P338
i=double(imread('vase.tif'));
[C,S]=wavedec2(i,2,'db1');
a2=appcoef2(C,S,'db1',2);
dh1=detcoef2('h',C,S,1);
dv1=detcoef2('v',C,S,1);
dd1=detcoef2('d',C,S,1);
dh2=detcoef2('h',C,S,2);
dv2=detcoef2('v',C,S,2);
dd2=detcoef2('d',C,S,2);
[x,y]=size(i);
img = zeros(x,y);
img(1:x/4,1:y/4) =im2uint8(mat2gray(a2));
img(((x/4)+1):y/2,1:y/4) = im2uint8(mat2gray(dv2));
img(((x/4)+1):x/2,1:y/4) = im2uint8(mat2gray(dv2));
img(1:x/4,((y/4)+1):y/2) = im2uint8(mat2gray(dh2));
img(((x/4)+1):x/2,((y/4)+1):y/2) = im2uint8(mat2gray(dd2));
img(((x/2)+1):x,1:y/2) = im2uint8(mat2gray(dv1));
img(1:x/2,((y/2)+1):y) = im2uint8(mat2gray(dh1));
img(((x/2)+1):x,((y/2)+1):y) = im2uint8(mat2gray(dd1));
imshow(img,[]);
P341-1
X1 = imread('cathe1.bmp');
X2 = imread('cathe2.bmp');
XFUS = wfusimg(X1,X2,'sym4',5,'mean','max');
imshow(XFUS,[]);
P341-2
X1 = imread('cathe1.bmp');
X2 = imread('cathe2.bmp');
M1 = double(X1) / 256;
M2 = double(X2) / 256;
N = 4;
wtype = 'sym4';
[c0,s0] = wavedec2(M1, N, wtype);
[c1,s1] = wavedec2(M2, N, wtype);
length = size(c1);
Coef_Fusion = zeros(1,length(2));
%低频系数的处理，取平均值
Coef_Fusion(1:s1(1,1)) = (c0(1:s1(1,1))+c1(1:s1(1,1)))/2;
%处理高频系数，取绝对值大者，这里用到了矩阵乘法
MM1 = c0(s1(1,1)+1:length(2));
MM2 = c1(s1(1,1)+1:length(2));
mm = (abs(MM1)) > (abs(MM2));
Y = (mm.*MM1) + ((~mm).*MM2);
Coef_Fusion(s1(1,1)+1:length(2)) = Y;
%重构
Y = waverec2(Coef_Fusion,s0,wtype);
imshow(Y,[]);
P344
I = imread('noise_lena.bmp');
[thr,sorh,keepapp] = ddencmp('den','wv',I);
de_I = wdencmp('gbl',I,'sym4',2,thr,sorh,keepapp);
imwrite(im2uint8(mat2gray(de_I)), 'denoise_lena.bmp');
P361
function diff_im = anisodiff(im, num_iter, delta_t, k, option)
im = double(im);
% 赋初值
diff_im = im;
% 用以计算方向梯度的卷积模板
hN = [0 1 0; 0 -1 0; 0 0 0];
hS = [0 0 0; 0 -1 0; 0 1 0];
hE = [0 0 0; 0 -1 1; 0 0 0];
hW = [0 0 0; 1 -1 0; 0 0 0];
hNE = [0 0 1; 0 -1 0; 0 0 0];
hSE = [0 0 0; 0 -1 0; 0 0 1];
hSW = [0 0 0; 0 -1 0; 1 0 0];
hNW = [1 0 0; 0 -1 0; 0 0 0];
% 各向异性扩散滤波
for t = 1:num_iter
% 计算梯度
nablaN = conv2(diff_im,hN,'same');
nablaS = conv2(diff_im,hS,'same');
nablaW = conv2(diff_im,hW,'same');
nablaE = conv2(diff_im,hE,'same');
nablaNE = conv2(diff_im,hNE,'same');
nablaSE = conv2(diff_im,hSE,'same');
nablaSW = conv2(diff_im,hSW,'same');
nablaNW = conv2(diff_im,hNW,'same');
% 计算扩散系数
% OPTION 1： c(x,y,t) = exp(-(nablaI/kappa).^2)
if option == 1
cN = exp(-(nablaN/k).^2);
cS = exp(-(nablaS/k).^2);
cW = exp(-(nablaW/k).^2);
cE = exp(-(nablaE/k).^2);
cNE = exp(-(nablaNE/k).^2);
cSE = exp(-(nablaSE/k).^2);
cSW = exp(-(nablaSW/k).^2);
cNW = exp(-(nablaNW/k).^2);
% OPTION 2： c(x,y,t) = 1./(1 + (nablaI/kappa).^2)
elseif option == 2
cN = 1./(1 + (nablaN/k).^2);
cS = 1./(1 + (nablaS/k).^2);
cW = 1./(1 + (nablaW/k).^2);
cE = 1./(1 + (nablaE/k).^2);
cNE = 1./(1 + (nablaNE/k).^2);
cSE = 1./(1 + (nablaSE/k).^2);
cSW = 1./(1 + (nablaSW/k).^2);
cNW = 1./(1 + (nablaNW/k).^2);
end
% 计算一次迭代结果
diff_im = diff_im + delta_t*(...
cN.*nablaN + cS.*nablaS + cW.*nablaW + cE.*nablaE + ...
cNE.*nablaNE + cSE.*nablaSE + cSW.*nablaSW + cNW.*nablaNW );
end
P363
num_iter=50; delta_t=0.125;
k=4; option=2;
i = imread('noise_lena.bmp');
diff = anisodiff(i, num_iter, delta_t, k, option);
P370
function x=Thomas(N, alpha, beta, gama, d)
x=d;
m=zeros(1,N); l=zeros(1,N);
m(1)=alpha(1);
for i=2:N
l(i)=gama(i)/m(i-1);
m(i)=alpha(i)-l(i)*beta(i-1);
end
y=zeros(1,N);
y(1)=d(1);
for i=2:N
y(i)=d(i)-l(i)*y(i-1);
end
x=zeros(1,N);
x(N)=y(N)/m(N);
for i=N-1:-1:1
x(i)=(y(i)-beta(i)*x(i+1))/m(i);
end
P371
function Ig=gauss(I,ks,sigma2)
[Ny,Nx]=size(I);
hks=(ks-1)/2; % 高斯核的一半
%%- 一维卷积
if (Ny<ks)
x=(-hks:hks);
flt=exp(-(x.^2)/(2*sigma2)); % 一维高斯函数
flt=flt/sum(sum(flt)); % 归一化
x0=mean(I(:,1:hks)); xn=mean(I(:,Nx-hks+1:Nx));
eI=[x0*ones(Ny,ks) I xn*ones(Ny,ks)];
Ig=conv(eI,flt);
Ig=Ig(:,ks+hks+1:Nx+ks+hks);
else
%%- 二维卷积
x=ones(ks,1)*(-hks:hks); y=x';
flt=exp(-(x.^2+y.^2)/(2*sigma2)); % 二维高斯函数
flt=flt/sum(sum(flt)); % 归一化
if (hks>1)
xL=mean(I(:,1:hks)')'; xR=mean(I(:,Nx-hks+1:Nx)')';
else
xL=I(:,1); xR=I(:,Nx);
end
eI=[xL*ones(1,hks) I xR*ones(1,hks)];
if (hks>1)
xU=mean(eI(1:hks,:)); xD=mean(eI(Ny-hks+1:Ny,:));
else
xU=eI(1,:); xD=eI(Ny,:);
end
eI=[ones(hks,1)*xU; eI; ones(hks,1)*xD];
Ig=conv2(eI,flt,'valid');
end
P372
Img = imread('Lena.bmp');
Img = double(Img);
[nrow, ncol] = size(Img);
N=max(nrow, ncol);
%储存三对角矩阵
alpha=zeros(1,N); beta=zeros(1,N); gama=zeros(1,N);
%储存中间结果
u1=zeros([nrow, ncol]);
u2=zeros([nrow, ncol]);
timestep=5;
%用以控制迭代次数
%iterations = 2;
%for times = 1:iterations
I_temp=gauss(Img,3,1);
Ix = 0.5*(I_temp(:,[2:ncol,ncol])-I_temp(:,[1,1:ncol-1]));
Iy = 0.5*(I_temp([2:nrow,nrow],:)-I_temp([1,1:nrow-1],:));
K = 10
grad=Ix.^2+Iy.^2;
g=1./(1+grad/K*K); %边缘压迫因子
% 使用Thomas算法逐行求解u1
for i=1:nrow
beta(1)=-0.5*timestep*(g(i,2)+g(i,1));
alpha(1)=1-beta(1);
for j=2:ncol-1
beta(j)=-0.5*timestep*(g(i,j+1)+g(i,j));
gama(j)=-0.5*timestep*(g(i,j-1)+g(i,j));
alpha(j)=1-beta(j)-gama(j);
end
gama(ncol)=-0.5*timestep*(g(i,ncol)+g(i,ncol-1));
alpha(ncol)=1- gama(ncol);
u1(i,:)=Thomas(ncol,alpha,beta,gama,Img(i,:));
end
% 使用Thomas算法逐列求解u2
for j=1:ncol
beta(1)=-0.5*timestep*(g(2,j)+g(1,j));
alpha(1)=1-beta(1);
for i=2:nrow-1
beta(j)=-0.5*timestep*(g(i+1,j)+g(i,j));
gama(j)=-0.5*timestep*(g(i-1,j)+g(i,j));
alpha(j)=1-beta(j)-gama(j);
end
gama(nrow)=-0.5*timestep*(g(nrow,j)+g(nrow-1,j));
alpha(nrow)=1- gama(nrow);
u2(:,j)=Thomas(nrow,alpha,beta,gama,Img(:,j));
end
Img=0.5*(u1+u2);
% 显示处理结果
imshow(uint8(Img));
%end
（代码发布未完，请待后续...）
