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In an image resizing interpolation problem, one could use np.meshgrid on row and col indices before operating on the meshed indices:

nrows = 600

ncols = 800

image_in = np.random.randint(0, 256, size=(nrows, ncols, 3))

scale_factor = 1.5



r = np.arange(nrows, dtype=float) * scale_factor

c = np.arange(ncols, dtype=float) * scale_factor



rr, cc = np.meshgrid(r, c, indexing='ij')



# Nearest Neighbor Interpolation

# np.floor if scale_factor >= 1. np.ceil otherwise

rr = np.floor(rr).astype(int).clip(0, nrows-1)

cc = np.floor(cc).astype(int).clip(0, ncols-1)



image_out = image_in[rr, cc, :]

Now, how would I reverse this process? Say given rr_1, cc_1 (product of np.meshgrid) that's processed in an unknown manner (here illustrated by np.random.randint), how do I get the r_1 and c_1, that is, the inputs to np.meshgrid (preferably with ij indexing)?

# Suppose rr_1, cc_1 = np.meshgrid(r_1, c_1, indexing='ij')

rr_1 = np.random.randint(0, nrows, size=(nrows, ncols, 3))

cc_1 = np.random.randint(0, ncols, size=(nrows, ncols, 3))



r_1 = ?

c_1 = ?

UPDATE:

I figured it out immediately after posting. The answer is:

# Suppose rr_1, cc_1 = np.meshgrid(r_1, c_1, indexing='ij')

rr_1 = np.random.randint(0, nrows, size=(nrows, ncols, 3))

cc_1 = np.random.randint(0, ncols, size=(nrows, ncols, 3))



r_1 = rr_1[:, 0]

c_1 = cc_1[0]

The numpy.meshgrid creates a higher dimensional array from input arrays in order to create grid-like arrays. So imagine you want to get a 2D grid by using some input 1D vectors r and c. numpy.meshgrid returns rr and cc as 2D arrays which respectively hold the y axis or x axis constant everywhere on the 2D array (this is why it is a grid).

Here is a test case:

import numpy as np



r = np.arange(5)      # [0 1 2 3 4]

c = np.arange(5,10,1) # [5 6 7 8 9]



rr, cc = np.meshgrid(r,c,indexing='ij')



r_original = rr[:,0]

c_original = cc[0,:]



print(r_original)     # [0 1 2 3 4]

print(c_original)     # [5 6 7 8 9]

Note that the grids we have created for rr and cc are

rr = [[0 0 0 0 0]

      [1 1 1 1 1]

      [2 2 2 2 2]

      [3 3 3 3 3]

      [4 4 4 4 4]]



cc = [[5 6 7 8 9]

      [5 6 7 8 9]

      [5 6 7 8 9]

      [5 6 7 8 9]

      [5 6 7 8 9]]

Since you are using indexing='ij' in your case and the 2D arrays are transposed. Hence, the values that hold constant for rr and cc respectively are the x axis and y axis (contrary to the case where you do not use indexing='ij').