作者提出了一種新的梯度域引導圖像濾波器，通過將明確的一階邊緣感知約束結合到現有的引導圖像濾波器中。

matlab代碼實現

轉載至：https://blog.csdn.net/majinlei121/article/details/50717777

%主程序
function q = gradient_guidedfilter(I, p, eps)  
%   GUIDEDFILTER   O(1) time implementation of guided filter.  
%  
%   - guidance image: I (should be a gray-scale/single channel image)  
 
%   - filtering input image: p (should be a gray-scale/single channel image)  
%   - regularization parameter: eps  
  
r=16;  
[hei, wid] = size(I);  
N = boxfilter(ones(hei, wid), r); % the size of each local patch; N=(2r+1)^2 except for boundary pixels.  
  
mean_I = boxfilter(I, r) ./ N;  
mean_p 
 
= boxfilter(p, r) ./ N;  
mean_Ip = boxfilter(I.*p, r) ./ N;  
cov_Ip = mean_Ip - mean_I .* mean_p; % this is the covariance of (I, p) in each local patch.  
  
mean_II = boxfilter(I.*I, r) ./ N;  
var_I = mean_II - mean_I .* mean_I;  
  
%weight  
epsilon=(0.001*(max(p(:))-min(p(:))))^2;  
r1=1;  
  
N1 
 
= boxfilter(ones(hei, wid), r1); % the size of each local patch; N=(2r+1)^2 except for boundary pixels.  
mean_I1 = boxfilter(I, r1) ./ N1;  
mean_II1 = boxfilter(I.*I, r1) ./ N1;  
var_I1 = mean_II1 - mean_I1 .* mean_I1;  
  
chi_I=sqrt(abs(var_I1.*var_I));      
weight=(chi_I+epsilon)/(mean(chi_I(:))+epsilon);       
  
gamma = (4/(mean(chi_I(:))-min(chi_I(:))))*(chi_I-mean(chi_I(:)));  
gamma = 1 - 1./(1 + exp(gamma));  
  
%result  
a = (cov_Ip + (eps./weight).*gamma) ./ (var_I + (eps./weight));   
b = mean_p - a .* mean_I;   
  
mean_a = boxfilter(a, r) ./ N;  
mean_b = boxfilter(b, r) ./ N;  
  
q = mean_a .* I + mean_b;   
end  
%子程序boxfilter()

[cpp] view plain copy
function imDst = boxfilter(imSrc, r)  
  
%   BOXFILTER   O(1) time box filtering using cumulative sum  
%  
%   - Definition imDst(x, y)=sum(sum(imSrc(x-r:x+r,y-r:y+r)));  
%   - Running time independent of r;   
%   - Equivalent to the function: colfilt(imSrc, [2*r+1, 2*r+1], ‘sliding‘, @sum);  
%   - But much faster.  
  
[hei, wid] = size(imSrc);  
imDst = zeros(size(imSrc));  
  
%cumulative sum over Y axis  
imCum = cumsum(imSrc, 1);  
%difference over Y axis  
imDst(1:r+1, :) = imCum(1+r:2*r+1, :);  
imDst(r+2:hei-r, :) = imCum(2*r+2:hei, :) - imCum(1:hei-2*r-1, :);  
imDst(hei-r+1:hei, :) = repmat(imCum(hei, :), [r, 1]) - imCum(hei-2*r:hei-r-1, :);  
  
%cumulative sum over X axis  
imCum = cumsum(imDst, 2);  
%difference over X axis  
imDst(:, 1:r+1) = imCum(:, 1+r:2*r+1);  
imDst(:, r+2:wid-r) = imCum(:, 2*r+2:wid) - imCum(:, 1:wid-2*r-1);  
imDst(:, wid-r+1:wid) = repmat(imCum(:, wid), [1, r]) - imCum(:, wid-2*r:wid-r-1);  
end

%運行程序

clear

I = double(imread(‘D:\數字圖像處理\研究方向\Filter Smooth\images\tulips.png‘)) / 255;
% if size(I,3)==3
% I=rgb2gray(I);
% end

p = I;
r=16;
eps = 0.8^2; % try eps=0.1^2, 0.2^2, 0.4^2

q_guide(:,:,1)=guidedfilter(I(:,:,1), p(:,:,1), r, eps);
q_guide(:,:,2)=guidedfilter(I(:,:,2), p(:,:,2), r, eps);
q_guide(:,:,3)=guidedfilter(I(:,:,3), p(:,:,3), r, eps);

q(:,:,1) = gradient_guidedfilter(I(:,:,1), p(:,:,1), eps);
q(:,:,2) = gradient_guidedfilter(I(:,:,2), p(:,:,2), eps);
q(:,:,3) = gradient_guidedfilter(I(:,:,3), p(:,:,3), eps);

figure;imshow([I,q_guide,q]);title(‘原圖，引導濾波，改進引導濾波 eps=0.8^2‘);

Gradient Domain Guided Image Filtering（梯度域導向濾波）