光照归一化算法——DoG滤波，自商图

来源：互联网发布：多普达t5399软件编辑：程序博客网时间：2024/05/20 23:05

DoG code：function pic=DoG(I)if size(I,3)==3    I=rgb2gray(I);endI=double(I);h1=fspecial('gaussian',15,1);h2=fspecial('gaussian',15,2);m=filter2(h2,I)-filter2(h1,I);R=m;mi=min(min(R));ma=max(max(R));newR=(R-mi)*255/(ma-mi);pic=uint8(newR);

处理效果：

理论：

Given a m-channels, n-dimensional image

$I:\{\mathbb{X}\subseteq\mathbb{R}^n\}\rightarrow\{\mathbb{Y}\subseteq\mathbb{R}^m\}$

The difference of Gaussians (DoG) of the image $I$ is the function

$\Gamma_{\sigma_1,\sigma_2}:\{\mathbb{X}\subseteq\mathbb{R}^n\}\rightarrow\{\mathbb{Z}\subseteq\mathbb{R}\}$

obtained by subtracting the image $I$ convolved with the Gaussian of variance $\sigma^2_2$ from the image $I$ convolved with a Gaussian of narrower variance $\sigma^2_1$ , with $\sigma_2 > \sigma_1$ . In one dimension, $\Gamma$ is defined as:

$\Gamma_{\sigma_1,\sigma_2}(x)=I*\frac{1}{\sigma_1\sqrt{2\pi}} \, e^{-(x^2)/(2\sigma^2_1)}-I*\frac{1}{\sigma_2\sqrt{2\pi}} \, e^{-(x^2)/(2\sigma_2^2)}.$

and for the centered two-dimensional case :

$\Gamma_{\sigma,K\sigma}(x,y)=I*\frac{1}{2\pi \sigma^2} e^{-(x^2 + y^2)/(2 \sigma^2)} - I*\frac{1}{2\pi K^2 \sigma^2} e^{-(x^2 + y^2)/(2 K^2 \sigma^2)}$

which is formally equivalent to:

$\Gamma_{\sigma,K\sigma}(x,y)=I*(\frac{1}{2\pi \sigma^2} e^{-(x^2 + y^2)/(2 \sigma^2)} - \frac{1}{2\pi K^2 \sigma^2} e^{-(x^2 + y^2)/(2 K^2 \sigma^2)})$

which represents an image convoluted to the difference of two Gaussians, which approximates aMexican Hat function.

自商图code：

function [pic,ipic]=selfQuotient(I)if size(I,3)==3G=rgb2gray(I);else    G=I;endG=double(G);G=(G-min(min(G)))/(max(max(G))-min(min(G)))*255;%对比度拉升% thr=mean(G);% w=zeros(rows,cols);% for i=1:rows%     for j=1:cols%         if(I(i,j)>thr)%             w(i,j)=0;%         else%             w(i,j)=1;%         end%     end% endh1=fspecial('gaussian',7,1);% h1=h1.*w;f1=filter2(h1,G);R=G./f1;mi=min(min(R));ma=max(max(R));newR=(R-mi)*255/(ma-mi);pic=uint8(newR);ipic=uint8(f1);

处理效果图：

ps：

自商图求滤波器h1的时候，赋了权值，不过实验中发现不设置权值效果似乎更佳，所以注释掉了权值部分。权值的设置应该是一个值得探讨的部分。