ISP-镜头阴影校正（LSC） – 图像质量与色彩技术知识库

概述介绍
镜头阴影校正（Lens Shading Correction）是为了解决由于lens的光学特性，由于镜头对于光学折射不均匀导致的镜头周围出现阴影的情况。

shading可以细分为luma shading和color shading：

luma shading：
由于Lens的光学特性，Sensor影像区的边缘区域接收的光强比中心小，所造成的中心和四角亮度不一致的现象。镜头本身就是一个凸透镜，由于凸透镜原理，中心的感光必然比周边多。如图所示：

chrom/color shading：
由于各种颜色的波长不同，经过了透镜的折射，折射的角度也不一样，因此会造成color shading的现象，这也是为什么太阳光经过三棱镜可以呈现彩虹的效果。如图所示：

此外，还有CRA的原因会导致shading现象的出现，这里不再赘述，这里推荐《What’s CRA》这篇文章，详细讲述了由于镜头的CRA带来的shading。

影响
luma shading：会造成图像边角偏暗，就是所谓的暗角。

color shading：中心和四周颜色不一致，体现出来一般为中心或者四周偏色。如图所示：

校正
lens shading的校正是分别对于bayer的四个通道进行校正，每个通道的校正过程是相对独立的过程。

考虑到芯片设计的成本，因此一般情况下不会存储整幅图像的lut，目前主流的都是存储128*128个点的增益，利用双线性插值的方法计算每个pixel的增益。

算法
由于条件限制，图像仅用于算法验证，不做图像质量评判标准
这里写了一个shading的算法，将图像分为16×16的方块，求取每个交点的增益值，对平面进行四次方拟合，分别计算了luma shading 和 chrom shading，先计算出来一个lut用于存储，校正的世行通过对这个lut进行双线性插值得到每个pixel的值乘以原本像素点。

16×16的分块并非固定，可以对块的大小进行调整，比如中心块偏大，靠近边缘的方块变小，这些都是可以自定义的，本算法由于做演示使用，故不做其他功能。如图所示：

code
由于代码量较大，这里分别附上一部分算法:

shading lut caculate:

function [image_r_gain, image_gr_gain, image_gb_gain, image_b_gain] = …
isp_lsc_lut(image_r, image_gr, image_gb, image_b, side_num)
[height, width] = size(image_r);
side_y = floor(height/side_num);
side_x = floor(width/side_num);

% figure,imshow(image_r);
% hold on;
% for k=0:side_num
% line_x = side_x * k;
% line_y = side_y * k;
% if(k==side_num && line_y ~= width) line_y = height;end
% if(k==side_num && line_x ~= width) line_x = width;end
% line([line_x,line_x],[0,height],’Color’,’red’);
% line([0,width], [line_y, line_y],’Color’,’red’);
% % line(Xd,Yd,’Color’,’red’);
% end
% hold off

%% compress resolution
image_point = zeros(side_num,side_num);
for i = 0:side_num
for j = 0:side_num
x_clip = floor([jside_x – side_x/2, jside_x + side_x/2]);
y_clip = floor([iside_y – side_y/2, iside_y + side_y/2]);
if(i==side_num && y_clip(2) ~= height) y_clip(2) = height;end
if(j==side_num && x_clip(2) ~= width) x_clip(2) = width;end
x_clip(x_clip<1) = 1;x_clip(x_clip>width) = width;
y_clip(y_clip<1) = 1;y_clip(y_clip>height) = height;
data_r_in = image_r(y_clip(1):y_clip(2), x_clip(1):x_clip(2));
image_r_point(i+1,j+1) = mean(mean(data_r_in));
data_gr_in = image_gr(y_clip(1):y_clip(2), x_clip(1):x_clip(2));
image_gr_point(i+1,j+1) = mean(mean(data_gr_in));
data_gb_in = image_gb(y_clip(1):y_clip(2), x_clip(1):x_clip(2));
image_gb_point(i+1,j+1) = mean(mean(data_gb_in));
data_b_in = image_b(y_clip(1):y_clip(2), x_clip(1):x_clip(2));
image_b_point(i+1,j+1) = mean(mean(data_b_in));
end
end

% figure,imshow(uint8(image_r_point));
%% caculate lsc luma gain
for i = 1:side_num+1
for j = 1:side_num+1
image_r_luma_gain_point(i,j) = mean2(image_r_point(uint8(side_num/2)-1:uint8(side_num/2)+1, uint8(side_num/2)-1:uint8(side_num/2)+1)) / image_r_point(i,j);
image_gr_luma_gain_point(i,j) = mean2(image_gr_point(uint8(side_num/2)-1:uint8(side_num/2)+1, uint8(side_num/2)-1:uint8(side_num/2)+1)) / image_gr_point(i,j);
image_gb_luma_gain_point(i,j) = mean2(image_gb_point(uint8(side_num/2)-1:uint8(side_num/2)+1, uint8(side_num/2)-1:uint8(side_num/2)+1)) / image_gb_point(i,j);
image_b_luma_gain_point(i,j) = mean2(image_b_point(uint8(side_num/2)-1:uint8(side_num/2)+1, uint8(side_num/2)-1:uint8(side_num/2)+1)) / image_b_point(i,j);
end
end

Bilinear interpolation:

image_r_luma_gain_reshape = reshape(image_r_luma_gain_point, [], 1);
image_gr_luma_gain_reshape = reshape(image_gr_luma_gain_point, [], 1);
image_gb_luma_gain_reshape = reshape(image_gb_luma_gain_point, [], 1);
image_b_luma_gain_reshape = reshape(image_b_luma_gain_point, [], 1);
for i = 1:17
for j = 1:17
x((i-1)17+j) = i; y((i-1)17+j) = j;
end
end
x=x’;
y=y’;
% scatter3(x,y,image_r_luma_gain_reshape)
% hold on
Z=[ones(length(x),1),x,y,x.^2,x.y,y.^2,x.^3,x.^2.y,x.y.^2,y.^3]; [x y]=meshgrid(1:17,1:17); A=Z\image_r_luma_gain_reshape; image_r_luma_gain=A(1)+A(2)x+A(3)y+A(4)x.^2+A(5)x.y+A(6)y.^2+A(7)x.^3+A(8)x.^2.y+A(9)x.y.^2+A(10)y.^3; A=Z\image_gr_luma_gain_reshape; image_gr_luma_gain=A(1)+A(2)x+A(3)y+A(4)x.^2+A(5)x.y+A(6)y.^2+A(7)x.^3+A(8)x.^2.y+A(9)x.y.^2+A(10)y.^3; A=Z\image_gb_luma_gain_reshape; image_gb_luma_gain=A(1)+A(2)x+A(3)y+A(4)x.^2+A(5)x.y+A(6)y.^2+A(7)x.^3+A(8)x.^2.y+A(9)x.y.^2+A(10)y.^3; A=Z\image_b_luma_gain_reshape; image_b_luma_gain=A(1)+A(2)x+A(3)y+A(4)x.^2+A(5)x.y+A(6)y.^2+A(7)x.^3+A(8)x.^2.y+A(9)x.y.^2+A(10)*y.^3;
% surf(x,y,image_r_luma_gain)
% hold on
% surf(x,y,image_r_luma_gain_point)

%% calulate lsc chroma gain
for i = 1:side_num+1
for j = 1:side_num+1
image_r_chroma_gain(i,j) = image_r_luma_gain(i,j) – image_r_luma_gain_point(i,j);
image_gr_chroma_gain(i,j) = image_gr_luma_gain(i,j) – image_gr_luma_gain_point(i,j);
image_gb_chroma_gain(i,j) = image_gb_luma_gain(i,j) – image_gb_luma_gain_point(i,j);
image_b_chroma_gain(i,j) = image_b_luma_gain(i,j) – image_b_luma_gain_point(i,j);
end
end
%% caculate lsc result gain
image_r_gain = image_r_luma_gain – image_r_chroma_gain;
image_gr_gain = image_gr_luma_gain – image_gr_chroma_gain;
image_gb_gain = image_gb_luma_gain – image_gb_chroma_gain;
image_b_gain = image_b_luma_gain – image_b_chroma_gain;

function image_gain_lut = lsc_data_gain_interpolation(image_gain, height, width, side_num)
side_y_ori = floor(height/side_num);
side_x_ori = floor(width/side_num);
k = 0;
l = 0;
[gain_height, gain_width] = size(image_gain);
for i = 1:gain_height-1
for j = 1:gain_width-1
data_gain_11 = image_gain(i, j);
data_gain_12 = image_gain(i, j+1);
data_gain_21 = image_gain(i+1, j);
data_gain_22 = image_gain(i+1, j+1);
if(j == gain_width-1 && ((j-1)side_x + l) ~= width) side_x = width – (j-1)side_x_ori;
else
side_x = side_x_ori;
end

    if(i == gain_width-1 && ((i-1)*side_y + k) ~= width)
        side_y = height - (i-1)*side_y_ori;
    else
        side_y = side_y_ori;
    end

    for k = 1:side_y
        for l = 1:side_x
            label_y1 = 1;
            label_x1 = 1;
            label_y2 = side_y;
            label_x2 = side_x;
            image_gain_lut((i-1)*side_y_ori + k, (j-1)*side_x_ori + l) = ...
                data_gain_22/(label_x2-label_x1)/(label_y2-label_y1)* ...
                (l - label_x1) * (k - label_y1) + ...
                data_gain_21/(label_x2-label_x1)/(label_y2-label_y1)* ...
                (label_x2 - l) * (k - label_y1) + ...
                data_gain_12/(label_x2-label_x1)/(label_y2-label_y1)* ...
                (l - label_x1) * (label_y2 - k) + ...
                data_gain_11/(label_x2-label_x1)/(label_y2-label_y1)* ...
                (label_x2 - l) * (label_y2 - k);
        end
    end

end

end
end

original image: