图像保边滤波算法集锦--其他滤波算法与实现

最新推荐文章于 2025-05-29 16:19:03 发布

Trent1985

最新推荐文章于 2025-05-29 16:19:03 发布

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分类专栏：图像保边滤波算法集锦文章标签：磨皮算法保边滤波器算法实现

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本文作为“保边滤波器集锦”的最后一篇，来概括一下其他的本文所未提及的保边滤波器。

本系列算法主要是空间域算法，对于频率域算法，本文没有相关实现，原因如下：

本系列主要研究适合做磨皮美颜功能的保边滤波器，这类滤波器要求如下：

①具有较好的保边能力；

②具有较好的皮肤平滑能力；

③具有耗时短的优点；

而大多数频域算法，都需要将图像变换到频率域，滤波之后在转换到空间域，耗时长，优化困难，因此，本人这里未单独介绍。

实际上，还有一些滤波器，也具有较好的保边效果：

加权最小二乘WLS滤波器；

L0范数平滑滤波器；

全变分(TV)降噪滤波器；

①WLS滤波器

参考论文如下：

Edge-Preserving Decompositions for Multi-Scale Tone and Detail Manipulation

公开源代码如下：

function OUT = wlsFilter(IN, lambda, alpha, L)
%WLSFILTER Edge-preserving smoothing based on the weighted least squares(WLS) 
%   optimization framework, as described in Farbman, Fattal, Lischinski, and
%   Szeliski, "Edge-Preserving Decompositions for Multi-Scale Tone and Detail
%   Manipulation", ACM Transactions on Graphics, 27(3), August 2008.
%
%   Given an input image IN, we seek a new image OUT, which, on the one hand,
%   is as close as possible to IN, and, at the same time, is as smooth as
%   possible everywhere, except across significant gradients in L.
%
%
%   Input arguments:
%   ----------------
%     IN              Input image (2-D, double, N-by-M matrix). 
%       
%     lambda          Balances between the data term and the smoothness
%                     term. Increasing lambda will produce smoother images.
%                     Default value is 1.0
%       
%     alpha           Gives a degree of control over the affinities by non-
%                     lineary scaling the gradients. Increasing alpha will
%                     result in sharper preserved edges. Default value: 1.2
%       
%     L               Source image for the affinity matrix. Same dimensions
%                     as the input image IN. Default: log(IN)
% 
%
%   Example 
%   -------
%     RGB = imread('peppers.png'); 
%     I = double(rgb2gray(RGB));
%     I = I./max(I(:));
%     res = wlsFilter(I, 0.5);
%     figure, imshow(I), figure, imshow(res)
%     res = wlsFilter(I, 2, 2);
%     figure, imshow(res)

if(~exist('L', 'var')),
    L = log(IN+eps);
end

if(~exist('alpha', 'var')),
    alpha = 1.2;
end

if(~exist('lambda', 'var')),
    lambda = 1;
end

smallNum = 0.0001;

[r,c] = size(IN);
k = r*c;

% Compute affinities between adjacent pixels based on gradients of L
dy = diff(L, 1, 1); %对L矩阵的第一维度上做差分，也就是下面的行减去上面的行，得到(N-1)xM维的矩阵
dy = -lambda./(abs(dy).^alpha + smallNum);
dy = padarray(dy, [1 0], 'post');%在最后一行的后面补上一行0
dy = dy(:);%按列生成向量，就是Ay对角线上的元素构成的矩阵

dx = diff(L, 1, 2); %对L矩阵的第二维度做差分，也就是右边的列减去左边的列，得到Nx(M-1)的矩阵
dx = -lambda./(abs(dx).^alpha + smallNum);
dx = padarray(dx, [0 1], 'post');%在最后一列的后面添加一列0
dx = dx(:);%按列生成向量，对应上面Ay的对角线元素


% Construct a five-point spatially inhomogeneous Laplacian matrix
B(:,1) = dx;
B(:,2) = dy;
d = [-r,-1];
A = spdiags(B,d,k,k);//把dx放在-r对应的对角线上，把dy放在-1对应的对角线上

e = dx;
w = padarray(dx, r, 'pre'); w = w(1:end-r);
s = dy;
n = padarray(dy, 1, 'pre'); n = n(1:end-1);

D = 1-(e+w+s+n);
A = A + A' + spdiags(D, 0, k, k);%A只有五个对角线上有非0元素

% Solve
OUT = A\IN(:);%
OUT = reshape(OUT, r, c);

②L0范数平滑滤波器是基于频域的滤波器

参考论文如下：

ImageSmoothing via L0 Gradient Minimization

公开源代码如下：

%   Distribution code Version 1.0 -- 09/23/2011 by Jiaya Jia Copyright 2011, The Chinese University of Hong Kong.
%
%   The Code is created based on the method described in the following paper 
%   [1] "Image Smoothing via L0 Gradient Minimization", Li Xu, Cewu Lu, Yi Xu, Jiaya Jia, ACM Transactions on Graphics, 
%   (SIGGRAPH Asia 2011), 2011. 
%  
%   The code and the algorithm are for non-comercial use only.


function S = L0Smoothing(Im, lambda, kappa)
%L0Smooth - Image Smoothing via L0 Gradient Minimization
%   S = L0Smooth(Im, lambda, kappa) performs L0 graidient smoothing of input
%   image Im, with smoothness weight lambda and rate kappa.
%
%   Paras: 
%   @Im    : Input UINT8 image, both grayscale and color images are acceptable.
%   @lambda: Smoothing parameter controlling the degree of smooth. (See [1]) 
%            Typically it is within the range [1e-3, 1e-1], 2e-2 by default.
%   @kappa : Parameter that controls the rate. (See [1])
%            Small kappa results in more iteratioins and with sharper edges.   
%            We select kappa in (1, 2].    
%            kappa = 2 is suggested for natural images.  
%
%   Example
%   ==========
%   Im  = imread('pflower.jpg');
%   S  = L0Smooth(Im); % Default Parameters (lambda = 2e-2, kappa = 2)
%   figure, imshow(Im), figure, imshow(S);


if ~exist('kappa','var')
    kappa = 2.0;
end
if ~exist('lambda','var')
    lambda = 2e-2;
end
S = im2double(Im);
betamax = 1e5;
fx = [1, -1];
fy = [1; -1];
[N,M,D] = size(Im);
sizeI2D = [N,M];
otfFx = psf2otf(fx,sizeI2D);
otfFy = psf2otf(fy,sizeI2D);
Normin1 = fft2(S);
Denormin2 = abs(otfFx).^2 + abs(otfFy ).^2;
if D>1
    Denormin2 = repmat(Denormin2,[1,1,D]);
end
beta = 2*lambda;
while beta < betamax
    Denormin   = 1 + beta*Denormin2;
    % h-v subproblem
    h = [diff(S,1,2), S(:,1,:) - S(:,end,:)];
    v = [diff(S,1,1); S(1,:,:) - S(end,:,:)];
    if D==1
        t = (h.^2+v.^2)<lambda/beta;
    else
        t = sum((h.^2+v.^2),3)<lambda/beta;
        t = repmat(t,[1,1,D]);
    end
    h(t)=0; v(t)=0;
    % S subproblem
    Normin2 = [h(:,end,:) - h(:, 1,:), -diff(h,1,2)];
    Normin2 = Normin2 + [v(end,:,:) - v(1, :,:); -diff(v,1,1)];
    FS = (Normin1 + beta*fft2(Normin2))./Denormin;
    S = real(ifft2(FS));
    beta = beta*kappa;
    fprintf('.');
end
fprintf('\n');
end

效果图如下：