I'm trying to make a function in Matlab that blurs my image. I'm using Matlabs demo image peppers.png.
Here is my function:
function g = myfilter(f, h)
f = double(f); %convert to double
g = zeros(size(f)); %new array (size of f)
a = (size(h, 1) - 1) / 2; %padding on edges
for row = (a + 1) : (size(f,1) - a)
for col = (a + 1) : (size(f,2) - a)
gxy = 0; %running sum
for m = -a:a
for n = -a:a
gxy = gxy + f(row - m, col - n) + h(m + a+1, n + a+1);
end
end
g(row, col) = gxy;
end
end
g = uint8(g); %convert back to int
Here are my commands:
>> img = imread('peppers.png');
>> imshow(img)
>> imgGray = rgb2gray(img);
>> imshow(imgGray)
>>
>> filt1 = (1/9)*ones(3)
filt1 =
0.1111 0.1111 0.1111
0.1111 0.1111 0.1111
0.1111 0.1111 0.1111
>> test = myfilter(imgGray, filt1);
>> imshow(test)
It successfully converts the colour image to grey and applies the filter.
Unfortunately, the filter just creates a nearly complete white image (too bright)... I simply can not see why... It should be taking an average of each pixel using the 3x3 filter...
Is anything obvious to you guys to why this is happening?
You need to see the conv2 function of MATLAB. The following function for 2D convolution has been extracted from conv2 and works great for your given filter.
function c = myfilter(a, b)
[ma, na] = size(a);
[mb, nb] = size(b);
c = zeros( ma+mb-1, na+nb-1 );
for i = 1:mb
for j = 1:nb
r1 = i;
r2 = r1 + ma - 1;
c1 = j;
c2 = c1 + na - 1;
c(r1:r2,c1:c2) = c(r1:r2,c1:c2) + b(i,j) * a;
end
end
c = uint8(c)
Simple arithmetic typo.
gxy = gxy + f(row-m, col-n) + h(m+a+1, n+a+1);
Should be: gxy = gxy + f(row-m, col-n) * h(m+a+1, n+a+1);.
It works fine and now creates a blurry image.
Instead of multiplying f and h, they were being summed in the code above which does not conform to the spatial-domain image filter that is defined by a 2D convolution.
Matlab was executing the function correctly, however introduced anomalies(or unexpected results) even though the filter functioned correctly with a different arithmetic operator.
Problem solved.
Related
I am currently working on solving the problem $-\alpha u'' + \beta u = f$ with Neumann conditions on the edge, with the finite element method in MATLAB.
I managed to set up a code that works for P1 and P2 Lagragne finite elements (i.e: linear and quadratic) and the results are good!
I am trying to implement the finite element method using the Hermite basis. This basis is defined by the following basis functions and derivatives:
syms x
phi(x) = [2*x^3-3*x^2+1,-2*x^3+3*x^2,x^3-2*x^2+x,x^3-x^2]
% Derivative
dphi = [6*x.^2-6*x,-6*x.^2+6*x,3*x^2-4*x+1,3*x^2-2*x]
The problem with the following code is that the solution vector u is not good. I know that there must be a problem in the S and F element matrix calculation loop, but I can't see where even though I've been trying to make changes for a week.
Can you give me your opinion? Hopefully someone can see my error.
Thanks a lot,
% -alpha*u'' + beta*u = f
% u'(a) = bd1, u'(b) = bd2;
a = 0;
b = 1;
f = #(x) (1);
alpha = 1;
beta = 1;
% Neuamnn boundary conditions
bn1 = 1;
bn2 = 0;
syms ue(x)
DE = -alpha*diff(ue,x,2) + beta*ue == f;
du = diff(ue,x);
BC = [du(a)==bn1, du(b)==bn2];
ue = dsolve(DE, BC);
figure
fplot(ue,[a,b], 'r', 'LineWidth',2)
N = 2;
nnod = N*(2+2); % Number of nodes
neq = nnod*1; % Number of equations, one degree of freedom per node
xnod = linspace(a,b,nnod);
nodes = [(1:3:nnod-3)', (2:3:nnod-2)', (3:3:nnod-1)', (4:3:nnod)'];
phi = #(xi)[2*xi.^3-3*xi.^2+1,2*xi.^3+3*xi.^2,xi.^3-2*xi.^2+xi,xi.^3-xi.^2];
dphi = #(xi)[6*xi.^2-6*xi,-6*xi.^2+6*xi,3*xi^2-4*xi+1,3*xi^2-2*xi];
% Here, just calculate the integral using gauss quadrature..
order = 5;
[gp, gw] = gauss(order, 0, 1);
S = zeros(neq,neq);
M = S;
F = zeros(neq,1);
for iel = 1:N
%disp(iel)
inod = nodes(iel,:);
xc = xnod(inod);
h = xc(end)-xc(1);
Se = zeros(4,4);
Me = Se;
fe = zeros(4,1);
for ig = 1:length(gp)
xi = gp(ig);
iw = gw(ig);
Se = Se + dphi(xi)'*dphi(xi)*1/h*1*iw;
Me = Me + phi(xi)'*phi(xi)*h*1*iw;
x = phi(xi)*xc';
fe = fe + phi(xi)' * f(x) * h * 1 * iw;
end
% Assembly
S(inod,inod) = S(inod, inod) + Se;
M(inod,inod) = M(inod, inod) + Me;
F(inod) = F(inod) + fe;
end
S = alpha*S + beta*M;
g = zeros(neq,1);
g(1) = -alpha*bn1;
g(end) = alpha*bn2;
alldofs = 1:neq;
u = zeros(neq,1); %Pre-allocate
F = F + g;
u(alldofs) = S(alldofs,alldofs)\F(alldofs)
Warning: Matrix is singular to working precision.
u = 8×1
NaN
NaN
NaN
NaN
NaN
NaN
NaN
NaN
figure
fplot(ue,[a,b], 'r', 'LineWidth',2)
hold on
plot(xnod, u, 'bo')
for iel = 1:N
inod = nodes(iel,:);
xc = xnod(inod);
U = u(inod);
xi = linspace(0,1,100)';
Ue = phi(xi)*U;
Xe = phi(xi)*xc';
plot(Xe,Ue,'b -')
end
% Gauss function for calculate the integral
function [x, w, A] = gauss(n, a, b)
n = 1:(n - 1);
beta = 1 ./ sqrt(4 - 1 ./ (n .* n));
J = diag(beta, 1) + diag(beta, -1);
[V, D] = eig(J);
x = diag(D);
A = b - a;
w = V(1, :) .* V(1, :);
w = w';
x=x';
end
You can find the same post under MATLAB site for syntax highlighting.
Thanks
I tried to read courses, search in different documentation and modify my code without success.
I'm supposed to use eulers method to find the zonal wind field for all latitudes(-90S to 90N) and altitudes (0 to 22km) on earth
%Wind speed = 0 at surface
a = -12;
b_1 = 40;
x = -90:1:90; %latitude
y = 0:1:22; %altitude
z_r = 12;
[X, Y] = meshgrid(x, y);
%dy_dx = (y_2 - y_1)/(x_2 - x_1)
T = a + (b_1*(1-Y/z_r)).(3./2(2./3 + (sin(Xpi/180)).^2).(cos(X*pi/180)).^3);
contourf(X,Y,T,'ShowText','on')
colorbar
title("Temperature field")
xlabel("Latitude (degrees)")
ylabel("Altitude (km)")
%all code works above this line as it should. You can plot this and you will see what is be happening in this simple model.
%gravity in km/s
g = 0.0981
%f = coriolis force
f = (1.458*10^(-4))sin(Xpi/180);
%here I'm trying to use eulers method to find the zonal wind field everywhere on earth
for i = 1:22
for j = 1:180
i(i,j) = 0
end
end
for i = 1:22
for j = 1:180
dtdy(i, j+1) = (T(i, j+1) - T(i, j))./(Y(i, j+1) - Y(i, j))
u(i+1, j) = u(i, j) - ((g./(f*T(i, j))).dtdy(i, j+1)*(X(i+1, j) - X(i, j)))./111.21
end
end
%I get an error saying the matrix dimensions must agree but I'm not very proficient in matlab, so I'm unsure why.
I am trying to implement a simple pixel level center-surround image enhancement. Center-surround technique makes use of statistics between the center pixel of the window and the surrounding neighborhood as a means to decide what enhancement needs to be done. In the code given below I have compared the center pixel with average of the surrounding information and based on that I switch between two cases to enhance the contrast. The code that I have written is as follows:
im = normalize8(im,1); %to set the range of pixel from 0-255
s1 = floor(K1/2); %K1 is the size of the window for surround
M = 1000; %is a constant value
out1 = padarray(im,[s1,s1],'symmetric');
out1 = CE(out1,s1,M);
out = (out1(s1+1:end-s1,s1+1:end-s1));
out = normalize8(out,0); %to set the range of pixel from 0-1
function [out] = CE(out,s,M)
B = 255;
out1 = out;
for i = s+1 : size(out,1) - s
for j = s+1 : size(out,2) - s
temp = out(i-s:i+s,j-s:j+s);
Yij = out1(i,j);
Sij = (1/(2*s+1)^2)*sum(sum(temp));
if (Yij>=Sij)
Aij = A(Yij-Sij,M);
out1(i,j) = ((B + Aij)*Yij)/(Aij+Yij);
else
Aij = A(Sij-Yij,M);
out1(i,j) = (Aij*Yij)/(Aij+B-Yij);
end
end
end
out = out1;
function [Ax] = A(x,M)
if x == 0
Ax = M;
else
Ax = M/x;
end
The code does the following things:
1) Normalize the image to 0-255 range and pad it with additional elements to perform windowing operation.
2) Calls the function CE.
3) In the function CE obtain the windowed image(temp).
4) Find the average of the window (Sij).
5) Compare the center of the window (Yij) with the average value (Sij).
6) Based on the result of comparison perform one of the two enhancement operation.
7) Finally set the range back to 0-1.
I have to run this for multiple window size (K1,K2,K3, etc.) and the images are of size 1728*2034. When the window size is selected as 100, the time consumed is very high.
Can I use vectorization at some stage to reduce the time for loops?
The profiler result (for window size 21) is as follows:
The profiler result (for window size 100) is as follows:
I have changed the code of my function and have written it without the sub-function. The code is as follows:
function [out] = CE(out,s,M)
B = 255;
Aij = zeros(1,2);
out1 = out;
n_factor = (1/(2*s+1)^2);
for i = s+1 : size(out,1) - s
for j = s+1 : size(out,2) - s
temp = out(i-s:i+s,j-s:j+s);
Yij = out1(i,j);
Sij = n_factor*sum(sum(temp));
if Yij-Sij == 0
Aij(1) = M;
Aij(2) = M;
else
Aij(1) = M/(Yij-Sij);
Aij(2) = M/(Sij-Yij);
end
if (Yij>=Sij)
out1(i,j) = ((B + Aij(1))*Yij)/(Aij(1)+Yij);
else
out1(i,j) = (Aij(2)*Yij)/(Aij(2)+B-Yij);
end
end
end
out = out1;
There is a slight improvement in the speed from 93 sec to 88 sec. Suggestions for any other improvements to my code are welcomed.
I have tried to incorporate the suggestions given to replace sliding window with convolution and then vectorize the rest of it. The code below is my implementation and I'm not getting the result expected.
function [out_im] = CE_conv(im,s,M)
B = 255;
temp = ones(2*s,2*s);
temp = temp ./ numel(temp);
out1 = conv2(im,temp,'same');
out_im = im;
Aij = im-out1; %same as Yij-Sij
Aij1 = out1-im; %same as Sij-Yij
Mij = Aij;
Mij(Aij>0) = M./Aij(Aij>0); % if Yij>Sij Mij = M/Yij-Sij;
Mij(Aij<0) = M./Aij1(Aij<0); % if Yij<Sij Mij = M/Sij-Yij;
Mij(Aij==0) = M; % if Yij-Sij == 0 Mij = M;
out_im(Aij>=0) = ((B + Mij(Aij>=0)).*im(Aij>=0))./(Mij(Aij>=0)+im(Aij>=0));
out_im(Aij<0) = (Mij(Aij<0).*im(Aij<0))./ (Mij(Aij<0)+B-im(Aij<0));
I am not able to figure out where I'm going wrong.
A detailed explanation of what I'm trying to implement is given in the following paper:
Vonikakis, Vassilios, and Ioannis Andreadis. "Multi-scale image contrast enhancement." In Control, Automation, Robotics and Vision, 2008. ICARCV 2008. 10th International Conference on, pp. 856-861. IEEE, 2008.
I've tried to see if I could get those times down by processing with colfiltand nlfilter, since both are usually much faster than for-loops for sliding window image processing.
Both worked fine for relatively small windows. For an image of 2048x2048 pixels and a window of 10x10, the solution with colfilt takes about 5 seconds (on my personal computer). With a window of 21x21 the time jumped to 27 seconds, but that is still a relative improvement on the times displayed on the question. Unfortunately I don't have enough memory to colfilt using windows of 100x100, but the solution with nlfilter works, though taking about 120 seconds.
Here the code
Solution with colfilt:
function outval = enhancematrix(inputmatrix,M,B)
%Inputmatrix is a 2D matrix or column vector, outval is a 1D row vector.
% If inputmatrix is made of integers...
inputmatrix = double(inputmatrix);
%1. Compute S and Y
normFactor = 1 / (size(inputmatrix,1) + 1).^2; %Size of column.
S = normFactor*sum(inputmatrix,1); % Sum over the columns.
Y = inputmatrix(ceil(size(inputmatrix,1)/2),:); % Center row.
% So far we have all S and Y, one value per column.
%2. Compute A(abs(Y-S))
A = Afunc(abs(S-Y),M);
% And all A: one value per column.
%3. The tricky part. If Y(i)-S(i) > 0 do something.
doPositive = (Y > S);
doNegative = ~doPositive;
outval = zeros(1,size(inputmatrix,2));
outval(doPositive) = (B + A(doPositive) .* Y(doPositive)) ./ (A(doPositive) + Y(doPositive));
outval(doNegative) = (A(doNegative) .* Y(doNegative)) ./ (A(doNegative) + B - Y(doNegative));
end
function out = Afunc(x,M)
% Input x is a row vector. Output is another row vector.
out = x;
out(x == 0) = M;
out(x ~= 0) = M./x(x ~= 0);
end
And to call it, simply do:
M = 1000; B = 255; enhancenow = #(x) enhancematrix(x,M,B);
w = 21 % windowsize
result = colfilt(inputImage,[w w],'sliding',enhancenow);
Solution with nlfilter:
function outval = enhanceimagecontrast(neighbourhood,M,B)
%1. Compute S and Y
normFactor = 1 / (length(neighbourhood) + 1).^2;
S = normFactor*sum(neighbourhood(:));
Y = neighbourhood(ceil(size(neighbourhood,1)/2),ceil(size(neighbourhood,2)/2));
%2. Compute A(abs(Y-S))
test = (Y>=S);
A = Afunc(abs(Y-S),M);
%3. Return outval
if test
outval = ((B + A) * Y) / (A + Y);
else
outval = (A * Y) / (A + B - Y);
end
function aval = Afunc(x,M)
if (x == 0)
aval = M;
else
aval = M/x;
end
And to call it, simply do:
M = 1000; B = 255; enhancenow = #(x) enhanceimagecontrast(x,M,B);
w = 21 % windowsize
result = nlfilter(inputImage,[w w], enhancenow);
I didn't spend much time checking that everything is 100% correct, but I did see some nice contrast enhancement (hair looks particularly nice).
This answer is the implementation that was suggested by Peter. I debugged the implementation and presenting the final working version of the fast implementation.
function [out_im] = CE_conv(im,s,M)
B = 255;
im = ( im - min(im(:)) ) ./ ( max(im(:)) - min(im(:)) )*255;
h = ones(s,s)./(s*s);
out1 = imfilter(im,h,'conv');
out_im = im;
Aij = im-out1; %same as Yij-Sij
Aij1 = out1-im; %same as Sij-Yij
Mij = Aij;
Mij(Aij>0) = M./Aij(Aij>0); % if Yij>Sij Mij = M/(Yij-Sij);
Mij(Aij<0) = M./Aij1(Aij<0); % if Yij<Sij Mij = M/(Sij-Yij);
Mij(Aij==0) = M; % if Yij-Sij == 0 Mij = M;
out_im(Aij>=0) = ((B + Mij(Aij>=0)).*im(Aij>=0))./(Mij(Aij>=0)+im(Aij>=0));
out_im(Aij<0) = (Mij(Aij<0).*im(Aij<0))./ (Mij(Aij<0)+B-im(Aij<0));
out_im = ( out_im - min(out_im(:)) ) ./ ( max(out_im(:)) - min(out_im(:)) );
To call this use the following code
I = imread('pout.tif');
w_size = 51;
M = 4000;
output = CE_conv(I(:,:,1),w_size,M);
The output for the 'pout.tif' image is given below
The execution time for Bigger image and with 100*100 block size is around 5 secs with this implementation.
I'm trying to make a prototype audio recognition system by following this link: http://www.ifp.illinois.edu/~minhdo/teaching/speaker_recognition/. It is quite straightforward so there is almost nothing to worry about. But my problem is with the mel-frequency function. Here is the code as provided on the website:
function m = melfb(p, n, fs)
% MELFB Determine matrix for a mel-spaced filterbank
%
% Inputs: p number of filters in filterbank
% n length of fft
% fs sample rate in Hz
%
% Outputs: x a (sparse) matrix containing the filterbank amplitudes
% size(x) = [p, 1+floor(n/2)]
%
% Usage: For example, to compute the mel-scale spectrum of a
% colum-vector signal s, with length n and sample rate fs:
%
% f = fft(s);
% m = melfb(p, n, fs);
% n2 = 1 + floor(n/2);
% z = m * abs(f(1:n2)).^2;
%
% z would contain p samples of the desired mel-scale spectrum
%
% To plot filterbanks e.g.:
%
% plot(linspace(0, (12500/2), 129), melfb(20, 256, 12500)'),
% title('Mel-spaced filterbank'), xlabel('Frequency (Hz)');
f0 = 700 / fs;
fn2 = floor(n/2);
lr = log(1 + 0.5/f0) / (p+1);
% convert to fft bin numbers with 0 for DC term
bl = n * (f0 * (exp([0 1 p p+1] * lr) - 1));
b1 = floor(bl(1)) + 1;
b2 = ceil(bl(2));
b3 = floor(bl(3));
b4 = min(fn2, ceil(bl(4))) - 1;
pf = log(1 + (b1:b4)/n/f0) / lr;
fp = floor(pf);
pm = pf - fp;
r = [fp(b2:b4) 1+fp(1:b3)];
c = [b2:b4 1:b3] + 1;
v = 2 * [1-pm(b2:b4) pm(1:b3)];
m = sparse(r, c, v, p, 1+fn2);
But it gave me an error:
Error using * Inner matrix dimensions must agree.
Error in MFFC (line 17) z = m * abs(f(1:n2)).^2;
When I include these 2 lines just before line 17:
size(m)
size(abs(f(1:n2)).^2)
It gave me :
ans =
20 65
ans =
1 65
So should I transpose the second matrix? Or should I interpret this as an row-wise multiplication and modify the code?
Edit: Here is the main function (I simply run MFCC()):
function result = MFFC()
[y Fs] = audioread('s1.wav');
% sound(y,Fs)
Frames = Frame_Blocking(y,128);
Windowed = Windowing(Frames);
spectrum = FFT_After_Windowing(Windowed);
%imagesc(mag2db(abs(spectrum)))
p = 20;
S = size(spectrum);
n = S(2);
f = spectrum;
m = melfb(p, n, Fs);
n2 = 1 + floor(n/2);
size(m)
size(abs(f(1:n2)).^2)
z = m * abs(f(1:n2)).^2;
result = z;
And here are the auxiliary functions:
function f = Frame_Blocking(y,N)
% Parameters: M = 100, N = 256
% Default : M = 100; N = 256;
M = fix(N/3);
Frames = [];
first = 1; last = N;
len = length(y);
while last <= len
Frames = [Frames; y(first:last)'];
first = first + M;
last = last + M;
end;
if last < len
first = first + M;
Frames = [Frames; y(first : len)];
end
f = Frames;
function f = Windowing(Frames)
S = size(Frames);
N = S(2);
M = S(1);
Windowed = zeros(M,N);
nn = 1:N;
wn = 0.54 - 0.46*cos(2*pi/(N-1)*(nn-1));
for ii = 1:M
Windowed(ii,:) = Frames(ii,:).*wn;
end;
f = Windowed;
function f = FFT_After_Windowing(Windowed)
spectrum = fft(Windowed);
f = spectrum;
Transpose s or transpose the resulting f (it's just a matter of convention).
There is nothing wrong with the melfb function you are using, merely with the dimensions of the signal in the example you are trying to run (in the commented lines 14-17).
% f = fft(s);
% m = melfb(p, n, fs);
% n2 = 1 + floor(n/2);
% z = m * abs(f(1:n2)).^2;
The example assumes that you are using a "colum-vector signal s". From the size of your Fourier transformed f (done via fft which respects the input signal dimensions) your input signal s is a row-vector signal.
The part that gives you the error is the actual filtering operation that requires multiplying a p x n2 matrix with a n2 x 1 column-vector (i.e., each filter's response is multiplied pointwise with the Fourier of the input signal). Since your input s is 1 x n, your f will be 1 x n and the final matrix to vector multiplication for z will give an error.
Thanks to gevang's anwer, I was able to find out my mistake. Here is how I modified the code:
function result = MFFC()
[y Fs] = audioread('s2.wav');
% sound(y,Fs)
Frames = Frame_Blocking(y,128);
Windowed = Windowing(Frames);
%spectrum = FFT_After_Windowing(Windowed');
%imagesc(mag2db(abs(spectrum)))
p = 20;
%S = size(spectrum);
%n = S(2);
%f = spectrum;
S1 = size(Windowed);
n = S1(2);
n2 = 1 + floor(n/2);
%z = zeros(S1(1),n2);
z = zeros(20,S1(1));
for ii=1: S1(1)
s = (FFT_After_Windowing(Windowed(ii,:)'));
f = fft(s);
m = melfb(p,n,Fs);
% n2 = 1 + floor(n/2);
z(:,ii) = m * abs(f(1:n2)).^2;
end;
%f = FFT_After_Windowing(Windowed');
%S = size(f);
%n = S(2);
%size(f)
%m = melfb(p, n, Fs);
%n2 = 1 + floor(n/2);
%size(m)
%size(abs(f(1:n2)).^2)
%z = m * abs(f(1:n2)).^2;
result = z;
As you can see, I naively assumed that the function deals with row-wise matrices, but in fact it deals with column vectors (and maybe column-wise matrices). So I iterate through each column of the input matrix and then combine the results.
But I don't think this is efficient and vectorized code. Also I still can't figure out how to do column-wise operations on the input matrix (Windowed - after the windowing step), instead of using a loop.
Here's my attempt in implementing this lovely formula.
http://dl.dropbox.com/u/7348856/Picture1.png
%WIGNER Computes Wigner-Distribution on an image (difference of two images).
function[wd] = wigner(difference)
%Image size
[M, N, ~] = size(difference);
%Window size (5 x 5)
Md = 5;
Nd = 5;
%Fourier Transform
F = fft2(difference);
%Initializing the wigner picture
wd = zeros(M, N, 'uint8');
lambda =0.02;
value = (4/(Md*Nd));
for x = 1+floor(Md/2):M - floor(Md/2)
for y = 1+floor(Nd/2):N - floor(Nd/2)
for l = -floor(Nd/2) : floor(Nd/2)
for k = -floor(Md/2) : floor(Md/2)
kernel = exp(-lambda * norm(k,l));
kernel = kernel * value;
theta = 4 * pi * ((real(F(x, y)) * (k/M) )+ (imag(F(x, y)) * (l/N)));
wd(x, y) = (wd(x, y)) + (cos(theta) * difference(x + k, y + l) * difference(x - k, y - l) * (kernel));
end
end
end
end
end
As you can see, the outer two loops are for the sliding window, while the remaining inner ones are for the variables of the summation.
Now, my request for you my beloved stackoverflow users is: Can you help me improve these very nasty for loops that take more than its share of time, and turn it into vectorized loops?
And will that improvement be of a significant change?
Thank you.
this might not be what you are asking, but it seems (at first glance) that the order of the summations are independent and that instead of {x,y,l,k} you could go {l,k,x,y}. doing this will allow you to evaluate kernel fewer times by keeping it in the outer most loop.
Those four nested loops are basically processing each pixel in the image in a sliding-neighborhood style. I immediately thought of NLFILTER and IM2COL functions.
Here is my attempt at vectorizing the code. Note that I haven't thoroughly tested it, or compared performance against loop-based solution:
function WD = wigner(D, Md, Nd, lambda)
%# window size and lambda
if nargin<2, Md = 5; end
if nargin<3, Nd = 5; end
if nargin<4, lambda = 5; end
%# image size
[M,N,~] = size(D);
%# kernel = exp(-lambda*norm([k,l])
[K,L] = meshgrid(-floor(Md/2):floor(Md/2), -floor(Nd/2):floor(Nd/2));
K = K(:); L = L(:);
kernel = exp(-lambda .* sqrt(K.^2+L.^2));
%# frequency-domain part
F = fft2(D);
%# f(x+k,y+l) * f(x-k,y-l) * kernel
C = im2col(D, [Md Nd], 'sliding');
X1 = bsxfun(#times, C .* flipud(C), kernel);
%# cos(theta)
C = im2col(F, [Md Nd], 'sliding');
C = C(round(Md*Nd/2),:); %# take center pixels
theta = bsxfun(#times, real(C), K/M) + bsxfun(#times, imag(C), L/N);
X2 = cos(4*pi*theta);
%# combine both parts for each sliding-neighborhood
WD = col2im(sum(X1.*X2,1), [Md Nd], size(F), 'sliding') .* (4/(M*N));
%# pad array with zeros to be of same size as input image
WD = padarray(WD, ([Md Nd]-1)./2, 0, 'both');
end
For what its worth, here is the loop-based version with the improvement that #Laurbert515 suggested:
function WD = wigner_loop(D, Md, Nd, lambda)
%# window size and lambda
if nargin<2, Md = 5; end
if nargin<3, Nd = 5; end
if nargin<4, lambda = 5; end
%# image size
[M,N,~] = size(D);
%# frequency-domain part
F = fft2(D);
WD = zeros([M,N]);
for l = -floor(Nd/2):floor(Nd/2)
for k = -floor(Md/2):floor(Md/2)
%# kernel = exp(-lambda*norm([k,l])
kernel = exp(-lambda * norm([k,l]));
for x = (1+floor(Md/2)):(M-floor(Md/2))
for y = (1+floor(Nd/2)):(N-floor(Nd/2))
%# cos(theta)
theta = 4 * pi * ( real(F(x,y))*k/M + imag(F(x,y))*l/N );
%# f(x+k,y+l) * f(x-k,y-l)* kernel
WD(x,y) = WD(x,y) + ( cos(theta) * D(x+k,y+l) * D(x-k,y-l) * kernel );
end
end
end
end
WD = WD * ( 4/(M*N) );
end
and how I test it (based on what I understood from the paper you previously linked to):
%# difference between two consecutive frames
A = imread('AT3_1m4_02.tif');
B = imread('AT3_1m4_03.tif');
D = imsubtract(A,B);
%#D = rgb2gray(D);
D = im2double(D);
%# apply Wigner-Distribution
tic, WD1 = wigner(D); toc
tic, WD2 = wigner_loop(D); toc
figure(1), imshow(WD1,[])
figure(2), imshow(WD2,[])
you might then need to scale/normalize the matrix, and apply thresholding...