Median filter for image Python3

Question

I wanted to implement a radial median filter. I have the following picture (size = (Nx,Ny))

I want to derive radius for each pixels. For each radius compute median value and put it to a new matrix in the place of all pixels with the same radius. I found Image Smoothing Using Median Filter, but it isn't fast enough. And I created my own script, unfortunately, it isn't fast too. I tested it on some generatic data:

import cv2
from PIL import Image
from scipy import stats, ndimage, misc
import matplotlib.pyplot as plt
import numpy as np
import matplotlib.image as mpimg
from scipy import stats


a = np.array([[0.,0.,0.,0.,0.],[0.,5.,1.,9.,0.],[0.,10.,2.,10.,0.],[0.,9.,1.,5.,0.],[0.,0.,0.,0.,0.]])

b = a.copy().flatten()

y,x = np.indices((a.shape))
center = [len(x)//2, len(y)//2]
r = np.hypot(x-center[0],y-center[1])

r = r.astype(np.int) # integer part of radii (bin size = 1)

set_r = set(r.flatten()) # get the list of r without duplication
max_r = max(set_r) # determine the maximum r

median_r = np.array([0.]*len(r.flatten())) # array of median I for each r


for j in set_r:
    result = np.where(r.flatten() == j) 
    median_r[result[0]] = np.median(b[result[0]])



a_med = median_r.reshape(a.shape)

am_med = ndimage.median_filter(a, 3)

plt.figure(figsize=(16, 5))

plt.subplot(141)
plt.imshow(a, interpolation='nearest')
plt.axis('off')
plt.title('Original image', fontsize=20)
plt.subplot(142)
plt.imshow(am_med, interpolation='nearest', vmin=0, vmax=5)
plt.axis('off')
plt.title('Median filter', fontsize=20)
plt.subplot(143)
plt.imshow(a_med, interpolation='nearest')
plt.axis('off')
plt.title('Own median', fontsize=20)


plt.subplots_adjust(wspace=0.02, hspace=0.02, top=0.9, bottom=0, left=0,
                    right=1)

plt.show()

I'd like to find a convenient way for solving this issue

Answer 1

Most of the answers here seem to center on performance optimizations of the naive median filtering algorithm. It's worth noting that the median filters you would find in imaging packages like OpenCV/scikit-image/MATLAB/etc. implement faster algorithms.

http://nomis80.org/ctmf.pdf

If you are median filtering uint8 data, there are a lot of clever tricks to be played with reusing histograms as you move from neighborhood to neighborhood.

I would use the median filter in an imaging package rather than trying to roll one yourself if you care about speed.