武汉理工大学数字图像处理英文课件 Chapter5（5）.pptVIP

Laplacian Filter Study Image of Gaussian Function Image of Laplacian of Gaussian Function Plot rms error vs. alpha Finding Alpha for Minimum Error Matlab Function imnorm * Construct a 256 x 256 image of the function gaus(r) = exp(-pi*r^2) over the domain -1.5 (x,y) 1.5. Then construct an image of the Laplacian of gaus(r) over the same domain. Find the rms difference between this image and those constructed by applying a Laplacian convolution filter to the original image. Plot the rms difference as a function of alpha. Find the value of alpha that minimizes this difference. global m1 m2 z lz range steps; range = 3; steps = 256; x = linspace(-range/2,range/2,steps); y = -x; x = ones(steps,1)*x; y = y * ones(1,steps); r2 = x.*x + y.*y; z = exp(-pi*r2); view = imnorm(z); imshow(view); imwrite(view,gaus.jpg); lz = -4*pi*(pi*r2-1).*exp(-pi*r2); view = imnorm(lz); imshow(view); imwrite(view,lgaus.jpg); The image constructed is the negative of the Laplacian. m1 = [0 1 0; 1 -4 1; 0 1 0]; m2 = [1 0 1; 0 -4 0; 1 0 1]; clear rms_error lmin = -.5; lmax = 0.5; lsteps = 31; for i = 0:(lsteps-1) a = lmin+ (lmax-lmin)*i/(lsteps-1); rms_error(i+1) = func(a); end %Plot the Error Graph plot(linspace(lmin,lmax,lsteps),rms_error); title(RMS Error vs. Alpha); xlabel(Alpha); ylabel(RMS Error); -0.5 0 0.5 2 4 6 8 x 10 -4 RMS Error vs. Alpha Alpha RMS Error function error = func(v) global m1 m2 z lz range steps a = v(1); lap = ((1-a)*m1+a*m2)/(1+a); zlap = -filter2(lap,z,valid)/(range/(steps-1))^2; diff = zlap-lz; error = sqrt(mean(diff(:).^2)); %Determine the Best Alpha based upon RMS Error amin = fminsearch(@func,0) %Show the Best Laplacian Matrix lap = ((1-amin).*m1+amin.*m2)/(1+amin) amin = -0.2174 lap = -0.2779 1.5557 -0.2779 1.5557 -5.1114 1.5557 -0.2779 1.5557 -0.2779 The final results are function out = imnorm(inp) % IMNORM % out = imnorm(inp) % normalizes input image between (0..1) % for unipolar image divide by the maximum val