视网膜机制启发的颜色恒常算法

注意：这篇文章上次更新于2016天前，文章内容可能已经过时。

This article was last updated2016 days ago, the content may be outdated.

算法流程

首先将输入图像从 RGB 色彩空间转换到与视锥细胞相对应的 LMS 色彩空间^[1]。

$\left(\begin{array}{c} L \\ M \\ S \end{array}\right)=\left(\begin{array}{lll} 0.3192 & 0.6098 & 0.0447 \\ 0.1647 & 0.7638 & 0.0870 \\ 0.0202 & 0.1296 & 0.9391 \end{array}\right)\left(\begin{array}{l} R \\ G \\ B \end{array}\right)$

使用 2 维高斯函数模拟视锥细胞对输入颜色信息的响应^[2]。

$F_{c}(x, y)=f_{c}(x, y) \otimes g(x, y ; \sigma)$

其中， $c \in\{L, M, S\}$ ，2 维高斯函数记为：

$g(x, y ; \sigma)=\frac{1}{2 \pi \sigma^{2}} \exp \left(-\left(x^{2}+y^{2}\right) /\left(2 \sigma^{2}\right)\right)$
使用自适应的伽马校正模拟水平细胞对光感受体的反馈。

$Out(x,y)_{c} = F_{c}^{\lambda_{c}}(x,y)$

其中， $\lambda _c$ 可由输入图像的色彩信息自适应求得：

$\lambda _c = \frac{\mu _c}{\mu _{max}}$

$\mu _c = mean(F_c(x,y))$

$\mu _{max} = max(\mu _L,\mu _M, \mu _S)$
最后将图像从 LMS 空间转换到 RGB 空间。

$\left(\begin{array}{c} R \\ G \\ B \end{array}\right)=\left(\begin{array}{ccc} 5.3341 & -4.2829 & 0.1428 \\ -1.1556 & 2.2581 & -0.1542 \\ 0.0448 & -0.2195 & 1.0831 \end{array}\right)\left(\begin{array}{c} L \\ M \\ S \end{array}\right)$

Matlab代码实现

function out = LMS_HC(I)
I = im2double(I);
LMS = [0.3192 0.6098 0.0447;0.1647 0.7638 0.0870 ; 0.0202 0.1296 0.9391];
invLMS = inv(LMS);

R = I(:,:,1);
G = I(:,:,2);
B = I(:,:,3);

L = LMS(1,1)*R + LMS(1,2)*G + LMS(1,3)*B;
M = LMS(2,1)*R + LMS(2,2)*G + LMS(2,3)*B;
S = LMS(3,1)*R + LMS(3,2)*G + LMS(3,3)*B;

h = fspecial('gaussian',[3 3],0.5);

Lg = imfilter(L,h);
Mg = imfilter(M,h);
Sg = imfilter(S,h);

Lmean = mean(Lg(:));
Mmean = mean(Mg(:));
Smean = mean(Sg(:));

MAX = max([Lmean Mmean Smean]);

lamL = Lmean / MAX;
lamM = Mmean / MAX;
lamS = Smean / MAX;

outL = L .^ lamL;
outM = M .^ lamM;
outS = S .^ lamS;

out(:,:,1) = invLMS(1,1)*outL + invLMS(1,2)*outM +invLMS(1,3)*outS;
out(:,:,2) = invLMS(2,1)*outL + invLMS(2,2)*outM +invLMS(2,3)*outS;
out(:,:,3) = invLMS(3,1)*outL + invLMS(3,2)*outM +invLMS(3,3)*outS;
end