how to get gradient of an image

hi im having a hyperspectral image and im trying to get the gradient operators of the horizontal and vertical directions but i can't any help? Thanks

Answer 1

[Walter Roberson]

for band = 1 : size(X,3)
  [GX(:,:,band), GY(:,:,band)] = gradient(X(:,:,band));
end

Note you get out two matrices the same size as the original.

[Rawan hamdi]

And what if i want to get the gradient from the perspective of the 1-D spectral domain pixel by pixel? And then i need to multiply the resulting gradient by 12. Any help would be much appreciated.

[Image Analyst]

This gets the gradients in the X and Y directions, not in the Z (wavelength) direction as you requested in your comment to me. But like I said, that (what you asked for) doesn't make sense anyway.

[Rawan hamdi]

Thank you, but what I'm doing is the cubic total variation to denoise a hyperspectral image and it requires calculating it as follows :

 Segma m = 1 to M (sqrt ( deltax.^2+deltay.^2+(deltaz.^2).*12)) ===> 1

where delta is the gradient operator in x,y and z directions, and M is the no of pixels.

and then adding this in a loop from 1 to b where b is the number of bands

So how can i implement this?

Thanks

[Image Analyst]

I don't know what the "cubic total variation" is. Nor do I understand what your pseudocode is trying to say. When you say "... ===> 1", what is being set to 1? And I really question the addition of a wavelength difference squared to a distance difference squared. The units don't even match up so I just can't see the justification for it. Maybe someone can explain it to me.

[Walter Roberson]

[GX, GY, GZ] = gradient(X);

I recommend you consider adding spacing values as discussed at http://www.mathworks.com/help/matlab/ref/gradient.html . You would need to think, though, about whether to specify the z spacing in terms of wavelength or frequency.

[Rawan hamdi]

Does GZ represents the gradient in the spectral domain? if yes can i multiply this value by a contant? Thank you

[Image Analyst]

12*GZ

[Rawan hamdi]

Thank you very much.

i have a question, how can i obtain the cost function :

u = arg min(||g-u||).^2 + lambda.R(u) where the term "(||g-u||).^2" is the data fidelity term between the original clean image and the noisy image and R(u) is a regularization parameter. Thanks

[Walter Roberson]

I recommend you start a new question for that.

Answer 2

[Image Analyst]

The Image Processing Toolbox has imgradient() and imgradientxy() functions.

[Rawan hamdi]

i'm using version 2010a of Matlab and there's no function called 'imgradient' Any help?

[Image Analyst]

Do it yourself then with conv2 and kernels [-1;1;0] and [-1,1,0].

verticalGradient = conv2(grayImage, [-1;1;0], 'same');  
horizontalGradient = conv2(grayImage, [-1,1,0], 'same');

[Rawan hamdi]

Okay but what if i need to calculate the gradient at the z dimension too?

[Image Analyst]

That does not make sense to me. In the lateral x,y direction you have units of "per pixel" but in the Z direction since the planes are different wavelengths, not distance in pixels, the gradient is not a spatial gradient. It would have units of "per wavelength". And you certainly wouldn't want a 3D gradient with spatial coordinates mixed with wavelength coordinates. It makes no sense, at least not to me.

[Rawan hamdi]

Okay the thing is im that im looping on both x and y and getting the gradient in the spectral domain (z direction) the image i have is [280,307,191] so i'm trying to get the gradient of each pixel in the spectral domain and having the result as a matrix same size of the image,What should i do? Any help would be much appreciated

Answer 3

[Anand]

Try this:

[~,~,Gy,Gx] = edge(imread('cameraman.tif'),'sobel');

[Venkat]

This works.