From image to vector and vice versa, rotated image - matlab

I read a DICOM image and for a variety of reasons, I had to turn the image matrix in a row vector.
After performing various operations on the bits of the vector, I need to reprocess the vector in a DICOM image of the same size as the original.
I've done all these steps but when I go to display the resulting image, this is rotated.
This is what I get:
That's part of the code:
function [I0, Iw] = watIns(filename, w)
I0 = dicomread(filename);
figure(1);
imshow(I0, []);
title('(1) I0 originale');
info = dicominfo(filename);
width = info.Width;
height = info.Height;
size = info.FileSize;
k = info.BitDepth;
% I extract the first k pixels and memorize their LBS in a variable S.
x = 1 : k;
y = 1;
firstKPixel = I0(x, y);
% convert in binary
firstKPixel2 = 0*firstKPixel;
for i = 1 : length(firstKPixel)
if firstKPixel(i) == 0
firstKPixel2(i) = 0;
else
firstKPixel2(i) = dec2bin(firstKPixel(i), 'left-msb');
end
end
% I take the LSB of each element in firstKPixel2 and concatenate in the string S
S = '';
for i = 1 : k
c = firstKPixel2(i, :);
s = num2str(c(end));
S = strcat(S, s);
end
% I compute the vector corresponding to I0 but without the first 0 pixels and the corresponding histogram
[vecComp, histComp] = histKtoEnd(I0, 0, k);
% I compute the vector corresponding to I0 but without the first k pixels and the corresponding histogram
[vecWithoutKPixel, histWithoutKPixel] = histKtoEnd(I0, k, k);
L = ...; % is a vector of values
% I save l_0 in the LSB of the first k pixels.
% prendo l_0, ovvero il primo elemento di L
l_0 = L(1);
l_02 = fliplr(bitget(l_0, 1:k));
% I take the LSB of each element in firstKPixel2 and I sret it to the i-th element of l0_2
for i = 1 : k
c = firstKPixel2(i, :);
c(end) = l_02(i);
firstKPixel2(i, :) = c;
end
% convert to decimal each element of firstKPixel2
for i = 1 : length(firstKPixel2)
str = int2str(firstKPixel2(i));
firstKPixel2_lsb10(i) = bin2dec(str);
end
% I set first k pixels in the image to those just modified
vecComp(1 : k) = firstKPixel2_lsb10(1 : k);
% Transform the vector image
mat = reshape(vecComp, [width, height]);
dicomwrite(mat, './I1.dcm', 'CompressionMode', 'None');
I1 = dicomread('./I1.dcm');
figure(7);
imshow(I1, []); % ROTATE IMAGE!!!
% ...
end
histKtoEnd function is:
function [vecWithoutKPixel, hist] = histKtoEnd(image, k, colorDepth)
imageVec = reshape(image.', [], 1);
l = length(imageVec);
vecWithoutKPixel = imageVec((k+1) : l-1);
vecWithoutKPixel(end+1) = imageVec(l);
hist = zeros(1, 2^colorDepth);
for i = 0 : (2^colorDepth - 1)
grayI = (vecWithoutKPixel == i);
hist(1, i+1) = sum(grayI(:));
end
end
I read here that Matlab shows images like a matrix with the first coordinates (rows) going top-down and the second (columns) left-right.
I couldn't solve, can anyone help me?
Thank you!

Somehow in the unrolling, processing and rolling of your data it seems to get transposed. You can try to find why that happens, but if you do not care, you can always just transpose the result in the end by
mat = reshape(vecComp, [width, height]).';

Related

How do I find local threshold for coefficients in image compression using DWT in MATLAB

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:

Histograms too different compared to how they should be

I have a black/white image I0 (512 x 512) to which I have to remove the first k pixel and calculate the histogram of the resulting image.
Let me explain: I have to build the histogram of the image I0 without considering the first k pixels.
This is my code:
k = 8;
% compute the histogram of the entire image I0
[vecComp, histComp] = histKtoEnd(I0, 0, k);
% compute the histogram of the image I0 without the first k pixel
[vecWithoutKPixel, histWithoutKPixel] = histKtoEnd(I0, k, k);
where:
function [vecWithoutKPixel, hist] = histKtoEnd(image, k, colorDepth)
% image to row vector
imageVec = reshape(image.', [], 1);
l = length(imageVec);
% I "delete" the first k pixel
vecWithoutKPixel = imageVec((k+1) : l-1);
vecWithoutKPixel(end+1) = imageVec(l);
% inizialization
hist = zeros(1, 2^colorDepth);
% create the vector of occurrences
for i = 0 : (2^colorDepth - 1)
grayI = (vecWithoutKPixel == i);
hist(1, i+1) = sum(grayI(:));
end
end
To display the two histograms do:
subplot(1, 2, 1);
bar(0:2^k-1, histComp, 'r');
title('Histogram of the entire image');
axis([minColor, maxColor, 0, numberOfPixels]);
subplot(1, 2, 2);
bar(0:2^k-1, histWithoutKPixel, 'r');
title('Histogram of the image without the first k pixels');
axis([minColor, maxColor, 0, numberOfPixels]);
and I get:
As you can see, the histograms are very different, yet should differ very little since the difference is only 8 pixels.
Where am I wrong?
Also in warkspace the newly created variables have these dimensions:
vecComp -> 262144 x 1 uint8
histComp -> 1 x 256 double
vecWithoutKPixel -> 65528 x 1 uint8
histWithoutKPixel -> 1 x 256 double
This is very strange. I should have:
vecComp -> 262144 x 1
vecWithoutKPixel -> 262136 x 1
Could someone help me?
Thank you
I'm working with DICOM images and the command info = dicominfo(filename) get
size = info.FileSize; % 262582;
colorType = info.ColorType; % grayscale
So I don't think that the problem is the image.
If I put a brakpoint on line vecWithoutKPixel(end+1) = imageVec(l); I get that imageVec is 262144 x 1 uint8, and:
function [vecWithoutKPixel, hist] = histKtoEnd(image, k, colorDepth)
% image to row vector
imageVec = reshape(image.', [], 1);
l = length(imageVec);
size(imageVec) % 262144 x 1
% I "delete" the first k pixel
vecWithoutKPixel = imageVec((k+1) : l-1);
vecWithoutKPixel(end+1) = imageVec(l);
% inizialization
hist = zeros(1, 2^colorDepth);
% create the vector of occurrences
for i = 0 : (2^colorDepth - 1)
grayI = (vecWithoutKPixel == i);
hist(1, i+1) = sum(grayI(:));
end
end
If I change the commands vecWithoutKPixel = imageVec((k+1) : l-1);
vecWithoutKPixel(end+1) = imageVec(l); with vecWithoutKPixel = imageVec((k+1) : l); I get that vecWithoutKPixel = [].
Creating a 'random-image' using I0=randi(255,100,100) and then running your code will produce a plot like this:
I guees this plot looks exactly like it should and the dimensions of the variables are correct as well:
vecComp 10000x1 double
vecWithoutKPixel 9992x1 double
Thus our problem is not actually your code, but your image. Your image is not really gray level valued which has been mentioned by others before. But instead of casting some variables to uint8 like #Richard suggested, you should cast your image to double. If your image is rgb valued use I0=double(rgb2gray(I0)); or if it is just uint8 for some other reason use I0=double(I0) and then pass it to the function. Hope this helps.
I believe the problem is that the image data is originally in uint8 format and gets converted to double at some point. Therefore, the line
grayI = (vecWithoutKPixel == i);
in histKtoEnd probably only works with the uint8 data ( since you compare the data with an integer).
Try adding the line
vecWithoutKPixel = uint8(vecWithoutKPixel);
to the histKtoEnd function:
function [vecWithoutKPixel, hist] = histKtoEnd(image, k, colorDepth)
% image to row vector
imageVec = reshape(image.', [], 1);
l = length(imageVec);
% I "delete" the first k pixel
vecWithoutKPixel = imageVec((k+1) : l-1);
vecWithoutKPixel(end+1) = imageVec(l);
% inizialization
hist = zeros(1, 2^colorDepth);
% create the vector of occurrences
for i = 0 : (2^colorDepth - 1)
vecWithoutKPixel = uint8(vecWithoutKPixel); % Cast to integer
grayI = (vecWithoutKPixel == i);
hist(1, i+1) = sum(grayI(:));
end
end

how to obtain the eigenfaces using eigenvalues and eigen vectors?

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.

Matlab figure keeps the history of the previous images

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.

Prewitt Filter implementation Matlab

I'm trying to implement the Prewitt Filter in Matlab. I know that Matlab has already this kind of filter but I need to code it myself. Below is my code, the only problem is that at the end of the filtering I get a bright image instead of seeing the edges.
I'm implementing the filter using the separability property of the Prewitt Filter. Any ideas? I will appreciate very much your help.
%% 3x3 Prewitt Filter
close all
imageIn = imread('images/Bikesgray.jpg');
imageGx = zeros(size(imageIn));
imageGy = zeros(size(imageIn));
imageOut = zeros(size(imageIn));
ny = size(imageIn, 1);
nx = size(imageIn, 2);
average = 3;
imshow(imageIn);
u = [];
v = [];
tic
%Compute Gx
%For every row use the mask (-1 0 1)
for i = 1:ny
u = imageIn(i,:);
v = zeros(1, nx);
for k = 2:nx-1
v(k) = (uint32(-1*u(k-1))+uint32(0*u(k))+uint32(u(k+1)));
end
v(1) = (uint32(-1*u(2))+uint32(0*u(1))+uint32(u(2)));
v(nx) = (uint32(-1*u(nx-1))+uint32(0*u(nx))+uint32(u(nx-1)));
imageGx(i,:) = v;
end
%For every column use the mask (1 1 1)
for j = 1:nx
u = imageGx(:,j);
v = zeros(ny, 1);
for k = 2:ny-1
v(k) = (uint32(u(k-1))+uint32(u(k))+uint32(u(k+1)));
end
v(1) = (uint32(u(2))+uint32(u(1))+uint32(u(2)));
v(ny) = (uint32(u(ny-1))+uint32(u(ny))+uint32(u(ny-1)));
imageGx(:,j) = v;
end
%Compute Gy
%For every row use the mask (1 1 1)
for i = 1:ny
u = imageIn(i,:);
v = zeros(1, nx);
for k = 2:nx-1
v(k) = (uint32(u(k-1))+uint32(u(k))+uint32(u(k+1)));
end
v(1) = (uint32(u(2))+uint32(u(1))+uint32(u(2)));
v(nx) = (uint32(u(nx-1))+uint32(u(nx))+uint32(u(nx-1)));
imageGy(i,:) = v;
end
%For every column use the mask (1 0 -1)
for j = 1:nx
u = imageGy(:,j);
v = zeros(ny, 1);
for k = 2:ny-1
v(k) = (uint32(u(k-1))+uint32(0*u(k))+uint32(-1*u(k+1)));
end
v(1) = (uint32(u(2))+uint32(0*u(1))+uint32(-1*u(2)));
v(ny) = (uint32(u(ny-1))+uint32(0*u(ny))+uint32(-1*u(ny-1)));
imageGy(:,j) = v;
end
toc
figure
imshow(imageGx, [0 255]);
figure
imshow(imageGy, [0 255]);
%Compute the magnitude G = sqrt(Gx^2 + Gy^2);
imageOut(:,:) = sqrt(imageGx(:,:).^2 + imageGy(:,:).^2);
figure
imshow(imageOut, [0 255]);
It's too bad you didn't use convn (convolution), since the weighted sum just screams it.
In a nutshell you produce Gx,Gy by using convn on the image matrix, using the appropriate kernels, as described in wikipedia
The solution was really obvious but took me some time to figure it out.
All I did is change the uint32 to int32 and be sure to perform the operations (e.g. multiplying by -1) after changing the values from uint32 to int32.