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?
Related
I'm trying to write an image compression script in MATLAB using multilayer 3D DWT(color image). along the way, I want to apply thresholding on coefficient matrices, both global and local thresholds.
I like to use the formula below to calculate my local threshold:
where sigma is variance and N is the number of elements.
Global thresholding works fine; but my problem is that the calculated local threshold is (most often!) greater than the maximum band coefficient, therefore no thresholding is applied.
Everything else works fine and I get a result too, but I suspect the local threshold is miscalculated. Also, the resulting image is larger than the original!
I'd appreciate any help on the correct way to calculate the local threshold, or if there's a pre-set MATLAB function.
here's an example output:
here's my code:
clear;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%% COMPRESSION %%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% read base image
% dwt 3/5-L on base images
% quantize coeffs (local/global)
% count zero value-ed coeffs
% calculate mse/psnr
% save and show result
% read images
base = imread('circ.jpg');
fam = 'haar'; % wavelet family
lvl = 3; % wavelet depth
% set to 1 to apply global thr
thr_type = 0;
% global threshold value
gthr = 180;
% convert base to grayscale
%base = rgb2gray(base);
% apply dwt on base image
dc = wavedec3(base, lvl, fam);
% extract coeffs
ll_base = dc.dec{1};
lh_base = dc.dec{2};
hl_base = dc.dec{3};
hh_base = dc.dec{4};
ll_var = var(ll_base, 0);
lh_var = var(lh_base, 0);
hl_var = var(hl_base, 0);
hh_var = var(hh_base, 0);
% count number of elements
ll_n = numel(ll_base);
lh_n = numel(lh_base);
hl_n = numel(hl_base);
hh_n = numel(hh_base);
% find local threshold
ll_t = ll_var * (sqrt(2 * log2(ll_n)));
lh_t = lh_var * (sqrt(2 * log2(lh_n)));
hl_t = hl_var * (sqrt(2 * log2(hl_n)));
hh_t = hh_var * (sqrt(2 * log2(hh_n)));
% global
if thr_type == 1
ll_t = gthr; lh_t = gthr; hl_t = gthr; hh_t = gthr;
end
% count zero values in bands
ll_size = size(ll_base);
lh_size = size(lh_base);
hl_size = size(hl_base);
hh_size = size(hh_base);
% count zero values in new band matrices
ll_zeros = sum(ll_base==0,'all');
lh_zeros = sum(lh_base==0,'all');
hl_zeros = sum(hl_base==0,'all');
hh_zeros = sum(hh_base==0,'all');
% initiate new matrices
ll_new = zeros(ll_size);
lh_new = zeros(lh_size);
hl_new = zeros(lh_size);
hh_new = zeros(lh_size);
% apply thresholding on bands
% if new value < thr => 0
% otherwise, keep the previous value
for id=1:ll_size(1)
for idx=1:ll_size(2)
if ll_base(id,idx) < ll_t
ll_new(id,idx) = 0;
else
ll_new(id,idx) = ll_base(id,idx);
end
end
end
for id=1:lh_size(1)
for idx=1:lh_size(2)
if lh_base(id,idx) < lh_t
lh_new(id,idx) = 0;
else
lh_new(id,idx) = lh_base(id,idx);
end
end
end
for id=1:hl_size(1)
for idx=1:hl_size(2)
if hl_base(id,idx) < hl_t
hl_new(id,idx) = 0;
else
hl_new(id,idx) = hl_base(id,idx);
end
end
end
for id=1:hh_size(1)
for idx=1:hh_size(2)
if hh_base(id,idx) < hh_t
hh_new(id,idx) = 0;
else
hh_new(id,idx) = hh_base(id,idx);
end
end
end
% count zeros of the new matrices
ll_new_size = size(ll_new);
lh_new_size = size(lh_new);
hl_new_size = size(hl_new);
hh_new_size = size(hh_new);
% count number of zeros among new values
ll_new_zeros = sum(ll_new==0,'all');
lh_new_zeros = sum(lh_new==0,'all');
hl_new_zeros = sum(hl_new==0,'all');
hh_new_zeros = sum(hh_new==0,'all');
% set new band matrices
dc.dec{1} = ll_new;
dc.dec{2} = lh_new;
dc.dec{3} = hl_new;
dc.dec{4} = hh_new;
% count how many coeff. were thresholded
ll_zeros_diff = ll_new_zeros - ll_zeros;
lh_zeros_diff = lh_zeros - lh_new_zeros;
hl_zeros_diff = hl_zeros - hl_new_zeros;
hh_zeros_diff = hh_zeros - hh_new_zeros;
% show coeff. matrices vs. thresholded version
figure
colormap(gray);
subplot(2,4,1); imagesc(ll_base); title('LL');
subplot(2,4,2); imagesc(lh_base); title('LH');
subplot(2,4,3); imagesc(hl_base); title('HL');
subplot(2,4,4); imagesc(hh_base); title('HH');
subplot(2,4,5); imagesc(ll_new); title({'LL thr';ll_zeros_diff});
subplot(2,4,6); imagesc(lh_new); title({'LH thr';lh_zeros_diff});
subplot(2,4,7); imagesc(hl_new); title({'HL thr';hl_zeros_diff});
subplot(2,4,8); imagesc(hh_new); title({'HH thr';hh_zeros_diff});
% idwt to reconstruct compressed image
cmp = waverec3(dc);
cmp = uint8(cmp);
% calculate mse/psnr
D = abs(cmp - base) .^2;
mse = sum(D(:))/numel(base);
psnr = 10*log10(255*255/mse);
% show images and mse/psnr
figure
subplot(1,2,1);
imshow(base); title("Original"); axis square;
subplot(1,2,2);
imshow(cmp); colormap(gray); axis square;
msg = strcat("MSE: ", num2str(mse), " | PSNR: ", num2str(psnr));
title({"Compressed";msg});
% save image locally
imwrite(cmp, 'compressed.png');
I solved the question.
the sigma in the local threshold formula is not variance, it's the standard deviation. I applied these steps:
used stdfilt() std2() to find standard deviation of my coeff. matrices (thanks to #Rotem for pointing this out)
used numel() to count the number of elements in coeff. matrices
this is a summary of the process. it's the same for other bands (LH, HL, HH))
[c, s] = wavedec2(image, wname, level); %apply dwt
ll = appcoeff2(c, s, wname); %find LL
ll_std = std2(ll); %find standard deviation
ll_n = numel(ll); %find number of coeffs in LL
ll_t = ll_std * (sqrt(2 * log2(ll_n))); %local the formula
ll_new = ll .* double(ll > ll_t); %thresholding
replace the LL values in c in a for loop
reconstruct by applying IDWT using waverec2
this is a sample output:
I have been working on a FastICA algorithm implementation using MatLab. Currently the code does not separate the signals as good as id like. I was wondering if anyone here could give me some advice on what I could do to fix this problem?
disp('*****Importing Signals*****');
s = [1,30000];
[m1,Fs1] = audioread('OSR_us_000_0034_8k.wav', s);
[f1,Fs2] = audioread('OSR_us_000_0017_8k.wav', s);
ss = size(f1,1);
n = 2;
disp('*****Mixing Signals*****');
A = randn(n,n); %developing mixing matrix
x = A*[m1';f1']; %A*x
m_x = sum(x, n)/ss; %mean of x
xx = x - repmat(m_x, 1, ss); %centering the matrix
c = cov(x');
sq = inv(sqrtm(c)); %whitening the data
x = c*xx;
D = diff(tanh(x)); %setting up newtons method
SD = diff(D);
disp('*****Generating Weighted Matrix*****');
w = randn(n,1); %Random weight vector
w = w/norm(w,2); %unit vector
w0 = randn(n,1);
w0 = w0/norm(w0,2); %unit vector
disp('*****Unmixing Signals*****');
while abs(abs(w0'*w)-1) > size(w,1)
w0 = w;
w = x*D(w'*x) - sum(SD'*(w'*x))*w; %perform ICA
w = w/norm(w, 2);
end
disp('*****Output After ICA*****');
sound(w'*x); % Supposed to be one of the original signals
subplot(4,1,1);plot(m1); title('Original Male Voice');
subplot(4,1,2);plot(f1); title('Original Female Voice');
subplot(4,1,4);plot(w'*x); title('Post ICA: Estimated Signal');
%figure;
%plot(z); title('Random Mixed Signal');
%figure;
%plot(100*(w'*x)); title('Post ICA: Estimated Signal');
Your covariance matrix c is 2 by 2, you cannot work with that. You have to mix your signal multiple times with random numbers to get anywhere, because you must have some signal (m1) common to different channels. I was unable to follow through your code for fast-ICA but here is a PCA example:
url = {'https://www.voiptroubleshooter.com/open_speech/american/OSR_us_000_0034_8k.wav';...
'https://www.voiptroubleshooter.com/open_speech/american/OSR_us_000_0017_8k.wav'};
%fs = 8000;
m1 = webread(url{1});
m1 = m1(1:30000);
f1 = webread(url{2});
f1 = f1(1:30000);
ss = size(f1,1);
n = 2;
disp('*****Mixing Signals*****');
A = randn(50,n); %developing mixing matrix
x = A*[m1';f1']; %A*x
[www,comp] = pca(x');
sound(comp(:,1)',8000)
i want to find eigenfaces from eigen values here is the code for reference.
clc;
clear all;
close all;
% I) READ IMAGES
for i = 1:9
img{i} = imread(['C:\Users\shree\Desktop\archana\target\' num2str(i) '.jpg']);
end
%II) CONVERTING TO GRAY SCALE
gray_img=cellfun(#rgb2gray,img,'uniformoutput',false);
%imshow(gray_img{2});
%III) RESIZING GRAY IMAGES
res_img = cellfun(#(x)(imresize(x, [50, 50])), gray_img, 'UniformOutput', false);
%imshow(res_img{2});
%DISPLAYING ALL IMAGE
D=[res_img{1} res_img{2} res_img{3}
res_img{4} res_img{5} res_img{6}
res_img{7} res_img{8} res_img{9}];
figure, imshow(D);
%MEAN IMAGE
mean_img=(res_img{1}+res_img{2}+res_img{3}+res_img{4}+res_img{5}+res_img{6}+res_img{7}+res_img{8}+res_img{9})/9;
figure,imshow(mean_img);
%III)SINGLE VECTOR CONVERSION
vect_img= cellfun(#(x)((x(:))), res_img, 'UniformOutput', false);
%MEAN OF SINGLE VECTOR
mean_vect=(vect_img{1}+vect_img{2}+vect_img{3}+vect_img{4}+vect_img{5}+vect_img{6}+vect_img{7}+vect_img{8}+vect_img{9})/9;
%DEVIATION MATRIX
dev_mat=cellfun(#(x) ((x)-mean_vect),vect_img,'uniformoutput',false);
%imshow(dev_mat{1})
U=[dev_mat{1} dev_mat{2} dev_mat{3} dev_mat{4} dev_mat{5} dev_mat{6} dev_mat{7} dev_mat{8} dev_mat{9} ]
figure ,imshow(U);
%COVARIENCE MATRIX
C=[double(U')*double(U)]/9;
%VARIENCE
v=var(C);
%EIGEN VALUES
lambda = eig(C);
[V,D] = eig(C) ;% eigenvalues (D) & eigenvectors (V),=> A*V = V*D
size(lambda);
% EXTRACT DIONAL OF MATRIX VECTOR
%V = diag(V);
%SORT VARIENCE ACC.DECREASING ORDER
sort(lambda,'descend');
i reached upto the arranging the eiganvalues into non-increasing order plz help me how to procced in order to get the eigenfaces.regards
Instead of loading each file one by one try this
ImageDatabasePath ='C:\Users\shree\Desktop\final data';
ImageFiles = dir(ImageDatabasePath);
Train_Number = 0;
for i = 1:size(ImageFiles,1)
if not(strcmp(ImageFiles(i).name,'.')|strcmp(ImageFiles(i).name,'..')...
|strcmp(ImageFiles(i).name,'Thumbs.db'))
Image_Number = Image_Number + 1;
end
end
Now to make the images into 1D image vectors
T = [ ];
for i = 1 : Image_Number
str = int2str(i);
str = strcat('\',str,'.jpg');
str = strcat(ImageDatabasePath,str);
imt = imread(str);
[irow icol] = size(imt);
temp = reshape(imt,irow*icol,1);
T = [T temp];
end
Calculates mean value
m = mean(T,2);
Train_Number = size(T,2);
Calculates the deviation of each image from the mean image
A = [ ];
for i = 1 : Image_Number
temp = double(T(:,i)) - m;
A = [A temp];
end
Create covariance matrix
L = A'*A;
Calculate eigen values and eigen vector V-eigen vector D-diagonal matrix with eigen values
[V D] = eig(L);
L_eig_vec = [];
for i = 1 : size(V,2)
if( D(i,i)>1 )
L_eig_vec = [L_eig_vec V(:,i)];
end
end
Eigenvectors of covariance matrix C (or so-called "Eigenfaces") can be recovered from L's eiegnvectors.
Eigenfaces = A * L_eig_vec;
Use double(NEW) * double(NEW');
Besides, do not use mean and cov as variable name. They are built-in functions. I guess you want C = cov(double(NEW) * double(NEW')); in the covariance calculation.
Normally, a Gabor filter, as its name suggests, is used to filter an image and extract everything that it is oriented in the same direction of the filtering.
In this question, you can see more efficient code than written in this Link
Assume 16 scales of Filters at 4 orientations, so we get 64 gabor filters.
scales=[7:2:37], 7x7 to 37x37 in steps of two pixels, so we have 7x7, 9x9, 11x11, 13x13, 15x15, 17x17, 19x19, 21x21, 23x23, 25x25, 27x27, 29x29, 31x31, 33x33, 35x35 and 37x37.
directions=[0, pi/4, pi/2, 3pi/4].
The equation of Gabor filter in the spatial domain is:
The equation of Gabor filter in the frequency domain is:
In the spatial domain:
function [fSiz,filters,c1OL,numSimpleFilters] = init_gabor(rot, RF_siz)
image=imread('xxx.jpg');
image_gray=rgb2gray(image);
image_gray=imresize(image_gray, [100 100]);
image_double=double(image_gray);
rot = [0 45 90 135]; % we have four orientations
RF_siz = [7:2:37]; %we get 16 scales (7x7 to 37x37 in steps of two pixels)
minFS = 7; % the minimum receptive field
maxFS = 37; % the maximum receptive field
sigma = 0.0036*RF_siz.^2 + 0.35*RF_siz + 0.18; %define the equation of effective width
lambda = sigma/0.8; % it the equation of wavelength (lambda)
G = 0.3; % spatial aspect ratio: 0.23 < gamma < 0.92
numFilterSizes = length(RF_siz); % we get 16
numSimpleFilters = length(rot); % we get 4
numFilters = numFilterSizes*numSimpleFilters; % we get 16x4 = 64 filters
fSiz = zeros(numFilters,1); % It is a vector of size numFilters where each cell contains the size of the filter (7,7,7,7,9,9,9,9,11,11,11,11,......,37,37,37,37)
filters = zeros(max(RF_siz)^2,numFilters); % Matrix of Gabor filters of size %max_fSiz x num_filters, where max_fSiz is the length of the largest filter and num_filters the total number of filters. Column j of filters matrix contains a n_jxn_j filter (reshaped as a column vector and padded with zeros).
for k = 1:numFilterSizes
for r = 1:numSimpleFilters
theta = rot(r)*pi/180; % so we get 0, pi/4, pi/2, 3pi/4
filtSize = RF_siz(k);
center = ceil(filtSize/2);
filtSizeL = center-1;
filtSizeR = filtSize-filtSizeL-1;
sigmaq = sigma(k)^2;
for i = -filtSizeL:filtSizeR
for j = -filtSizeL:filtSizeR
if ( sqrt(i^2+j^2)>filtSize/2 )
E = 0;
else
x = i*cos(theta) - j*sin(theta);
y = i*sin(theta) + j*cos(theta);
E = exp(-(x^2+G^2*y^2)/(2*sigmaq))*cos(2*pi*x/lambda(k));
end
f(j+center,i+center) = E;
end
end
f = f - mean(mean(f));
f = f ./ sqrt(sum(sum(f.^2)));
p = numSimpleFilters*(k-1) + r;
filters(1:filtSize^2,p)=reshape(f,filtSize^2,1);
fSiz(p)=filtSize;
end
end
% Rebuild all filters (of all sizes)
nFilts = length(fSiz);
for i = 1:nFilts
sqfilter{i} = reshape(filters(1:(fSiz(i)^2),i),fSiz(i),fSiz(i));
%if you will use conv2 to convolve an image with this gabor, so you should also add the equation below. But if you will use imfilter instead of conv2, so do not add the equation below.
sqfilter{i} = sqfilter{i}(end:-1:1,end:-1:1); %flip in order to use conv2 instead of imfilter (%bug_fix 6/28/2007);
convv=imfilter(image_double, sqfilter{i}, 'same', 'conv');
figure;
imagesc(convv);
colormap(gray);
end
phi = ij*pi/4; % ij = 0, 1, 2, 3
theta = 3;
sigma = 0.65*theta;
filterSize = 7; % 7:2:37
G = zeros(filterSize);
for i=(0:filterSize-1)/filterSize
for j=(0:filterSize-1)/filterSize
xprime= j*cos(phi);
yprime= i*sin(phi);
K = exp(2*pi*theta*sqrt(-1)*(xprime+ yprime));
G(round((i+1)*filterSize),round((j+1)*filterSize)) =...
exp(-(i^2+j^2)/(sigma^2))*K;
end
end
As of R2015b release of the Image Processing Toolbox, you can create a Gabor filter bank using the gabor function in the image processing toolbox, and you can apply it to an image using imgaborfilt.
In the frequency domain:
sigma_u=1/2*pi*sigmaq;
sigma_v=1/2*pi*sigmaq;
u0=2*pi*cos(theta)*lambda(k);
v0=2*pi*sin(theta)*lambda(k);
for u = -filtSizeL:filtSizeR
for v = -filtSizeL:filtSizeR
if ( sqrt(u^2+v^2)>filtSize/2 )
E = 0;
else
v_theta = u*cos(theta) - v*sin(theta);
u_theta = u*sin(theta) + v*cos(theta);
E=(1/2*pi*sigma_u*sigma_v)*((exp((-1/2)*(((u_theta-u0)^2/sigma_u^2))+((v_theta-v0)^2/sigma_v^2))) + (exp((-1/2)*(((u_theta+u0)^2/sigma_u^2))+((v_theta+v0)^2/sigma_v^2))));
end
f(v+center,u+center) = E;
end
end
I am working on rotating image manually in Matlab. Each time I run my code with a different image the previous images which are rotated are shown in the Figure. I couldn't figure it out. Any help would be appreciable.
The code is here:
[screenshot]
im1 = imread('gradient.jpg');
[h, w, p] = size(im1);
theta = pi/12;
hh = round( h*cos(theta) + w*abs(sin(theta))); %Round to nearest integer
ww = round( w*cos(theta) + h*abs(sin(theta))); %Round to nearest integer
R = [cos(theta) -sin(theta); sin(theta) cos(theta)];
T = [w/2; h/2];
RT = [inv(R) T; 0 0 1];
for z = 1:p
for x = 1:ww
for y = 1:hh
% Using matrix multiplication
i = zeros(3,1);
i = RT*[x-ww/2; y-hh/2; 1];
%% Nearest Neighbour
i = round(i);
if i(1)>0 && i(2)>0 && i(1)<=w && i(2)<=h
im2(y,x,z) = im1(i(2),i(1),z);
end
end
end
end
x=1:ww;
y=1:hh;
[X, Y] = meshgrid(x,y); % Generate X and Y arrays for 3-D plots
orig_pos = [X(:)' ; Y(:)' ; ones(1,numel(X))]; % Number of elements in array or subscripted array expression
orig_pos_2 = [X(:)'-(ww/2) ; Y(:)'-(hh/2) ; ones(1,numel(X))];
new_pos = round(RT*orig_pos_2); % Round to nearest neighbour
% Check if new positions fall from map:
valid_pos = new_pos(1,:)>=1 & new_pos(1,:)<=w & new_pos(2,:)>=1 & new_pos(2,:)<=h;
orig_pos = orig_pos(:,valid_pos);
new_pos = new_pos(:,valid_pos);
siz = size(im1);
siz2 = size(im2);
% Expand the 2D indices to include the third dimension.
ind_orig_pos = sub2ind(siz2,orig_pos(2*ones(p,1),:),orig_pos(ones(p,1),:), (1:p)'*ones(1,length(orig_pos)));
ind_new_pos = sub2ind(siz, new_pos(2*ones(p,1),:), new_pos(ones(p,1),:), (1:p)'*ones(1,length(new_pos)));
im2(ind_orig_pos) = im1(ind_new_pos);
imshow(im2);
There is a problem with the initialization of im2, or rather, the lack of it. im2 is created in the section shown below:
if i(1)>0 && i(2)>0 && i(1)<=w && i(2)<=h
im2(y,x,z) = im1(i(2),i(1),z);
end
If im2 exists before this code is run and its width or height is larger than the image you are generating the new image will only overwrite the top left corner of your existing im2. Try initializing im2 by adding adding
im2 = zeros(hh, ww, p);
before
for z = 1:p
for x = 1:ww
for y = 1:hh
...
As a bonus it might make your code a little faster since Matlab won't have to resize im2 as it grows in the loop.