With a 5x5, the gradient detection will be less sensitive to local noise since that more neighbourhood will be taken into account.

Then, I am not sure that you can define this property as an advantage. This parameter has to be decided depending of the application, the type of noise, etc.

Gradient is used for finding magnitude and direction. If you choose more size of the window then the direction will be more accurate. However, as Guillaume Lemaître says above that it totally depends upon your application.

You can clarify your application here, then may be we can put more light on the same.

In general, I am working on edge detection for low contrast image and medical application (MRI, Retina) , but when I applied the 5x5 Sobel operator on an artificial ima, the edge intensity increases and the edge becomes big .

Usually, you can enhance the image first. Also, you have other method to detect image. I prefer the phase congruency: http://www.csse.uwa.edu.au/~pk/research/matlabfns/#phasecong

AS others have said the size of the edge enchancement filter will depend on the application.  I did pubish a paper (on the list within research gate) about using the variance / Std Dev of the horizontal 1st difference / derivative to determine the size of the optimum window / kernel size for edge enhancement.  Basically, the lower the variance the larger the window; for example, an image with low variance in the 1st difference might require a window size of 11 by 11 pixels while one with a high amount of variance might need a 3 by 3 window.  The work was done quite a while agoe (early to mid 80s) so I am sure there are other and perhaps better methods that have been published.

Pat

Undoubtedly, using 5x5 window , you can get better results , because it takes into account more information about the focused pixel. But, the algorithms used in the case 5x5 must be more sophisticated than those used in the case of 3x3. Thus , one can obtain thin lines for edge representation.

Mr Pat S. Chavez, Jr. 

Could you share with me or let me know the name of the paper you describe to read it?

Best regards.

Ramon,

The title of the paper is:

An automatic Optimum kernel-size selection technique for edge enhancement

Pat Chavez, Brian Bauer

Remote Sensing of Environment

I published this paper in the 80s and will try to find a copy for you; perhaps you can Google it and see what shows up.

Pat

Ramon,

I found a copy and down loaded it into the research gate list of pubs so you should be able to down loaded from there.   Let me know if you have any problems getting a copy of it.

Pat

This is also a good explanation https://www.iasj.net/iasj?func=fulltext&aId=52927

The robustness, 5x5 mask presents a bet stability one a border is found