I am working on ridge frequency estimation for which I have to obtain an blockwise oriented image. I have developed the code but unable to remove an error.
the process goes like this. Input image is G(m,n) and theta(m,n) is an image containing theta. Input image G is divide into w*w block (w = 17) and for each block centred at pixel(i,j) compute an oriented window of size l*w (33*17). For each block we have to compute the x signature as
x[0],x[1],x[2].....x[l-1]...
x[k] = 1/w * summation(d=0 to w-1)G(u,v)
u = i+ (d-(w/2))cos(theta(i,j))+(k-(l/2))sin(theta(i,j))
v = i+ (d-(w/2))sin(theta(i,j))+((l/2)-k)cos(theta(i,j))
here is my code
% To compute ridge frequency
theta_image; theta image as input
im = imread('cameraman.tif');
[m,n] = size(im);
l = (2*w-1);
w = 17;
ww = floor(w/2);
for i1 = 9:w:m
for j1 = 9:w:n
G = im(i1-ww:i1+ww,j1-ww:j1+ww);
O = theta(i1-ww:i1+ww,j1-ww:j1+ww);
G = padarray(G,[10 10],'both'); not sure its correct?
for k = 0:l-1
for d = 0:w-1
cnst_1 = (d-floor(w/2));
cnst_2 = (k-floor(l/2));
cnst_3 = (floor((l/2)-k);
u = i1+(cnst_1.*cos(O(i1,j1)) + cnst_2.*sin(O(i1,j1)));
v = j1+(cnst_1.*sin(O(i1,j1)) + cnst_3.*cos(O(i1,j1)));
u = fix(u);
v = fix(v);
store(k,d) = G(u,v);
x(k) = (sum(G(u,v)))/w; not sure will it be stored block-wise?
end;
end;
end;
end;
the error is
Attempted to access G(22,0); index must be a positive integer or logical.
Error in ridge_frequency (line 76)
store(k,d) = G(u,v);
Related
I want to compute gradient of a volume in MATLAB using Gaussian derivative. but I could not. can any one help me please? I do this in a 2D image using this code:
k = gaussiankernel(sigma1,1); % first order derivative of a gaussian with std
sigma1
gx = imfilter(I,k','replicate','conv');
gy = imfilter(I,k,'replicate','conv');
please help me. How can I compute gz using kernel k? or How can I extend this code to 3D?
Thank you in advance.
This is the code to generate adaptive ellipsoid using structuretensor3d:
function SE = AESE3(I,M,l1,l2,l3,phi3,theta3)
%I = input('Enter the input 3d volume: ');
%M = input('Enter the maximum allowed semi-major axes length: ');
% determining ellipsoid parameteres from eigen value decomposition of 3d
% structure tensor
row = size(I,1);
col = size(I,2);
hei = size(I,3);
SE = cell(row,col,hei);
padI = padarray(I,[M M M],'replicate','both');
padrow = size(padI,1);
padcol = size(padI,2);
padhei = size(padI,3);
[se_x,se_y,se_z] = meshgrid(-M:M,-M:M,-M:M);
for m = M+1:padrow-M
for n = M+1:padcol-M
for p = M+1:padhei-M
i = m-M;
j = n-M;
k = p-M;
a = (l1(i,j,k)+eps)/(l1(i,j,k)+l2(i,j,k)+l3(i,j,k)+3*eps)*M;
b = (l2(i,j,k)+eps)/(l1(i,j,k)+l2(i,j,k)+l3(i,j,k)+3*eps)*M;
c = (l3(i,j,k)+eps)/(l1(i,j,k)+l2(i,j,k)+l3(i,j,k)+3*eps)*M;
cos(phi3(i,j,k)) = cos_phi3;
sin(phi3(i,j,k)) = sin_phi3;
cos(theta3(i,j,k)) = cos_theta3;
sin(theta3(i,j,k)) = sin_theta3;
% defining structuring element for each pixel of image
se = ((se_x.*cos_theta3 - se_y.*sin_theta3.*cos_phi3 +
se_z.*sin_theta3.*sin_phi3).^2)./a.^2+((se_x.*sin_theta3 +
se_y.*cos_theta3.*cos_phi3 - se_z.*cos_theta3.*sin_phi3).^2)./b.^2+
((se_y.*sin_phi3 + se_z.*cos_phi3).^2)./c.^2 <= 1;
SE{i,j,k} = se;
end
end
end
end
Can I do this without zero padding?
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 am writing a graphical representation of numerical stability of differential operators and I am having trouble removing a nested for loop. The code loops through all entries in the X,Y, plane and calculates the stability value for each point. This is done by finding the roots of a polynomial of a size dependent on an input variable (length of input vector results in a polynomial 3d matrix of size(m,n,(lenght of input vector)). The main nested for loop is as follows.
for m = 1:length(z2)
for n = 1:length(z1)
pointpoly(1,:) = p(m,n,:);
r = roots(pointpoly);
if isempty(r),r=1e10;end
z(m,n) = max(abs(r));
end
end
The full code of an example numerical method (Trapezoidal Rule) is as follows. Any and all help is appreciated.
alpha = [-1 1];
beta = [.5 .5];
Wind = 2;
Wsize = 500;
if numel(Wind) == 1
Wind(4) = Wind(1);
Wind(3) = -Wind(1);
Wind(2) = Wind(4);
Wind(1) = Wind(3);
end
if numel(Wsize) == 1
Wsize(2) = Wsize;
end
z1 = linspace(Wind(1),Wind(2),Wsize(1));
z2 = linspace(Wind(3),Wind(4),Wsize(2));
[Z1,Z2] = meshgrid(z1,z2);
z = Z1+1i*Z2;
p = zeros(Wsize(2),Wsize(1),length(alpha));
for n = length(alpha):-1:1
p(:,:,(length(alpha)-n+1)) = alpha(n)-z*beta(n);
end
for m = 1:length(z2)
for n = 1:length(z1)
pointpoly(1,:) = p(m,n,:);
r = roots(pointpoly);
if isempty(r),r=1e10;end
z(m,n) = max(abs(r));
end
end
figure()
surf(Z1,Z2,z,'EdgeColor','None');
caxis([0 2])
cmap = jet(255);
cmap((127:129),:) = 0;
colormap(cmap)
view(2);
title(['Alpha Values (',num2str(alpha),') Beta Values (',num2str(beta),')'])
EDIT::
I was able to remove one of the for loops using the reshape command. So;
for m = 1:length(z2)
for n = 1:length(z1)
pointpoly(1,:) = p(m,n,:);
r = roots(pointpoly);
if isempty(r),r=1e10;end
z(m,n) = max(abs(r));
end
end
has now become
gg = reshape(p,[numel(p)/length(alpha) length(alpha)]);
r = zeros(numel(p)/length(alpha),1);
for n = 1:numel(p)/length(alpha)
temp = roots(gg(n,:));
if isempty(temp),temp = 0;end
r(n,1) = max(abs(temp));
end
z = reshape(r,[Wsize(2),Wsize(1)]);
This might be one for loop, but I am still going through the same number of elements. Is there a way to use the roots command on all of my rows at the same time?
I am trying to do a set of integrations for a particular value of psi and theta. These integrations are then combined into a formula to give P. The idea is then to do this for a set of psi and theta from 0 to pi/2 and then plot the results of P against a function of theta and psi.
I get two errors, firstly
integral2Calc>integral2t/tensor
not sure how to change the integral to make it the right dimensions to psi no longer being a scalar.
I also get Warning: Reached the maximum number of function evaluations (10000) for i3, is this a serious error, (as in has the integration not been computed) I tried changing the type of integration or changing the error tolerance and this seemed to have no effect on removing the actual error..
eta = input('Enter Dielectric Constant 1.5-4: ');
sdev = input('Enter STD DEV (roughness) maybe 0.1: ');
psi = [0:0.01:pi/2];
theta = [0:0.01:pi/2];
r = sqrt((sin(psi)).^2+(sin(theta).*(cos(psi))).^2);
calpha = (cos(theta+dtheta)).*(cos(psi+dpsi));
rp01 = calpha-sqrt(eta-1+((calpha).^2));
rp02 = calpha+sqrt(eta-1+((calpha).^2));
rperp = (rp01./rp02).^2;
rp11 = ((eta.*calpha)-sqrt(eta-1+((calpha).^2)));
rp12 = ((eta.*calpha)+sqrt(eta-1+((calpha).^2)));
rpar = (rp11./rp12).^2;
qthingy1 = ((sin(psi+dpsi)).^2)-((sin(theta+dtheta)).^2).*((cos(psi+dpsi)).^2);
qthingy2 = ((sin(psi+dpsi)).^2)+((sin(theta+dtheta)).^2).*((cos(psi+dpsi)).^2);
qthingy = qthingy1./qthingy2;
wthingy1 = (sin(2*(psi+dpsi))).*(sin(theta+dtheta));
wthingy2 = ((sin(psi+dpsi)).^2)+(sin((theta+dtheta)).^2).*((sin(psi+dpsi)).^2);
wthingy = wthingy1./wthingy2;
roughness = (cos(psi)./(2*pi*(sdev.^2))).*exp(-((cos(psi).*dtheta).^2+(dpsi).^2)/(2*sdev.^2));
fun = matlabFunction((rpar+rperp).*roughness,'vars',{dtheta,dpsi});
fun2 = matlabFunction(roughness,'vars',{dtheta,dpsi});
fun3 = matlabFunction((rpar+rperp).*roughness.*qthingy,'vars',{dtheta,dpsi});
fun4 = matlabFunction((rpar+rperp).*roughness.*wthingy,'vars',{dtheta,dpsi});
thetamax = (pi/2) - theta;
psimax = (pi/2) - psi;
A = integral2(fun2,-pi/2,pi/2,-pi/2,pi/2);
i1 = (integral2(fun,-pi/2,thetamax,-pi/2,psimax))./A;
q = 2 - i1;
i2 = (integral2(fun3,-pi/2,thetamax,-pi/2,psimax))./A;
i3 = (integral2(fun4,-pi/2,thetamax,-pi/2,psimax))./A;
P = sqrt(i2.^2+i3.^2)./i1
plot(P, r);
I'm trying to implement a very basic eigenface calculation in Matlab. It kind of works but I get only two meaningful eigenvalues - the rest are zero. The corresponding eigenvectors seem to be right since most of them will show an eigenface when converting to an image.
So why are most of my eigenvalues zero? I need them to be different from zero in order to sort the eigenfaces by their significance (greatest magnitude eigenvalues).
I am reading 400 images, each size h/w = 112/92 px
They can be found here: http://www.cl.cam.ac.uk/Research/DTG/attarchive/pub/data/att_faces.zip
The code:
clear all;
files = dir('eigenfaces2/training/*.pgm');
[numFaces, discard] = size(files);
h = 112;
w = 92;
s = h * w;
%calculate average face
avgFace = zeros(s, 1);
faces = [];
for i=1:numFaces
file = strcat('eigenfaces2/training/', files(i).name);
im = double(imread(file));
im = reshape(im, s, 1);
avgFace = avgFace + im;
faces(:,i) = im;
end
avgFace = avgFace ./ numFaces;
A = [];
for i=1:numFaces
diff = avgFace - faces(i);
A(:,i) = diff;
end
numEigs = 20;
L = (A' * A) / numFaces;
[tmpEigs, discard] = eigs(L, numEigs);
eigenfaces = [];
for i=1:numEigs
v = tmpEigs(:,i);
eigenfaces(:,i) = A * v;
end
%visualize largest eigenfaces
figure;
for i=1:numEigs
eigface = eigenfaces(:,i);
mmax = max(eigface);
mmin = min(eigface);
eigface = 255 .* (eigface-mmin) ./ (mmax-mmin);
eigface = reshape(eigface, h, w);
subplot(4,5,i); imshow(uint8(eigface));
end
I've don't have much experience with computer vision/image recognition, but I think you might want
diff = avgFace - faces(:,i);
in your second for loop. Otherwise it's just subtracting a constant from avgFace each time, and so A (and hence L) only gets a rank of 2.