I work on a function in Matlab that calculates the DCT (discrete cosine transform) of an image. I don't know what is not working in my code, but I got an output image with the same number. I want to use this formula for my DCT.
Any ideas please.
function image_comp = dctII(image, b)
[h w] = size(image);
image = double(image) - 128;
block = zeros(b,b);
image_t=zeros(size(image));
for k=1:b:h
for l=1:b:w
image_t(k:k+b-1,l:l+b-1)= image(k:k+b-1,l:l+b-1);
for u=1:b
for v=1:b
if u == 0
Cu = 1/sqrt(2);
else
Cu = 1;
end
if v == 0
Cv = 1/sqrt(2);
else
Cv = 1;
end
Res_sum=0;
for x=1:b;
for y=1:b
Res_sum = Res_sum + ((image_t(x,y))*cos(((2*x)+1)*u*pi/(2*b))*cos(((2*y)+1)*v*pi/(2*b)));
end
end
dct= (1/4)*Cu*Cv*Res_sum;
block(u,v) = dct;
end
end
image_comp(k:k+b-1,l:l+b-1)=block(u,v);
end
end
end
In the inner loop over x and y, you are not reading from the correct place in image_t. You have copied the local block into a location with k,l as the upper left corner for use in processing, but in the inner loop you are always reading from the same block that starts at 1,1 as the upper left corner in image_t.
Related
I am working in MATLAB to process two 512x512 images, the domain image and the range image. What I am trying to accomplish is the following:
Divide both domain and range images into 8x8 pixel blocks
For each 8x8 block in the domain image, I have to apply a linear transformations to it and compare each of the 4096 transformed blocks with each of the 4096 range blocks.
Compute error in each case between the transformed block and the range image block and find the minimum error.
Finally I'll have for each 8x8 range block, the id of the 8x8 domain block for which the error was minimum (error between the range block and the transformed domain block)
To achieve this, I have written the following code:
RangeImagecolor = imread('input.png'); %input is 512x512
DomainImagecolor = imread('input.png'); %Range and Domain images are identical
RangeImagetemp = rgb2gray(RangeImagecolor);
DomainImagetemp = rgb2gray(DomainImagecolor);
RangeImage = im2double(RangeImagetemp);
DomainImage = im2double(DomainImagetemp);
%For the (k,l)th 8x8 range image block
for k = 1:64
for l = 1:64
minerror = 9999;
min_i = 0;
min_j = 0;
for i = 1:64
for j = 1:64
%here I compute for the (i,j)th domain block, the transformed domain block stored in D_trans
error = 0;
D_trans = zeros(8,8);
R = zeros(8,8); %Contains the pixel values of the (k,l)th range block
for m = 1:8
for n = 1:8
R(m,n) = RangeImage(8*k-8+m,8*l-8+n);
%ApplyTransformation can depend on (k,l) so I can't compute the transformation outside the k,l loop.
[m_dash,n_dash] = ApplyTransformation(8*i-8+m,8*j-8+n);
D_trans(m,n) = DomainImage(m_dash,n_dash);
error = error + (R(m,n)-D_trans(m,n))^2;
end
end
if(error < minerror)
minerror = error;
min_i = i;
min_j = j;
end
end
end
end
end
As an example ApplyTransformation, one can use the identity transformation:
function [x_dash,y_dash] = Iden(x,y)
x_dash = x;
y_dash = y;
end
Now the problem I am facing is the high computation time. The order of computation in the above code is 64^5, which is of the order 10^9. This computation should take at the worst minutes or an hour. It takes about 40 minutes to compute just 50 iterations. I don't know why the code is running so slow.
Thanks for reading my question.
You can use im2col* to convert the image to column format so each block forms a column of a [64 * 4096] matrix. Then apply transformation to each column and use bsxfun to vectorize computation of error.
DomainImage=rand(512);
RangeImage=rand(512);
DomainImage_col = im2col(DomainImage,[8 8],'distinct');
R = im2col(RangeImage,[8 8],'distinct');
[x y]=ndgrid(1:8);
function [x_dash, y_dash] = ApplyTransformation(x,y)
x_dash = x;
y_dash = y;
end
[x_dash, y_dash] = ApplyTransformation(x,y);
idx = sub2ind([8 8],x_dash, y_dash);
D_trans = DomainImage_col(idx,:); %transformation is reduced to matrix indexing
Error = 0;
for mn = 1:64
Error = Error + bsxfun(#minus,R(mn,:),D_trans(mn,:).').^2;
end
[minerror ,min_ij]= min(Error,[],2); % linear index of minimum of each block;
[min_i min_j]=ind2sub([64 64],min_ij); % convert linear index to subscript
Explanation:
Our goal is to reduce number of loops as much as possible. For it we should avoid matrix indexing and instead we should use vectorization. Nested loops should be converted to one loop. As the first step we can create a more optimized loop as here:
min_ij = zeros(4096,1);
for kl = 1:4096 %%% => 1:size(D_trans,2)
minerror = 9999;
min_ij(kl) = 0;
for ij = 1:4096 %%% => 1:size(R,2)
Error = 0;
for mn = 1:64
Error = Error + (R(mn,kl) - D_trans(mn,ij)).^2;
end
if(Error < minerror)
minerror = Error;
min_ij(kl) = ij;
end
end
end
We can re-arrange the loops and we can make the most inner loop as the outer loop and separate computation of the minimum from the computation of the error.
% Computation of the error
Error = zeros(4096,4096);
for mn = 1:64
for kl = 1:4096
for ij = 1:4096
Error(kl,ij) = Error(kl,ij) + (R(mn,kl) - D_trans(mn,ij)).^2;
end
end
end
% Computation of the min
min_ij = zeros(4096,1);
for kl = 1:4096
minerror = 9999;
min_ij(kl) = 0;
for ij = 1:4096
if(Error(kl,ij) < minerror)
minerror = Error(kl,ij);
min_ij(kl) = ij;
end
end
end
Now the code is arranged in a way that can best be vectorized:
Error = 0;
for mn = 1:64
Error = Error + bsxfun(#minus,R(mn,:),D_trans(mn,:).').^2;
end
[minerror ,min_ij] = min(Error, [], 2);
[min_i ,min_j] = ind2sub([64 64], min_ij);
*If you don't have the Image Processing Toolbox a more efficient implementation of im2col can be found here.
*The whole computation takes less than a minute.
First things first - your code doesn't do anything. But you likely do something with this minimum error stuff and only forgot to paste this here, or still need to code that bit. Never mind for now.
One big issue with your code is that you calculate transformation for 64x64 blocks of resulting image AND source image. 64^5 iterations of a complex operation are bound to be slow. Rather, you should calculate all transformations at once and save them.
allTransMats = cell(64);
for i = 1 : 64
for j = 1 : 64
allTransMats{i,j} = getTransformation(DomainImage, i, j)
end
end
function D_trans = getTransformation(DomainImage, i,j)
D_trans = zeros(8);
for m = 1 : 8
for n = 1 : 8
[m_dash,n_dash] = ApplyTransformation(8*i-8+m,8*j-8+n);
D_trans(m,n) = DomainImage(m_dash,n_dash);
end
end
end
This serves to get allTransMat and is OUTSIDE the k, l loop. Preferably as a simple function.
Now, you make your big k, l, i, j loop, where you compare all the elements as needed. Comparison could be also done block-wise instead of filling a small 8x8 matrix, yet doing it per element for some reason.
m = 1 : 8;
n = m;
for ...
R = RangeImage(...); % This will give 8x8 output as n and m are vectors.
D = allTransMats{i,j};
difference = sum(sum((R-D).^2));
if (difference < minDifference) ...
end
Even though this is a simple no transformations case, this speeds up code a lot.
Finally, are you sure you need to compare each block of transformed output with each block in the source? Typically you compare block1(a,b) with block2(a,b) - blocks (or pixels) on the same position.
EDIT: allTransMats requires k and l too. Ouch. There is NO WAY to make this fast for a single iteration, as you require 64^5 calls to ApplyTransformation (or a vectorization of that function, but even then it might not be fast - we would have to see the function to help here).
Therefore, I will re-iterate my advice to generate all transformations and then perform lookup: this upper part of the answer with allTransMats generation should be changed to have all 4 loops and generate allTransMats{i,j,k,l};. It WILL be slow, there is no way around that as I mentioned in the upper part of edit. But, it is a cost you pay once, as after saving the allTransMats, all further image analyses will be able to simply load it instead of generating it again.
But ... what do you even do? Transformation that depends on source and destination block indices plus pixel indices (= 6 values total) sounds like a mistake somewhere, or a prime candidate to optimize instead of all the rest.
I am working on Matlab 17.a program's image processing. My work is about histogram equalization. The code is as follows. But when I run the code "Undefined function or variable 'cumulavite_hist'." I get an error. How do I fix this problem? Thank you for your help.
The output will be the histogram next to the original image. Below it will be the changing picture and histogram. Thank you for your help.
>> img= imread ('C:\Users\emre.guzel\Desktop\homeworkimage.png');
if (size(img,3)>1)
img=rgb2gray(img);
end
max_r = size (img,1);
max_c =size (img,2);
histogram =zeros ([1 256]);
cumulative_hist = zeros ([1 256]);
for r=1:max_r
for c=1:max_c
for count =1:256
if(img(r,c) == count-1 )
histogram (count) =histogram (count)+ 1;
break ;
end
end
end
end
%find cumulative histogram
current_value = 0;
for count=1:256
current_value = current_value + histogram (count);
cumulative_hist(count) = current_value;
end
%find h =(cdf-cdf(min) / (MN - cdf (min) )) * 255
%this is the normalized cumulative histogram normalize dediğine bakma sen.
%histogram equalization formulu bu . aşağıda da bunu uygulamış.
normalized_hist = zeros ([1 256]);
cdf_min = min (cumulavite_hist) ;
for count = 1:256
normalized_hist(count) = cumulative_hist(count) - cdf_min;
normalized_hist(count) = normalized_hist (count) / ((max_r*max_c)- cdf_min);
normalized_hist(count) = round (normalized_hist (count) * 255);
end
%replace the values with given equalized values
equalized_image = zeros ([max_r max_c]);
for r =1:max_r
for c=1:max_c
for count = 1:256
if(img(r,c) ==(count-1))
%
%
equlized_img(r,c) = normalized_hist(count);
break;
end
end
end
end
subplot(2,2,1)
imshow(img);
title('Orijinal Image');
subplot (2,2,2);
imhist(img) ;
title ('Hist of Orijinal Image');
subplot(2,2,3) ;
imhist (uint8(equalized_img));
title('Histogram Equalized Image');
H = uint (equalized_img);
subplot(2,2,4) ;
imhist(H) ;
title ('Histogram of Histogram Equalized Image');
a = histeq(img);
figure
imshow(a)
You have cumulative_hist variable at line 10 and cumulavite_hist variable used in line 33. It's just wrong name in line 33. Fix it and program will work.
I want to apply following transformation function to a grayscale image, i know how to apply it to the following function,
my question is how do i apply a program to the following transformation function,
code so far,
clear;
pollen = imread('Fig3.10(b).jpg');
u = double(pollen);
[nx ny] = size(u)
nshades = 256;
r1 = 80; s1 = 10; % Transformation by piecewise linear function.
r2 = 140; s2 = 245;
for i = 1:nx
for j = 1:ny
if (u(i,j)< r1)
uspread(i,j) = ((s1-0)/(r1-0))*u(i,j)
end
if ((u(i,j)>=r1) & (u(i,j)<= r2))
uspread(i,j) = ((s2 - s1)/(r2 - r1))*(u(i,j) - r1)+ s1;
end
if (u(i,j)>r2)
uspread(i,j) = ((255 - s2)/(255 - r2))*(u(i,j) - r2) + s2;
end
end
end
hist= zeros(nshades,1);
for i=1:nx
for j=1:ny
for k=0:nshades-1
if uspread(i,j)==k
hist(k+1)=hist(k+1)+1;
end
end
end
end
plot(hist);
pollenspreadmat = uint8(uspread);
imwrite(pollenspreadmat, 'pollenspread.jpg');
Thanks in advance
The figure says that for any intensities that are between A and B, they should be set to C. All you have to do is modify your two for loops so that for any values between A and B, set the output location to C. I'll also assume the range is inclusive. You can simply remove the first and last if conditions and use the middle one:
for i = 1:nx
for j = 1:ny
if ((u(i,j)>=r1) && (u(i,j)<= r2))
uspread(i,j) = C;
end
end
end
C is a constant that you would set yourself. Usually for segmentation, this result is very high to distinguish the foreground from the background. You have a uint8 image here, so C = 255; would work.
However, I would recommend you achieve a more vectorized solution. Avoid for loops and use logical indexing instead:
uspread = u;
uspread(u >= r1 & u <= r2) = C;
Hello I am new at Matlab..I am trying to do histogram equilzation without using histeq...
but for some reason i always get an error of : ??? Index exceeds matrix dimensions.
here is my code..................................................Thanks for your help
clc
I = imread ('Machine-Edge.PNG');
I2 = rgb2gray(I);
colormap gray;
y = imhist(I2);
%using hist eq. built in fn
I3= histeq(I2);
z= imhist(I3);
%my equalization
r = size(I2,1);
c = size(I2,2);
A= zeros(1,256);
%counting number of pixels of the image and putting the count in Array A
for j=1:r
for x=1:c
v=I2(j,x);
A(v+1)=A(v+1)+1;
end
end
%pi=n/size
for y=1;256
pi(y)= ((A(y))/(r*c));
end
%calculate CI (cumulated pi )
ci(1)=pi(1);
for yy=2;256
ci(yy) = ci(yy-1)+ pi(yy);
end
%calculate T=range *Ci
for b=1;256
T(b)=ci(b)*255;
end
%equilization..replacing each pixel with T value
for j=1:r
for x=1:c
I4(j,x) =T(I2(j,x));
end
end
vv= imhist(I4);
figure
subplot(3,2,1)
imagesc(I2)
subplot(3,2,2)
plot(y)
subplot(3,2,3)
imagesc(I3)
subplot(3,2,4)
plot(z)
subplot(3,2,5)
imagesc(I4)
subplot(3,2,6)
plot(vv)
This is an old post but the OP used ; instead of : in their for loops (i.e. for y=1;256 should read for y=1:256). the corrected code is below:
clc
I = imread ('Machine-Edge.PNG');
I2 = rgb2gray(I);
colormap gray;
y = imhist(I2);
%using hist eq. built in fn
I3= histeq(I2);
z= imhist(I3);
%my equalization
r = size(I2,1);
c = size(I2,2);
A= zeros(1,256);
%counting number of pixels of the image and putting the count in Array A
for j=1:r
for x=1:c
v=I2(j,x);
A(v+1)=A(v+1)+1;
end
end
%pi=n/size
for y=1:256
pi(y)= ((A(y))/(r*c));
end
%calculate CI (cumulated pi )
ci(1)=pi(1);
for yy=2:256
ci(yy) = ci(yy-1)+ pi(yy);
end
%calculate T=range *Ci
for b=1:256
T(b)=ci(b)*255;
end
%equilization..replacing each pixel with T value
for j=1:r
for x=1:c
I4(j,x) =T(I2(j,x));
end
end
vv= imhist(I4);
figure
subplot(3,2,1)
imagesc(I2)
subplot(3,2,2)
plot(y)
subplot(3,2,3)
imagesc(I3)
subplot(3,2,4)
plot(z)
subplot(3,2,5)
imagesc(I4)
subplot(3,2,6)
plot(vv)
I have tried to make a Gaussian filter in Matlab without using imfilter() and fspecial().
I have tried this but result is not like the one I have with imfilter and fspecial.
Here is my codes.
function Gaussian_filtered = Gauss(image_x, sigma)
% for single axis
% http://en.wikipedia.org/wiki/Gaussian_filter
Gaussian_filtered = exp(-image_x^2/(2*sigma^2)) / (sigma*sqrt(2*pi));
end
for 2D Gaussian,
function h = Gaussian2D(hsize, sigma)
n1 = hsize;
n2 = hsize;
for i = 1 : n2
for j = 1 : n1
% size is 10;
% -5<center<5 area is covered.
c = [j-(n1+1)/2 i-(n2+1)/2]';
% A product of both axes is 2D Gaussian filtering
h(i,j) = Gauss(c(1), sigma)*Gauss(c(2), sigma);
end
end
end
and the final one is
function Filtered = GaussianFilter(ImageData, hsize, sigma)
%Get the result of Gaussian
filter_ = Gaussian2D(hsize, sigma);
%check image
[r, c] = size(ImageData);
Filtered = zeros(r, c);
for i=1:r
for j=1:c
for k=1:hsize
for m=1:hsize
Filtered = Filtered + ImageData(i,j).*filter_(k,m);
end
end
end
end
end
But the processed image is almost same as the input image. I wonder the last function GaussianFiltered() is problematic...
Thanks.
here's an alternative:
Create the 2D-Gaussian:
function f=gaussian2d(N,sigma)
% N is grid size, sigma speaks for itself
[x y]=meshgrid(round(-N/2):round(N/2), round(-N/2):round(N/2));
f=exp(-x.^2/(2*sigma^2)-y.^2/(2*sigma^2));
f=f./sum(f(:));
Filtered image, given your image is called Im:
filtered_signal=conv2(Im,gaussian2d(N,sig),'same');
Here's some plots:
imagesc(gaussian2d(7,2.5))
Im=rand(100);subplot(1,2,1);imagesc(Im)
subplot(1,2,2);imagesc(conv2(Im,gaussian2d(7,2.5),'same'));
This example code is slow because of the for-loops. In matlab you can better use conv2, as suggested by user:bla, or just use filter2.
I = imread('peppers.png'); %load example data
I = I(:,:,1);
N=5; %must be odd
sigma=1;
figure(1);imagesc(I);colormap gray
x=1:N;
X=exp(-(x-((N+1)/2)).^2/(2*sigma^2));
h=X'*X;
h=h./sum(h(:));
%I=filter2(h,I); %this is faster
[is,js]=size(I);
Ib = NaN(is+N-1,js+N-1); %add borders
b=(N-1)/2 +1;
Ib(b:b+is-1,b:b+js-1)=I;
I=zeros(size(I));
for i = 1:is
for j = 1:js
I(i,j)=sum(sum(Ib(i:i+N-1,j:j+N-1).*h,'omitnan'));
end
end
figure(2);imagesc(I);colormap gray