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Finding local maximum in grayscale image

Hello,

I'm new to OpenCV and still learning so I'm looking for an as simple as possible solution to my problem.

I have a sample picture that looks like this

grayscaleImage

I want to find the local maximums in the picture using Python and OpenCV and anything else that could possibly be useful. Scikit-image possibly?

I have researched and found people saying that first I need to dilate the image using a 5x5 kernel with a 0 pixel in the middle and then replace every pixel with the maximum of it's neighbors, although I'm not sure how I should do the 2nd part.

Anyone here willing to help out a noob with a noob-friendly answer? :)