CSC/CSM正本清源

本文系微信公眾號《大話成像》，知乎專欄《all in camera》原創文章

大話成像讀者QQ交流羣：237427716 大話計算機視覺QQ交流羣：651805282

本站教學視頻大話成像之《數字成像系統》32講已上線淘寶，搜索關鍵字『大話成像』即可找到，或使用鏈接

PC用戶： https://item.taobao.com/item.htm?id=568925736204：

手機用戶可使用鏈接： 複製這條信息￥adMo0tqbc2N￥後打開手淘

請購買了視頻的讀者加入QQ羣：679050565，羣名稱：數字成像系統課程，驗證消息請輸入購買課程時候的個人ID。

從ISP RGB信號輸出到encoder,中間有一步色彩空間轉換（color space conversion），把信號從RGB變換成YCbCr,我們把這個模塊叫做CSC或者CSM。

一般ISP公司在tuning或者測試驗證的時候都只用RGB ，顯示也是隻用RGB，不會經過CSC，所以CSC的Setting有時候就會處在ISP和encoder兩家的邊界地帶，經常會因為兩邊色彩空間不一致而出現問題。造成這種不一致，有其歷史原因。

ISP本身不是國際標準化的主體，但是數字視頻是很長時間以來都有國際標準化的。1982年bt601/656標準建立，它第一次提出了ISP的基本標準化。

BT601把量化和色彩空間轉換做了標準化，BT656把數據格式化做了標準化。

BT601是針對標清電視提出的，這個標準本來的題目叫做：Studio encoding parameters of digital television for standard 4:3 and wide-screen 16:9 aspect ratios。

這個標準下：視頻解析度是：720 × 480 或者 720 × 576，採樣頻率是：13.5 MHz。

如果輸入為模擬RGB信號，那麼量化後的RGB信號按8bit數字信號表示為16到235的219個數。然後再用一個3x3 CSC矩陣把這個RGB信號變成YCbCr信號。

同樣別的標準：比如針對高清信號的bt709，針對超高清信號的BT.2020都有各自的規定，所以他們的色彩空間轉換也都不一樣，也就是不僅轉換後的圖像是不同的，從同一YCbCr圖像反變換到RGB也將不同。所以，ISP的CSC設定一定要遵循一個標準所推薦的變換公式，否則後邊的顯示或者編碼，反變換都無法對應正確。

有人梳理了bt601，bt709 的幾種常用的變換矩陣，如下。

function [Y,U,V]=rgb2yuv(R,G,B,yuvformat,convmtrx)

%Converts RGB to YUV

%[Y,U,V]=rgb2yuv(R,G,B,yuvformat)

%Input:

% R,G,B - R,G and B components of the frame

% yuvformat - YUV format [optional, default = YUV444_8]. Supported YUV

% formats are:

% YUV444_8 = 4:4:4 sampling, 8-bit precision (default)

% YUV420_8 = 4:2:0 sampling, 8-bit precision

% convmtrx - Conversion matrix [optional, default = BT709_l]. The

% following conversions ase defined (see in Notes for more

% details):

% BT601_f = ITU-R BT.601, RGB full [0...255] (in BT601_f.mat)

% BT601_219 = ITU-R BT.601, RGB limited [0...219] (in

% BT601_219.mat)

% BT601_l = ITU-R BT.601, RGB limited [16...235] (in BT601_l.mat)

% BT709_f = ITU-R BT.709, RGB limited [0...255] (in BT709_f.mat)

% BT709_l = ITU-R BT.709, RGB limited [16...235] (in BT709_l.mat)

% SMPTE_240M = SMPTE 240M (almost the same as Rec.709)

%Output:

% Y,U,V - Y,U and V components of the frame

%Uses:

% imresize.m - Matlab Image Processing Toolbox (when formats other than

% 4:4:4 used)

%Note:

% Note that a more correct term for what is here called YUV would be YCbCr,

% since it is used for YUV representation in digital domain. Also, the R, G

% and B components are actually non-linear because of gamma correction, and

% are more correctly denoted as R, G and B. YCbCr is expected to be in

% the range (below that is "footroom" range and above is "headroom"):

% Y = [16...235]

% Cb,Cr = [16...240]

% Some more details on the defined conversions follow.

% ITU-R BT.601 - for SD (720x576) and lower resolutions. Three versions are

% available:

% 1) RGB in full range [0...255], rgb2yuvT matrix:

% 0.257 0.504 0.098

% -0.148 -0.291 0.439

% 0.439 -0.368 -0.071

% yuvoffset = [16; 128; 128]

% (Resulting output range is

Y=[16...235];Cb=[16...240];Cr=[16...240]

% (Coefficients taken from [3],[4],[5],[6]. Integer implementation in [7])

% 2) RGB limited to [0...219], rgb2yuvT matrix:

% 0.299 0.587 0.114

% -0.173 -0.339 0.511

% 0.511 -0.428 -0.083

% yuvoffset = [16; 128; 128]

% (Resulting output range is

Y=[16...235];Cb=[16...240];Cr=[16...240])

% (Note that in [1] the coeffcients are rounded to the nearest integer,

% while the coefficients here are from [4] and [6]. If original signal is in

% range [16...235] then offset of 16 for Y signal is not necessary, e.g.

% definition from [6])

% 3) RGB limited to [16...235], rgb2yuvT matrix:

% 0.299 0.587 0.114

% -0.169 -0.331 0.500

% 0.500 -0.419 -0.081

% yuvoffset = [0; 128; 128]

% (Resulting output range is

Y=[16...235];Cb=[18.5...237.5];Cr=[18.5...237.5])

% (This conversion is also used in JPEG, which allows the input to be in the

% full [0...255] range, where the output is in range

Y=[0...255];

% Cb=[0.5...255.5];Cr=[0.5...255.5])

% (Coefficients taken from [1],[3])

% ITU-R BT.709 - for HD resolutions (i.e. higher than SD). Two versions are

% available:

% 1) RGB in full range [0...255], rgb2yuvT matrix:

% 0.1826 0.6142 0.0620

% -0.1006 -0.3386 0.4392

% 0.4392 -0.3989 -0.0403

% yuvoffset = [16; 128; 128]

% (Resulting output range is

Y=[16...235];Cb=[16...240];Cr=[16...240])

% (Coefficients taken from [5], less precise version in [6]. Appears to be a

% scaled version of the next one, where RGB is limited.)

% 2) RGB limited to [16...235], rgb2yuvT matrix:

% 0.2126 0.7152 0.0722

% -0.1146 -0.3854 0.5000

% 0.5000 -0.4542 -0.0468

% yuvoffset = [0; 128; 128]

% (Resulting output range is

Y=[16...235];Cb=[18.5...237.5];Cr=[18.5...237.5])

% (Coefficients taken from [2]. The ones in [6] are slightly different, for no

% obvious reason)

前面追溯歷史的目的是說：這些標準都是基於當年的模擬信號所考慮的（模擬信號很難做準確低於16和高於235的信號，所以要留所謂的footroom和headroom，如果你現在的應用其輸入信號和顯示/處理設備都是數字設備，是沒有這種侷限的，就可以都是full range轉換（也是Jpeg encoder的典型格式），input RGB【0，255】，output YCbCr【0，255】。

Full range RGB2YCbCr變換公式：