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。
ISP-镜头阴影校正（LSC）

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：
ISP-镜头阴影校正（LSC）

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16x16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。

16x16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：
ISP-镜头阴影校正（LSC）

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([j*side_x - side_x/2, j*side_x + side_x/2]);
        y_clip = floor([i*side_y - side_y/2, i*side_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