Python denoising algorithm

The denoise algorithm in programming computer vision with Python is wrong, and the available code is posted on the web for later use.

The wrong code in the book:

defDenoise (im,u_init,tolerance=0.1,tau=0.125,tv_weight=100): M,n=Im.shape U=U_init Px=im Py=im Error= 1 while(Error >tolerance): Uold=U Gradux= Roll (U,-1,axis=1)-U Graduy= Roll (u,-1,axis=0)-U pxnew= Px + (tau/tv_weight) *Gradux pynew= Py + (tau/tv_weight) *Graduy normnew= Maximum (1,sqrt (pxnew**2+pynew**2)) Px= pxnew/normnew py= pynew/normnew rxpx= Roll (Px,1,axis=1) Rypy= Roll (py,1,axis=0) DIVP= (PX-RXPX) + (Py-rypy) U= im + tv_weight*DIVP Error= Linalg.norm (u-uold)/sqrt (nm)returnU,im-u

Code available on the Web:

defDenoise (IM, U_init, tolerance=0.1, tau=0.125, tv_weight=100):    """An implementation of the Rudin-osher-fatemi (ROF) denoising model using the numerical procedure presented in E Q. (one) of A. Chambolle (2005).            Implemented using periodic boundary conditions (essentially turning the rectangular image domain into a torus!). Input:im-noisy input Image (grayscale) u_init-initial guess for U tv_weight-weight Of the tv-regularizing term tau-steplength in the Chambolle algorithm tolerance-tolerance for Determinin G The Stop criterion Output:u-denoised and detextured image (also the primal variable) T-tex ture residual"""        #---initializationM,n = Im.shape#size of Noisy imageU=U_init Px= IM#X-component to the dual fieldPy = IM#Y-component of the dual fieldError = 1Iteration=0#---Main iteration     while(Error >tolerance): Uold=U#Gradient of primal variableLyu = Vstack ((u[1:,:],u[0,:]))#Left translation w.r.t. The y-directionLxU = Hstack ((U[:,1:],u.take ([0],axis=1))#Left translation w.r.t. The x-directionGradux= Lxu-u#x-component of U ' s gradientGraduy = Lyu-u#y-component of U ' s gradient        #First We update the dual variblePxnew = Px + (tau/tv_weight) *gradux#non-normalized update of x-component (dual)Pynew = Py + (tau/tv_weight) *graduy#non-normalized update of y-component (dual)Normnew = Maximum (1,sqrt (pxnew**2+pynew**2)) Px= Pxnew/normnew#Update of X-component (dual)Py = Pynew/normnew#Update of Y-component (dual)        #Then we update the primal variableRxpx =hstack ((Px.take ([ -1],axis=1), px[:,0:-1])#Right x-translation of X-componentRypy = Vstack ((py[-1,:],py[0:-1,:]))#Right y-translation of Y-componentDIVP = (px-rxpx) + (Py-rypy)#divergence of the dual field.U = im + TV_WEIGHT*DIVP#Update of the primal variable        #Update of Error-measureError = Linalg.norm (u-uold)/sqrt (nm); Iteration+ = 1; PrintIteration, Error#The texture residualT = im-UPrint 'Number of ROF iterations:', IterationreturnU,t

Test code:

 fromNumPyImport* fromNumPyImportRandom fromScipy.ndimageImportFiltersImportROF fromScipy.miscImportImsaveim= Zeros ((500,500)) im[100:400,100:400] = 128im[200:300,200:300] = 255im= im + 30*random.standard_normal (500,500)) Imsave ('synth_ori.pdf', IM) U,t= Rof.denoise (im,im,0.07) G= Filters.gaussian_filter (im,10) Imsave ('synth_rof.pdf', U) Imsave ('synth_gaussian.pdf'G