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copied!<p>The location of the local minima can be found for an array of arbitrary dimension using <a href="https://stackoverflow.com/questions/3684484/peak-detection-in-a-2d-array/3689710#3689710">Ivan</a>'s <a href="https://stackoverflow.com/questions/3684484/peak-detection-in-a-2d-array/3689710#3689710">detect_peaks function</a>, with minor modifications:</p> <pre><code>import numpy as np import scipy.ndimage.filters as filters import scipy.ndimage.morphology as morphology def detect_local_minima(arr): # https://stackoverflow.com/questions/3684484/peak-detection-in-a-2d-array/3689710#3689710 """ Takes an array and detects the troughs using the local maximum filter. Returns a boolean mask of the troughs (i.e. 1 when the pixel's value is the neighborhood maximum, 0 otherwise) """ # define an connected neighborhood # http://www.scipy.org/doc/api_docs/SciPy.ndimage.morphology.html#generate_binary_structure neighborhood = morphology.generate_binary_structure(len(arr.shape),2) # apply the local minimum filter; all locations of minimum value # in their neighborhood are set to 1 # http://www.scipy.org/doc/api_docs/SciPy.ndimage.filters.html#minimum_filter local_min = (filters.minimum_filter(arr, footprint=neighborhood)==arr) # local_min is a mask that contains the peaks we are # looking for, but also the background. # In order to isolate the peaks we must remove the background from the mask. # # we create the mask of the background background = (arr==0) # # a little technicality: we must erode the background in order to # successfully subtract it from local_min, otherwise a line will # appear along the background border (artifact of the local minimum filter) # http://www.scipy.org/doc/api_docs/SciPy.ndimage.morphology.html#binary_erosion eroded_background = morphology.binary_erosion( background, structure=neighborhood, border_value=1) # # we obtain the final mask, containing only peaks, # by removing the background from the local_min mask detected_minima = local_min - eroded_background return np.where(detected_minima) </code></pre> <p>which you can use like this:</p> <pre><code>arr=np.array([[[0,0,0,-1],[0,0,0,0],[0,0,0,0],[0,0,0,0],[-1,0,0,0]], [[0,0,0,0],[0,-1,0,0],[0,0,0,0],[0,0,0,-1],[0,0,0,0]]]) local_minima_locations = detect_local_minima(arr) print(arr) # [[[ 0 0 0 -1] # [ 0 0 0 0] # [ 0 0 0 0] # [ 0 0 0 0] # [-1 0 0 0]] # [[ 0 0 0 0] # [ 0 -1 0 0] # [ 0 0 0 0] # [ 0 0 0 -1] # [ 0 0 0 0]]] </code></pre> <p>This says the minima occur at indices [0,0,3], [0,4,0], [1,1,1] and [1,3,3]:</p> <pre><code>print(local_minima_locations) # (array([0, 0, 1, 1]), array([0, 4, 1, 3]), array([3, 0, 1, 3])) print(arr[local_minima_locations]) # [-1 -1 -1 -1] </code></pre>

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