As you may know there are several edge detection algorithms available. An overview is given at wikipedia: http://en.wikipedia.org/wiki/Edge_detection

I think the most popular ones are Canny, Sobel and Prewitt but know that there are a lot more algorithms out there. Many of those algorithms utilize in one way or another the (approximated) gradient direction and magnitude at each image point. Commonly those are computed by convolving the image with a kernel (filter mask) yielding the image derivatives in x and y direction. The magnitude and direction of the gradients can then be computed using those derivatives. Since it is kind of awkward to write formulas here at RG I would advise you to look e.g. at the explanation of the Sobel operator here: http://en.wikipedia.org/wiki/Sobel_operator.

It is a good excercise to implement an edge detection by yourself in a language of your choice. Note however, that implementations of many algorithms do exists in all of the commonly used image processing tools. Just to name a few:

• In Matlab you could use the edge function if you have the Image Processing Toolbox
• In openCV there is the Sobel function
• in ITK the SobelEdgeDetectionImageFilter

You could use simple convolution filters, like Sobel or Prewitt.

Or compute the horizontal derivative by subtracting each pixelvalue from the one on the right to it, then compute the vertical derivative by subtracting each pixelvalue from the one below it. If you then apply Pythagoras on the two resulting images, you get the first derivative. This method is more sensitive to noise than the Sobel and the Prewitt operators, because they do some averaging as well. Beware that the first derivative is shifted half a pixel to the right and to the bottom!

Do the same on the first derivative, and you get the second order derivative.

You could use Matlab function imgradient...

Just use the matlab function  gradient as follows: [H, V]=gradient (im). You obtain the horizontal and the  vertical gradient.

As you may know there are several edge detection algorithms available. An overview is given at wikipedia: http://en.wikipedia.org/wiki/Edge_detection

I think the most popular ones are Canny, Sobel and Prewitt but know that there are a lot more algorithms out there. Many of those algorithms utilize in one way or another the (approximated) gradient direction and magnitude at each image point. Commonly those are computed by convolving the image with a kernel (filter mask) yielding the image derivatives in x and y direction. The magnitude and direction of the gradients can then be computed using those derivatives. Since it is kind of awkward to write formulas here at RG I would advise you to look e.g. at the explanation of the Sobel operator here: http://en.wikipedia.org/wiki/Sobel_operator.

It is a good excercise to implement an edge detection by yourself in a language of your choice. Note however, that implementations of many algorithms do exists in all of the commonly used image processing tools. Just to name a few:

• In Matlab you could use the edge function if you have the Image Processing Toolbox
• In openCV there is the Sobel function
• in ITK the SobelEdgeDetectionImageFilter

Partial derivative w.r.t. x-axis and partial derivative w.r.t. y-axis is required to be computed to get the gradient of the image.

http://www.seas.upenn.edu/~cse399b/Lectures/CSE399b-04-edge.pdf

You can try these various edge detectors in matlab such as Robert, Prewit, sobel, canny. see finally see  which suits your requirement

I = imread('circuit.tif');

BW1 = edge(I,'prewitt');

BW2 = edge(I,'canny');

figure, imshow(BW1);

figure, imshow(BW2);

or use fspecial

H = FSPECIAL('prewitt') returns 3-by-3 filter that emphasizes

horizontal edges by approximating a vertical gradient. If you need to

emphasize vertical edges, transpose the filter H: H'.

[1 1 1;0 0 0;-1 -1 -1].

H = FSPECIAL('sobel') returns 3-by-3 filter that emphasizes

horizontal edges utilizing the smoothing effect by approximating a

vertical gradient. If you need to emphasize vertical edges, transpose

the filter H: H'.

[1 2 1;0 0 0;-1 -2 -1].

I established matrix im0 and try to understand the values in Gmag and Gdir but I can not.!!??

im0=[110 54 36 255 0;255 255 0 0 1;0 0 1 255 120;255 4 87 66 0;0 0 0 0 0]

[Gmag, Gdir] = imgradient(im0)

Please, I need to understand how be computed the first value in Gmag and Gdir (657.8146  and  -104.7968) which corresponding to first value 110  in im0.

%--------------------------------------------------------------------------

% computes and displays both the directional gradients

% and the gradient magnitude and gradient direction for the image

%--------------------------------------------------------------------------

[Gx, Gy] = imgradientxy(I);

[Gmag, Gdir] = imgradient(Gx, Gy);

figure, imshow(Gmag, []), title('Gradient magnitude')

figure, imshow(Gdir, []), title('Gradient direction')

% figure, imshow(Gx, []), title('Directional gradient: X axis')

% figure, imshow(Gy, []), title('Directional gradient: Y axis')

title('Gradient Magnitude and Gradient Direction')

figure; imshowpair(Gx, Gy, 'montage'); axis off;

title('Directional Gradients, Gx and Gy')

The following article in my blog explains how to calculate Image gradients in both X and Y directions without using imgradient ()  function. 

Visit the following link. 

https://naveenideas.blogspot.in/2016/07/image-gradients.html.

if i want to compute the second parial derivation of an image for Dxx Dyy and Dxy using mask ? 

Hi, imgradientxy is a function in matlab, what about opencv C++? how I can compute gradient there? thank you