图像修复序列——混合稀疏表示(Hybrid Sparse Representations)模型

1. 参考文献

2. Hybrid Sparse Representations模型

% demo_Hybrid_Sparse_Representation.m
% Author: HSW
% Date: 2015/3/28
% HARBIN INSTITUTE OF TECHNOLOGY
%
% set matlab
close all;
clear all;
clc;
% ADD PATH
addpath(genpath('inpainting'));
options.null = 0;
% read image
Img = imread('Image\butterfly.bmp');
% Img = imread('Image\peppers.bmp');Img = rgb2gray(Img);
Img = im2double(Img);
if max(Img(:)) < 2Img = Img*255;
endFlagColor = (size(Img,3) == 3);% set mask
SetMask = 2;
if SetMask == 1% read maskMask = imread('Mask\peppers_mask512.bmp');Mask = Mask > 5;MFlagColor = (size(Mask,3) == 3);if MFlagColor ~= FlagColor && FlagColor == 1Mask = repmat(Mask,[1,1,3]);elseif MFlagColor ~= FlagColor && FlagColor == 0Mask = Mask(:,:,1);end
elseif SetMask == 2% Interactively set maskif not(exist('grab_mode'))grab_mode = 'line';endoptions.grab_mode = grab_mode;if not(exist('grab_radius'))grab_radius = 4;endswitch grab_modecase 'points'options.r = grab_radius;U = grab_inpainting_mask(Img,options);case 'line'options.r = grab_radius;[U,options.point_list] = grab_inpainting_mask(Img,options);end %switchIin = find(U(:,:,1) == Inf);Iout = find(U(:,:,1) ~= Inf);m1 = length(Iin); % 缺损点的总数% product the maskMask = zeros(size(Img));if FlagColor == 1tmpMask = zeros([size(Img,1),size(Img,2)]);for channel = 1:3tmpMask(Iin) = 1 ;Mask(:,:,channel) = tmpMask;endelseMask(Iin) = 1; % 缺损区域为1end % if FlagColor
end% if SetMask
nImg = (1-Mask).*Img;
PSNRin = 10*log10(255^2/mean((Img(:)-nImg(:)).^2));
% parameter of Hybrid Sparse Representation Model
Levels = 3;
% Main Hybrid Sparse Representation Model
I = zeros(size(Img));
for channel = 1:size(Img,3)ChannelImg = Img(:,:,channel);ChannelMask = Mask(:,:,channel);TempX = Hybrid_Sparse_Representation(ChannelImg,ChannelMask,Levels);I(:,:,channel) = TempX{Levels};
end %for channel
I = max(0,min(I,255));
PSNRout = 10*log10(255^2/mean((I(:) - Img(:)).^2));
figure;
subplot(1,3,1);
imshow(Img/255,[]);
title('Original Image');
subplot(1,3,2);
imshow(nImg/255,[]);
title(['Masked Image PSNR = ',num2str(PSNRin), ' dB']);
subplot(1,3,3);
imshow(I/255,[]);
title(['Inpainting Image PSNR = ', num2str(PSNRout), ' dB']);

2.2 混合稀疏表示模型

function [xx]=Hybrid_Sparse_Representation(x,mask,levels)N=50;
para=[4 15 10 1;8 21 10 2;16 31 10 4];for level=1:levelsfprintf('level=%d\n',level);step=(2^(levels-level));x_buf=imresize(x,size(x)/step);mask_buf=mask(1:step:end,1:step:end);if level==1;xx_buf=iter_recover(x_buf,x_buf.*~mask_buf,mask_buf,4,para(level,:));xx_init=xx_buf{end};elsefor iter=1:2xx_init=combine_recovery(x_buf,x_init,mask_buf,level,N,para(level,:));x_init=xx_init;endendxx{level}=xx_init;x_init=imresize(xx_init,2);
end

function [xx,snr,dif]=iter_recover(x,x_init,mask,iter,para)N=50;
snr=[];dif=[];[xx{1},snr1,dif1]=combine_recovery(x,x_init,mask,1,N,para);
snr=[snr snr1];dif=[dif dif1];
for i=1:iter[xx{i+1},snr1,dif1]=combine_recovery(x,xx{i},mask,i+1,N,para);  snr=[snr snr1];dif=[dif dif1];
end

% ergodic image inpainting
% 遍历图像修复
% x - M-by-N original image, mask - inpainting mask
function [xx,snr_save,dif,xx_buf]=combine_recovery(x,xx,mask,iter_outer,iter_max,para)% generate damaged image y
% mask=1 - lost block
y=x.*(1-mask);
[M,N]=size(y);
%T=15;W=31;pmax=10;step=4;
T=para(1);W=para(2);pmax=para(3);step=para(4);
if mod(T,2)==0T2=T/2;
else T2=(T-1)/2;end
mask2=zeros(size(mask));
if step>1sx=step/2;sy=step/2;
elsesx=1;sy=1;
end
mask2(sx:step:end,sy:step:end)=mask(sx:step:end,sy:step:end);
[i,j]=find(mask2==1);
nn=bwmorph(mask,'dilate',2)-mask;
J=find(nn);
if iter_outer==1Th=sqrt(var(x(J)))*1.5;xx=y;xx(find(xx==0))=mean(x(J));
elseTh=sqrt(var(x(J)))/(iter_outer-1);
end
Win=kaiser(2*T+1,4)*kaiser(2*T+1,4)';x_save=xx;% main loop
loc=cell(1,length(i));
for k=1:length(i)if mod(k,100)==0fprintf('%d\n',k);endii=i(k);jj=j(k);if ii>T&ii<M-T&jj>T&jj<N-T% build a patch and a dictionaryp1=xx(ii-T:ii+T,jj-T:jj+T);%lm1=1-mask(ii-T:ii+T,jj-T:jj+T);cnt=1;d=[];pos=[];% collect NNs in the resampled spacefor sx=-W:Wfor sy=-W:WSx=ii+sx-T:ii+sx+T;Sy=jj+sy-T:jj+sy+T;if ii+sx-T>0&ii+sx+T<M&jj+sy-T>0&jj+sy+T<Np2=xx(Sx,Sy);%lm2=1-mask(Sx,Sy);e=(p1-p2);%dist=mean2(abs(e));dist=mean2(e.*e);%if dist<th&cnt<pmaxd(cnt)=dist;pos(:,cnt)=[sx sy];cnt=cnt+1;%endendendend% reorder NNs for maximizing sparsification[d1,J]=sort(d);loc{k}=pos(:,J);if iter_outer==1J1=find(d/var2(p1)<1);elseJ1=find(d/var2(p1)<0.5);enddiv(k)=min(pmax,length(J1));end
end
%plot(div);pause;
% transform domain thresholdingTh_step=.05;
iter_total=round(Th/Th_step);
for iter=1:min(iter_max,iter_total)Th=Th-Th_step;%for inner=1:1w=zeros(M,N);xr=w;% nonlocal modelfor k=1:length(i)%fprintf('%d\n',k);pos=loc{k};ii=i(k);jj=j(k);if size(pos,2)>0%pp=div(k);pp=pmax;Y1=zeros(2*T+1,2*T+1,pp);for l=1:ppsx=pos(1,l);sy=pos(2,l);Sx=ii+sx-T:ii+sx+T;Sy=jj+sy-T:jj+sy+T;Y1(:,:,l)=xx(Sx,Sy);end%Z1=dct2(Y1);Z1=fftn(Y1)/sqrt(prod(size(Y1)));%if mean(abs(Z1(:)))<tv_old(k)temp=abs(Z1);TV(iter,k)=mean(temp(:));Z=Z1.*(abs(Z1)>Th);%SIG=1;SIG=sum(abs(Z1(:))>Th)/prod(size(Z));Y2=real(ifftn(Z))*sqrt(prod(size(Y1)));% put all patches back to their original positionsfor l=1:ppsx=pos(1,l);sy=pos(2,l);Sx=ii+sx-T:ii+sx+T;Sy=jj+sy-T:jj+sy+T;xr(Sx,Sy)=xr(Sx,Sy)+Y2(:,:,l).*Win/SIG;w(Sx,Sy)=w(Sx,Sy)+Win/SIG;end%     else%         TV(iter,k)=tv_old(k);%         xr(Sx,Sy)=xx(Sx,Sy);w(Sx,Sy)=1;%     endendend% local model[ii,jj]=find(mask);for k=1:length(ii)Sx=max(1,ii(k)-T2):min(M,ii(k)+T2);Sy=max(1,jj(k)-T2):min(N,jj(k)+T2);Win2=kaiser(length(Sx),4)*kaiser(length(Sy),4)';Z1=dct2(xx(Sx,Sy));Z=Z1.*(abs(Z1)>Th);%SIG2=1;SIG2=sum(abs(Z1(:))>Th)/prod(size(Z));Y2=idct2(Z);xr(Sx,Sy)=xr(Sx,Sy)+Y2.*Win2/SIG2;w(Sx,Sy)=w(Sx,Sy)+Win2/SIG2;end% leave undamaged pixels aloneI=find(w>0);xr(I)=xr(I)./w(I);xx=x.*(1-mask)+xr.*mask;u=xx-x_save;x_save=xx;xx_buf(:,:,iter)=xx;J=find(mask==1);e=x-xx;mse=mean(e(J).^2);snr=10*log10(255*255/mse);dif(iter)=mean(u(J).^2);snr_save(iter)=snr;fprintf('Iteration %d, Th=%f, PSNR=%f, dif=%f\n',iter,Th,snr,dif(iter));imshow(xx,[]);pause(0.1);%end%diff=max(dif(iter-5:iter))-min(dif(iter-5:iter));%     if iter>10&max(dif(iter-5:iter))-min(dif(iter-5:iter))<0.01%         break;%     end
end

2.3 交互式掩模(Mask)相关函数

function v = getoptions(options, name, v, mendatory)% getoptions - retrieve options parameter
%
%   v = getoptions(options, 'entry', v0);
% is equivalent to the code:
%   if isfield(options, 'entry')
%       v = options.entry;
%   else
%       v = v0;
%   end
%
%   Copyright (c) 2007 Gabriel Peyreif nargin<4mendatory = 0;
endif isfield(options, name)v = eval(['options.' name ';']);
elseif mendatoryerror(['You have to provide options.' name '.']);
end

function [U,point_list] = grab_inpainting_mask(M, options)% grab_inpainting_mask - create a mask from user input
%
%   U = grab_inpainting_mask(M, options);
%
%   Select set of point in an image (useful to select a region for
%   inpainting). The set of point is U==Inf.
%
%   options.r is the radius for selection (default r=5).
%
%   Selection stops with right click.
%
%   Set options.mode='points' to gather disconnected points.
%   Set options.mode='line' to gather connected lines.
%
%   Copyright (c) 2006 Gabriel Peyreif nargin==3 && method==1U = grab_inpainting_mask_old(M, options);return;
endoptions.null = 0;
r = getoptions(options, 'r', 5);
method = getoptions(options, 'mode', 'points');if strcmp(method, 'line')if not(isfield(options, 'point_list'))[V,point_list] = pick_polygons(rescale(sum(M,3)),r);elsepoint_list = options.point_list;V = draw_polygons(rescale(sum(M,3)),r,point_list);end        U = M; U(V==1) = Inf;return;
endm = size(M,1);
n = size(M,2);
s = size(M,3);U = sum(M,3)/3;
b = 1;
[Y,X] = meshgrid(1:n,1:m);
point_list = [];
while b==1clf;hold on;imagesc(rescale(M)); axis image; axis off; colormap gray(256);[y,x,b] = ginput(1);point_list(:,end+1) = [x;y];I = find((X-x).^2 + (Y-y).^2 <= r^2 );U(I) = Inf;for k=1:sMa = M(:,:,k);Ma(I) = 0;M(:,:,k) = Ma;end
end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_polygons(mask,r,point_list)sk = mask*0;
for i=1:length(point_list)pl = point_list{i};for k=2:length(pl)sk = draw_line(sk,pl(1,k-1),pl(2,k-1),pl(1,k),pl(2,k),r);end
endfunction [sk,point_list] = pick_polygons(mask,r)% pick_polygons - ask for the user to build a set of curves
%
%   sk = pick_polygons(mask,r);
%
%   mask is a background image (should be in [0,1] approx).
%
%   The user right-click on a set of point which create a curve.
%   Left click stop a curve.
%   Another left click stop the process.
%
%   Copyright (c) 2007 Gabriel Peyren = size(mask,1);sk = zeros(n);
point_list = {};
b = 1;
while b(end)==1% draw a lineclf;imagesc(mask+sk); axis image; axis off;colormap gray(256);[y1,x1,b] = ginput(1);pl = [x1;y1];while b==1clf;imagesc(mask+sk); axis image; axis off;[y2,x2,c] = ginput(1);if c~=1if length(pl)>1point_list{end+1} = pl;endbreak;endpl(:,end+1) = [x2;y2];sk = draw_line(sk,x1,y1,x2,y2,r);x1 = x2; y1 = y2;end
end%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function sk = draw_line(sk,x1,y1,x2,y2,r)n = size(sk,1);
[Y,X] = meshgrid(1:n,1:n);
q = 80;
t = linspace(0,1,q);
x = x1*t+x2*(1-t); y = y1*t+y2*(1-t);
if r==0x = round( x ); y = round( y );sk( x+(y-1)*n ) = 1;
elsefor k=1:qI = find((X-x(k)).^2 + (Y-y(k)).^2 <= r^2 );sk(I) = 1;end
endfunction U = grab_inpainting_mask_old(M, r)% grab_inpainting_mask - create a mask from user input
%
%   U = grab_inpainting_mask(M, r);
%
%   r is the radius for selection (default r=5).
%
%   Selection stops with right click.
%
%   Copyright (c) 2006 Gabriel Peyr?if nargin<2r = 5;
endm = size(M,1);
n = size(M,2);
s = size(M,3);U = sum(M,3)/3;
b = 1;
[Y,X] = meshgrid(1:n,1:m);
while b==1clf;hold on;imagesc(rescale(M)); axis image; axis off; colormap gray(256);[y,x,b] = ginput(1);I = find((X-x).^2 + (Y-y).^2 <= r^2 );U(I) = Inf;for k=1:sMa = M(:,:,k);Ma(I) = 0;M(:,:,k) = Ma;end
end

function y = rescale(x,a,b)% rescale - rescale data in [a,b]
%
%   y = rescale(x,a,b);
%
%   Copyright (c) 2004 Gabriel Peyr?if nargin<2a = 0;
end
if nargin<3b = 1;
endm = min(x(:));
M = max(x(:));if M-m<epsy = x;
elsey = (b-a) * (x-m)/(M-m) + a;
end

3. 模型效果

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图像修复序列——混合稀疏表示(Hybrid Sparse Representations)模型

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