L0 Smoothing 笔记（二）

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本篇主要记录Image Smoothing via L0 Gradient Minimization这篇论文的MATLAB代码以及笔者改写的python代码。笔者初学python，若代码有不合理之处，还望读者指正。

（一）原文的MATLAB代码：

function S = L0Smoothing(Im, lambda, kappa)if ~exist('kappa','var')    kappa = 2.0;endif ~exist('lambda','var')    lambda = 2e-2;endS = 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]);endbeta = 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('.');endfprintf('\n');end

(二)python代码：

def psf2otf(psf,size):import numpy as npif not(0 in psf):#Pad the PSF to outsizepsf=np.double(psf)psfsize=np.shape(psf)psfsize=np.array(psfsize)padsize=size-psfsizepsf=np.lib.pad(psf,((0,padsize[0]),(0,padsize[1])),'constant')#Circularly shift otf so that the "center" of the PSF is at the (1,1) element of the array.psf=np.roll(psf,-np.array(np.floor(psfsize/2),'i'),axis=(0,1))#Compute the OTFotf=np.fft.fftn(psf,axes=(0,1))#Estimate the rough number of operations involved in the computation of the FFT.nElem=np.prod(psfsize,axis=0)nOps=0for k in range(0,np.ndim(psf)):nffts=nElem/psfsize[k]nOps=nOps+psfsize[k]*np.log2(psfsize[k])*nfftsmx1=(abs(np.imag(otf[:])).max(0)).max(0)mx2=(abs(otf[:]).max(0)).max(0)eps= 2.2204e-16if mx1/mx2<=nOps*eps:otf=np.real(otf)else:otf=np.zeros(size)return otfdef L0Smoothing(Im,lamda=2e-2,kappa=2.0):import numpy as npS=Im/255betamax=1e5fx=np.array([[1,-1]])fy=np.array([[1],[-1]])N,M,D=np.shape(Im)sizeI2D=np.array([N,M])otfFx=psf2otf(fx,sizeI2D)otfFy=psf2otf(fy,sizeI2D)Normin1=np.fft.fft2(S,axes=(0,1))Denormin2=abs(otfFx)**2+abs(otfFy)**2if D>1:D2=np.zeros((N,M,D),dtype=np.double)for i in range(D):D2[:,:,i]=Denormin2Denormin2=D2beta=lamda*2while beta<betamax:Denormin=1+beta*Denormin2#h-v subproblemh1=np.diff(S,1,1)h2=np.reshape(S[:,0],(N,1,3))-np.reshape(S[:,-1],(N,1,3))h=np.hstack((h1,h2))v1=np.diff(S,1,0)v2=np.reshape(S[0,:],(1,M,3))-np.reshape(S[-1,:],(1,M,3))v=np.vstack((v1,v2))if D==1:t=(h**2+v**2)<lamda/betaelse:t=np.sum((h**2+v**2),2)<lamda/betat1=np.zeros((N,M,D),dtype=np.bool)for i in range(D):t1[:,:,i]=tt=t1h[t]=0v[t]=0#S subproblemNormin2=np.hstack((np.reshape(h[:,-1],(N,1,3))-np.reshape(h[:,0],(N,1,3)),-np.diff(h,1,1)))Normin2=Normin2+np.vstack((np.reshape(v[-1,:],(1,M,3))-np.reshape(v[0,:],(1,M,3)),-np.diff(v,1,0)))FS=(Normin1+beta*np.fft.fft2(Normin2,axes=(0,1)))/DenorminS=np.real(np.fft.ifft2(FS,axes=(0,1)))beta*=kappaprint('.')print('\n')return Sdef main():import PILimport numpy as npimport pylabIm=np.array(PIL.Image.open("文件名"),'d')S=L0Smoothing(Im,0.01)pylab.imshow(S)main()

该代码的处理效果：

另外，看到的几个用其它代码编写的程序链接：

1、http://blog.csdn.net/panda1234lee/article/details/52825113

2、http://download.csdn.net/download/bluecol/9175395

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