I have to find the local minima and maxima corresponding to the "peaks" and "valleys" of a data file.

Given this data file (which contains two vectors for x and y coordinates along with a 2D matrix corresponding to altitude), I have to find the specific local maxima and minima (coordinates and altitude) that correspond to the "peaks" and "valleys" of the data (excluding hills on the borders of the plot). After plotting the altitude matrix using surf, it's easy to see that there are three obvious peaks and three obvious valleys, but I'm not sure how to find specific coordinates or altitude. How should I do this? I'm sure the way to do it is by writing a specific loop that allows you to examine the points to find the largest ones, but I've been messing around with it for a while and haven't gotten anywhere. For reference, I've been told that I can't use add-ons or toolboxes that would simplify this procedure, so that's made it a lot more annoying.

Answer 1

[Sulaymon Eshkabilov]

Have you worked with fminsearch() fcn of optimization toolbox:

https://www.mathworks.com/help/matlab/ref/fminsearch.html

[John Henderson]

I have not used it before, no. Would that provide me with all of the necessary minimums or just the global minimum?

Answer 2

[Image Analyst]

You can try imregionalmin() and imregionalmax() to find where the local max and min lie.

Also see Steve's blog on finding peaks in 2-D images:

https://blogs.mathworks.com/steve/2021/09/17/small-peak-suppression-with-the-h-maxima-transform/

[John Henderson]

Don't both those functions require the image processing toolbox? I've definitely explored that route, but I'm more interested in doing this without the use of additional toolboxes that I have to install.

[Image Analyst]

Yes. However you can simply do a brute force search. Search every location in the array and see if it's greater than or equal to any other elements in the local window. Shouldn't take too long for a few million pixels.