what is the LSC?

lens shading 分为：Y-shading , color shading。

在讲LSC之前，我们先来理解一个重要的术语--CRA(Chief ray angle)。

CRA：分为lens cra , sensor cra两种。

1.1什么是lens CRA?

定义：最大像高处的主光线与光轴的倾角。备注：最大像高定义为 像素响应降低为零度角像素响应的80%的像素点。

因为Lens CRA 的存在，所以就出现了FOV （filed of view) 所谓的视角的概念。视角大小=2*CRA。

下图为lens CRA示意图。

1.2 什么是sensor的CRA

               sensor的CRA 说白了是sensor与之配对的micro lens的CRA.

圈1 表示lens折射过来的光，圈2表示micro lens再次折射的光。可以看出，sensor的光电转换二极管接收到的光并不是                 lens直接折射过来的，而是经过microlens再次折射过来的。所以你明白了什么呢？！ 这也就是为什么图像边缘会变暗                   的原因，光电转换二极管并不会全部接收到光能。这是LensShading中Y-shading的主要原因。

一般情况下，当lens_cra < micro_cra的时候，在sensor传感器的边缘只会出现Y-shading。

倘若，lens_cra > micro_cra, sensor传感器可能会因为无法有效捕捉某频率的光，就会出现偏色的情况，即Color-                          shading。比如microlens 对R ,G,B的折射率不同，在R_pixel上接收了很小的能量，而在B_pixel上接受了相对较多的能                  量。

如何处理或者叫减轻shading带来的图像不均问题呢？

              1.lens cra要小于micro cra,这样既可以减缓y-shading,又可以大大避免color-shading.

              2.因为镜头是圆的，画面的对角线是最接近镜头成像直径的，所以sensor有效区域最大尺寸是对角线尺寸

3.硬件矫正

4.软件矫正（下面会细讲）

how to LSC with software?

一般模组厂会根据矫正工具将图像划分为17*13(qualcomm),15*15(MTK),33*25(Samsung)等区间，计算每一块的四通道平均值，然后对每个通道与中心块的四通道平均值做除法，得到每个点的增益倍数，整个lut存储在otp中，手机端就可以根据lut进行插值计算每个pixel的增益。

一般用双线性差值或者多项式拟合的方法，确定每个pixel的增益。

原始图片的rgb通道(节选自网络)：

y-shading 增益之后，基本与中心数值在同一个平面(节选自网络)：

color-shading 增益之后，各区域的r/g，b/g均值相同(节选自网络)：

上面三张图片为了让大家理解，节选自网络。本人也模拟了shading矫正过程，但由于colorshading不严重所以矫正效果不明显。下面是我的矫正过程：

1.原始图：

2.三通道三维图

3.(17*13block)r,g,b平均

4.colorgain

5、lensgain=ygain+colorgain

6. 还原后三通道值

7.还原后图片

附上我的代码：

clc
clear all;
close all;
BLOCK_H = 17
BLOCK_V = 13
img = imread('1.bmp');
r= medfilt2(img(:,:,1));%中值滤波抑制边缘凸起噪声
g= medfilt2(img(:,:,2));
b= medfilt2(img(:,:,3));
figure(1)
[rows,cols,channels] = size(img);
width = 1:cols; height = 1:rows; [X1,Y1] = meshgrid(width,height);
mesh(X1,Y1,im2double(r)); hold on; mesh(X1,Y1,im2double(g)); hold on; mesh(X1,Y1,im2double(b));subSampleRGB=ones(BLOCK_V+1,BLOCK_H+1,3);%6*6*3 gainlutstrideX=floor(cols/BLOCK_H)
strideY=floor(rows/BLOCK_V)
for i=1:BLOCK_H+1%colsfor j=1:BLOCK_V+1%rowsfor k=1:3%channelsif i==1if j==1%left_topsubSampleRGB(j,i,k)=mean2( img(1:floor(strideY*0.5),                                1:floor(strideX*0.5),k) );elseif j==BLOCK_V+1 %left_bottomsubSampleRGB(j,i,k)=mean2( img(floor((BLOCK_V-0.5)*strideY):BLOCK_V*strideY,        1:floor(strideX*0.5),k) );else %left_middlesubSampleRGB(j,i,k)=mean2( img(floor((j-1-0.5)*strideY):floor((j-1+0.5)*strideY),   1:floor(strideX*0.5),k) );endelseif i==BLOCK_H+1if j==1%right_topsubSampleRGB(j,i,k)=mean2( img(1:floor(strideY*0.5),                                floor(strideX*(BLOCK_H-0.5)):BLOCK_H*strideX,k) );elseif j==BLOCK_V+1 %right_bottomsubSampleRGB(j,i,k)=mean2( img(floor((BLOCK_V-0.5)*strideY):BLOCK_V*strideY,        floor(strideX*(BLOCK_H-0.5)):BLOCK_H*strideX,k) );else %right_middlesubSampleRGB(j,i,k)=mean2( img(floor((j-1-0.5)*strideY):floor((j-1+0.5)*strideY),        floor(strideX*(BLOCK_H-0.5)):BLOCK_H*strideX,k) );endelseif j==1%top without cornerif i~=1&&i~=BLOCK_H+1subSampleRGB(j,i,k)=mean2( img(1:floor(0.5*strideY),                               floor(strideX*(i-1-0.5)):floor(strideX*(i-1+0.5)),k) );endelseif j==BLOCK_V+1%bottom without cornerif i~=1&&i~=BLOCK_H+1subSampleRGB(j,i,k)=mean2( img(floor((BLOCK_V-0.5)*strideY):BLOCK_V*strideY,       floor(strideX*(i-1-0.5)):floor(strideX*(i-1+0.5)),k));endelseif i~=1&&i~=BLOCK_H+1&&j~=1&&j~=BLOCK_V+1 %center areasubSampleRGB(j,i,k)=mean2( img(floor((j-1-0.5)*strideY):floor((j-1+0.5)*strideY),  floor(strideX*(i-1-0.5)):floor(strideX*(i-1+0.5)),k));endendendend
endfigure(2)
[A,B] = meshgrid(1:BLOCK_H+1,1:BLOCK_V+1);
mesh(A,B,subSampleRGB(:,:,1));
hold on
mesh(A,B,subSampleRGB(:,:,2));
hold on
mesh(A,B,subSampleRGB(:,:,3));%Gainlut luma gain (Y-shading gain)
gainlut=zeros(BLOCK_V+1,BLOCK_H+1,3);% gainlut
for i = 1:BLOCK_H+1for j =1:BLOCK_V+1for k = 1:3gainlut(j,i,k)=mean2( subSampleRGB(floor(BLOCK_V/2+1) : floor(BLOCK_V/2+1)+1,  floor(BLOCK_H/2+1) : floor(BLOCK_H/2+1)+1,k)) / subSampleRGB(j,i,k);endend
end%Gainlut chroma gain (colorshading gain)
gainlut_c = zeros(BLOCK_V+1,BLOCK_H+1,2);
center_RoverG = mean2( subSampleRGB(floor(BLOCK_V/2+1) : floor(BLOCK_V/2+1)+1,  floor(BLOCK_H/2+1) : floor(BLOCK_H/2+1)+1,1)) / mean2( subSampleRGB(floor(BLOCK_V/2+1) : floor(BLOCK_V/2+1)+1,  floor(BLOCK_H/2+1) : floor(BLOCK_H/2+1)+1,2));
center_BoverG = mean2( subSampleRGB(floor(BLOCK_V/2+1) : floor(BLOCK_V/2+1)+1,  floor(BLOCK_H/2+1) : floor(BLOCK_H/2+1)+1,3)) / mean2( subSampleRGB(floor(BLOCK_V/2+1) : floor(BLOCK_V/2+1)+1,  floor(BLOCK_H/2+1) : floor(BLOCK_H/2+1)+1,2));
for i = 1:BLOCK_H+1for j =1:BLOCK_V+1RoverG = subSampleRGB(j,i,1)/subSampleRGB(j,i,2);BoverG = subSampleRGB(j,i,3)/subSampleRGB(j,i,2);gainlut_c(j,i,1) = center_RoverG/RoverG-1;gainlut_c(j,i,2) = center_BoverG/BoverG-1;end
end%chroma+luma gain
gainlut_full = zeros(BLOCK_V+1,BLOCK_H+1,2);
for i = 1:BLOCK_H+1for j =1:BLOCK_V+1gainlut_full(:,:,1) = gainlut(:,:,1) + gainlut_c(j,i,1);gainlut_full(:,:,2) = gainlut(:,:,2) + gainlut_c(j,i,2);end
end%(BLOCK_H+1)*(BLOCK_V+1) colorgain
figure(3)
[C,D] = meshgrid(1:BLOCK_H+1,1:BLOCK_V+1);
mesh(C,D,gainlut_c(:,:,1))
hold on
mesh(C,D,gainlut_c(:,:,2))figure(4)
mesh(C,D,gainlut_full(:,:,1))
hold on
mesh(C,D,gainlut_full(:,:,2))
hold on
mesh(C,D,gainlut(:,:,2))%双线性插值FullGainLut
x = 1:strideX:cols+1;
x(end) = cols;
y = 1:strideY:rows+1;
y(end) = rows;xitp = 1:cols;
yitp = 1:rows;
[Xitp,Yitp]=meshgrid(xitp,yitp);
rgain=interp2(x,y,gainlut(:,:,1),Xitp,Yitp);
ggain=interp2(x,y,gainlut(:,:,2),Xitp,Yitp);
bgain=interp2(x,y,gainlut(:,:,3),Xitp,Yitp);%shading r,b,g gain
figure(5)
r=im2uint8( (im2double(r).*rgain) );
mesh(X1,Y1,im2double(r));
b=im2uint8( (im2double(b).*bgain) );
hold on
mesh(X1,Y1,im2double(b));
g=im2uint8( (im2double(g).*ggain) );
hold on
mesh(X1,Y1,im2double(g));%shading corrected img
figure(6)
lscgain = cat(3,rgain,ggain,bgain);%merge三通道gain
imgDoubleType = im2double(img);
imgDoubleType = imgDoubleType.*lscgain;
imgUint = im2uint8(imgDoubleType);
imshow(imgUint)