How to calculate gradient of 512*512*4 image?

Is this wrong or write?

If my output image is g(512*512*4) then gradient of g() is

gradver1=sqrt(g1(:,:,1).^2+g1(:,:,2).^2+g1(:,:,3).^2+g1(:,:,4).^2);

Answer 1

[Raghava S N]

Hi,

From my understanding, you are looking to calculate the gradient of a 3D image.

Refer to this link which describes how to find the gradient magnitude and direction of 3-D image using the “imgradient3” function - https://www.mathworks.com/help/images/ref/imgradient3.html.

The directional gradients of a 3-D image can be found using the “imgradientxyz” function. Refer to this link for more information - https://www.mathworks.com/help/images/ref/imgradientxyz.html.

Hope this helps!

Answer 2

[KALYAN ACHARJYA]

This 512×512×4 representation corresponds to four channels. It simplifies the computation of gradients for individual channels. Each channel g(:,:,1),g(:,:,2),g(:,:,3),g(:,:,4) is treated as a separate 2D image, and the gradient is calculated independently for each channel across the spatial dimensions.

[gx1, gy1] = gradient(g(:,:,1)); 
[gx2, gy2] = gradient(g(:,:,2)); 
[gx3, gy3] = gradient(g(:,:,3)); 
[gx4, gy4] = gradient(g(:,:,4)); 

Gradient Magnitude of each Channel

gradMag1 = sqrt(gx1.^2 + gy1.^2); 
gradMag2 = sqrt(gx2.^2 + gy2.^2); 
gradMag3 = sqrt(gx3.^2 + gy3.^2); 
gradMag4 = sqrt(gx4.^2 + gy4.^2); 

Now compute the combine gradient of all channels

grad_final= sqrt(gradMag1.^2 + gradMag2.^2 + gradMag3.^2 + gradMag4.^2); 

Hope it helps!

[DGM]

We can also use imgradient to skip a step here too. If we want the same behavior as gradient(), we need to specify the non-default method for calculating the directional derivative.

inpict = imread('pep_cmyk.tif.fakeextension.txt'); % CMYK, uint8
inpict = im2double(inpict); % needs to be float

% using gradient()
[gx1, gy1] = gradient(inpict(:,:,1)); 
[gx2, gy2] = gradient(inpict(:,:,2)); 
[gx3, gy3] = gradient(inpict(:,:,3)); 
[gx4, gy4] = gradient(inpict(:,:,4)); 
gradMag1 = sqrt(gx1.^2 + gy1.^2); 
gradMag2 = sqrt(gx2.^2 + gy2.^2); 
gradMag3 = sqrt(gx3.^2 + gy3.^2); 
gradMag4 = sqrt(gx4.^2 + gy4.^2); 
grad_final0 = sqrt(gradMag1.^2 + gradMag2.^2 + gradMag3.^2 + gradMag4.^2); 

% using IPT imgradient()
gradMag1 = imgradient(inpict(:,:,1),'central'); 
gradMag2 = imgradient(inpict(:,:,2),'central'); 
gradMag3 = imgradient(inpict(:,:,3),'central'); 
gradMag4 = imgradient(inpict(:,:,4),'central'); 
grad_final = sqrt(gradMag1.^2 + gradMag2.^2 + gradMag3.^2 + gradMag4.^2); 

% the error is negligible
immse(grad_final0,grad_final)

ans = 2.4301e-35