamut volume)之連續且固定的延伸，因而允許在誤差計算中使用未投影輸入值而沒有輸出值不穩定的風險。其他類型的投影沒有提供量化器域邊界之連續且固定的延伸；例如，朝輸入顏色投影直到達到色域邊界為止不能提供量化器域邊界的固定延伸，然而，取而代之，量化器域隨著輸入值而改變，以及在這些情況下，應該使用投影輸入值來判定誤差值，因為使用未投影值可能會導致誤差值可能無限制增加的不穩定方法。
從前述可看出，本發明可以在有限調色顯示器中提供具有比使用傳統誤差擴散技術獲得還少的偽影之改良顏色。本發明可以使用於能夠顯示連續的顏色(或至少非常大數量的顏色)之顯示系統中，然而其中，可用的原色在整個色域係不均勻的分佈；例如，控制間隙寬度的以干涉為基礎的顯示器(interference based displays)可以在每個像素處顯示大量的顏色，但是在原色間具有預定結構，而原色取決於一維流形(one-dimensional manifold)。本發明亦可以使用於電致變色顯示器。
關於可應用本發明的彩色顯示系統之進一步細節，將讀者指引到上述ECD專利(這些專利亦給出電泳 顯示器的詳細討述)以及下面專利和出版物：美國專利第6,017,584；6,545,797；6,664,944；6,788,452；6,864,875；6,914,714；6,972,893；7,038,656；7,038,670；7,046,228；7,052,571；7,075,502；7,167,155；7,385,751；7,492,505；7,667,684；7,684,108；7,791,789；7,800,813；7,821,702；7,839,564；7,910,175；7,952,790；7,956,841；7,982,941；8,040,594；8,054,526；8,098,418；8,159,636；8,213,076；8,363,299；8,422,116；8,441,714；8,441,716；8,466,852；8,503,063；8,576,470；8,576,475；8,593,721；8,605,354；8,649,084；8,670,174；8,704,756；8,717,664；8,786,935；8,797,634；8,810,899；8,830,559；8,873,129；8,902,153；8,902,491；8,917,439；8,964,282；9,013,783；9,116,412；9,146,439；9,164,207；9,170,467；9,170,468；9,182,646；9,195,111；9,199,441；9,268,191；9,285,649；9,293,511；9,341,916；9,360,733；9,361,836；9,383,623；及9,423,666號；以及美國專利申請案公開第2008/0043318；2008/0048970；2009/0225398；2010/0156780；2011/0043543；2012/0326957；2013/0242378；2013/0278995；2014/0055840；2014/0078576；2014/0340430；2014/0340736；2014/0362213；2015/0103394；2015/0118390；2015/0124345；2015/0198858；2015/0234250；2015/0268531；2015/0301246；2016/0011484；2016/0026062；2016/0048054；2016/0116816；2016/0116818；及2016/0140909號。
102‧‧‧輸入端
104‧‧‧處理器
106‧‧‧誤差濾波器
206‧‧‧色域投影機
208‧‧‧單形體
210‧‧‧處理器
212‧‧‧量化器
ei,j‧‧‧誤差值
xi,j‧‧‧顏色值
ui,j‧‧‧經修改輸入
u’i,j‧‧‧投影輸入
yi,j‧‧‧輸出
λ‧‧‧輸出

Claims (13)

  1. 一種在顯示器上渲染影像之方法，該方法包括：接收表示一待渲染像素之顏色的輸入資料(102)；結合(104)該輸入資料與由先前被渲染之至少一像素所產生的誤差資料(ei,j)，以形成經修改輸入資料(ui,j、u’i,j)；將該輸入資料轉換(210、212)成輸出資料(yi,j)；計算(214)該像素之該經修改輸入資料(ui,j、u’i,j)與該輸出資料(yi,j)間的差異及藉以產生該像素之誤差資料(ei,j)；應用(106)因此產生的誤差資料(ei,j)至至少一後面待渲染像素；以及提供複數個像素之輸出資料(yi,j)至該顯示器及藉以在該顯示器上渲染該影像，該方法之特徵在於：在一色空間中判定(208)包含該經修改輸入資料(ui,j、u’i,j)之單形體及與該單形體(simplex)相關聯之顯示原色{Pks}；根據該單形體轉換(210)該經修改影像(ui,j、u’i,j)資料成重心坐標且設定(212)輸出資料(yi,j)為具有最大重心坐標之原色。
  2. 如請求項1之方法，進一步包括測試(206)該經修改輸入資料(ui,j)，以判定該經修改輸入資料(ui,j)是否在該顯示器之色域內，以及如果該經修改輸入資料係在此色域之外，則藉由將該經修改輸入資料投影至該色域上 ，進一步修改該經修改輸入資料。
  3. 如請求項2之方法，其中，朝該色空間之中性軸沿著固定亮度及色相之線條進行投影。
  4. 如請求項2之方法，其中，朝該像素之輸入資料所表示的顏色進行投影，直到達到色域邊界為止。
  5. 如請求項2至4中任一項之方法，其中，藉由該投影產生之該經修改輸入資料(u’i,j)係用於至重心坐標之轉換(210)及該誤差資料之計算(214)。
  6. 如請求項2至4中任一項之方法，其中，藉由該投影產生之該經修改輸入資料(u’i,j)係用於至重心坐標之轉換(210)，但是在該投影前之該經修改影像資料(ui,j)係用於該誤差資料之計算(214)。
  7. 如請求項1至6中任一項之方法，其中，該色空間係三維的，使得該單形體係四面體。
  8. 如請求項1至7中任一項之方法，其中，該誤差資料(ei,j)係分佈在超過一個像素上。
  9. 如請求項8之方法，其中，該誤差資料(ei,j)係分佈在至少四個像素上。
  10. 如請求項9之方法，其中，應用於不同像素之該誤差資料的比例會變動。
  11. 如請求項1至10中任一項之方法，其中，該顯示器係電泳顯示器。
  12. 一種設備，該設備包括一顯示裝置，其具有複數個像素，該等像素之每一者係配置成顯示複數個原色中之任一者；以及一計算裝置，其能實施如請求項1至11中 任一項之方法且提供其輸出資料至該顯示裝置，藉以促使該顯示裝置顯示影像。
  13. 一種非暫態電腦儲存媒體，其包括指令，當該等指令被一處理器執行時，該等指令使該處理器實施如請求項1至11中任一項之方法。
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