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2044天前，文章内容可能已经过时。

This article was last updated2044 days ago, the content may be outdated.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。

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

Algorithm Flow

First, convert the input image from the RGB color space to the LMS color space corresponding to the cone cells^[1].

Use a 2D Gaussian function to simulate the response of cone cells to the input color information^[2].

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

where $c \in\{L, M, S\}$ , and the 2D Gaussian function is written as:

$g(x, y ; \sigma)=\frac{1}{2 \pi \sigma^{2}} \exp \left(-\left(x^{2}+y^{2}\right) /\left(2 \sigma^{2}\right)\right)$
Use adaptive gamma correction to simulate the feedback of horizontal cells to the photoreceptors.

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

where $\lambda _c$ can be adaptively obtained from the color information of the input image:

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

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

$\mu _{max} = max(\mu _L,\mu _M, \mu _S)$
Finally, convert the image from the LMS space back to the RGB space.

Matlab代码实现

Matlab Code Implementation

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

实验结果对比

首先选取 4 张原颜色恒常算法也可以获得较好结果的图片。

其中，第一行为原图，第二行为目前（组内)颜色恒常算法结果图，第三行为此处颜色恒常算法结果图。

由于水下成像环境恶劣，往往会出现红光衰减特别严重的情况。以下四张图片中，其红色通道像素的平均值都不超过 0.15 ，个别图片红通道像素均值甚至仅为 0.02，这会导致原有的基于伽马校正的颜色恒常算法中 $\gamma$ 值过小，最终引起红通道过度补偿。

从算法流程和实验结果上看，此处基于 LMS 空间的颜色恒常算法并没有解决红通道过度补偿的问题，但可以获得一个较好视觉效果的最终结果图。

以下四张图片为原算法不能很好处理的图片。

其中，第一行为原图，第二行为现有（组内)颜色恒常算法结果，第三行为此处颜色恒常算法结果。

为了验证算法的鲁棒性，在数据集上运行了此处算法。

实验结果已汇总在 Google Drive 中，点击下载

~~中国特色社会主义互联网可以点击这里尝试下载~~

~~用户名：wgx~~

~~密码：123456~~

~~文件：LMS_HC_890.zip~~

Comparison of Experimental Results

First, 4 images are selected for which the original color constancy algorithm can also produce good results.

Here, the first row shows the original images, the second row shows the results of the current (in-group) color constancy algorithm, and the third row shows the results of the color constancy algorithm described here.

Due to the harsh underwater imaging environment, severe attenuation of the red light often occurs. Among the following four images, the mean values of the red channel pixels are all no more than 0.15, and in some images the red channel pixel mean is even as low as 0.02. This causes the $\gamma$ value in the original gamma-correction-based color constancy algorithm to be too small, ultimately leading to over-compensation of the red channel.

From the algorithm flow and the experimental results, the LMS-space-based color constancy algorithm described here does not solve the over-compensation problem of the red channel, but it can produce a final result image with a better visual effect.

The following four images are ones the original algorithm cannot handle well.

Here, the first row shows the original images, the second row shows the results of the existing (in-group) color constancy algorithm, and the third row shows the results of the color constancy algorithm described here.

To verify the robustness of the algorithm, it was run on a dataset.

The experimental results have been summarized in Google Drive. Click to download

~~You can try downloading through the internet of socialism with Chinese characteristics by clicking here~~