How can I improve the performance of my MATLAB code when using loops?

[UrIkOn]

I use looping to implement this formula
https://www.physicsforums.com/attachment.php?
attachmentid=46840&stc=1&d=1335864568
But,when I run, mathlab will hang?Why?

%Import picture into Matlab
img=imread('picture.jpg','jpg');
img512=imresize(img, [512 512]);
imgGRAY=uint8(rgb2gray(img512));
figure(1);imshow(img);
figure(2);imshow(imgGRAY);

M=512;
N=512;
f=double(imgGRAY);
F=zeros(512);
for u=1:512
    for v=1:512
        TotalN=0;
        for x=1:512
            for y=1:512
                TotalN=TotalN+(f(x,y)*exp(-1i*2*pi*(((u*x)/512)+((v*y)/512))));
            end
        end
        F(u,v)=(1/(M*N))*TotalN;
    end
end

 

[D H]

But,when I run, mathlab will hang?Why?

That innermost statement, TotalN=TotalN+(f(x,y)*exp(-1i*2*pi*(((u*x)/512)+((v*y)/512)))); is being performed 512⁴ or 68,719,476,736 times! Even if you coded this in Fortran or C it would take a long time. Matlab is a couple of orders of magnitude slower than either of those languages. If I did this calculation in python on my computer it would take over a day to complete. Matlab is perhaps a bit faster than python, but not much.

Try seeing how long your convolution takes with a 64x64 image. Multiply by 4096. That's how long your convolution will take with a 512x512 image.

 

[UrIkOn]

Then is there any solution?

 

[D H]

Then is there any solution?

Either wait a long time or do something else. What motivated this particular kernel?

 

[UrIkOn]

I don't understand, what you mean for?

 

[D H]

I don't understand, what you mean for?

Why are you using this kernel?

 

[UrIkOn]

School Assignment:image processing

 

[D H]

Tell us the assignment. Perhaps you misread it. If not, you might be stuck waiting for a day or so to see the results.

Have you learned about FFTs?

 

[UrIkOn]

Ya,I learned fft before.
This is the assignment question:
1. Take a photo with your own camera and import it into Matlab converting it to a 8-bit512x512
pixel gray scale imageI(x,y).
2. Display the original and the gray-scale image.
3. Write your own function to implement the Discrete Fourier Transform (DFT) in Matlab (do NOT use the Matlab function for FFT) of I:
4. Write the Matlab code to implement the functionf(x,y) for the inverse DFT of a 2D array of complex numberF(u,v):
5. Visualise the DFT of your grayscale imageIusingimshow().
(Hint: You may need to scale using log to display the information within the range of the image pixel values, and center so that the origin is shifted to the centre of a 512x512.)
6. Construct a 512x512 template for alow pass lter using a Cosine curve, where thehigh frequency components are zeroed. Apply this lter to the DFT of your image. Take the inverse DFT and visualise the Real, Imaginary and Phase. Compare with your original image. Describe each of the 5 visualised outputs (Original image, Filtered image, DFT Real, DFT Imaginary and DFT Phase).
7. Construct a 512x512 template for ahigh pass lterusing a Sine curve where thelow frequency components are zeroed. Apply this lter to the DFT of your image. Take the inverse DFT and visualise the Real, Imaginary and Phase. Describe each of the 5 visualised outputs (Original image, Filtered image, DFT Real, DFT Imaginary and DFT Phase).

 

[D H]

The chief culprit here is that you are computing the complex exponential 512⁴ = 68,719,476,736 times. The complex exponential obeys the identity $\exp(u+v) = \exp(u)\cdot \exp(v)$. Couple this identity with the fact that your image is square and you can reduce the number of calls to the complex exponential to 512² = 262,144.

 

[jhae2.718]

Also, MATLAB is horrible with loops. If you can vectorize your problem it will compute much faster.