如何（稳健地）在 python 的二维数组上找到局部最小值？

Question

I have a 2D array which represent the value of a certain function f(x, y), and I would like to detect the minimum on the array. Generally it just looks like that, so it's easy to spot the minimum.

Example normal minimum

But sometimes there is a kind of drift, which means that the actual minimum is not the one I'm looking for.

Example failed minimum

On the above image the minimum I'm looking for is on the left, but the right part of the image has smaller values.

It is really important for me that I get an , which is why I can't really use a maximum filter or stuff like that. I'm looking for a computationally efficient way to detect this minimum, so I'd rather use an existing method instead of doing my own code.

Answer 1

To get the index of the smallest value in a 2D array I would suggest something like this:

find_smallest = lambda arr: np.unravel_index(np.argmin(arr),arr.shape)

Answer 2

Maybe you could try some of the solvers in scipy.optimize (for example Nelder-Mead ). These will look for local minima.

Then, to get the minimum that you're looking for, you could try to launch several optimizations from different random points and discard the solutions that end up close to the border of the image. This is, supposing that your minimum is somewhere away from the border. It's an ugly method and probably not very efficient, but I have a little hope that it could work. Also, you'll probably have to tune the parameters.

Otherwise maybe there is some magic that can be done with the gradient function. I guess you'll have to look for some point that has positive derivatives all around it.