Unusual histogram after image decimation

Question

After simple image decimation using: img_decim_arr = img_arr[::2,::2], I obtained histogram very similar to original image histogram:
Decimation using: skimage.measure.block_reduce(img_arr, block_size = (2,2), func=np.mean) (2x2 block averaging) which is recommended method for downsampling (found on stackoverflow in some discussion) produces very characteristic histogram:
Every second bin is bigger. I am not sure maybe this is due to some aliasing effect. Can anyone please explain and give some theoretical hints about how downsampling affects image (2D signal) histogram?

Answer 1

The problem is the np.mean function, because it does not round to integers and returns floats.

import numpy as np
import skimage.measure

a = (10 * np.random.randn(10,10) + 127).astype(np.uint8)
a
Out[4]: 
array([[121, 124, 139, 129, 130, 114, 127,  96, 114, 135],
       [127, 132, 102, 142, 119, 107, 138, 130, 141, 132],
       [113, 132, 132, 118, 121, 120, 142, 115, 124, 128],
       [127, 121, 129, 129, 121, 119, 126, 113, 128, 116],
       [144, 131, 123, 131, 130, 137, 140, 142, 127, 128],
       [127, 126, 124, 115, 127, 125, 122, 126, 147, 132],
       [118, 119, 117, 117, 133, 149, 122, 120, 116, 138],
       [147, 147, 127, 117, 123, 123, 136, 121, 139, 129],
       [142, 129, 113, 111, 130, 116, 137, 127, 106, 148],
       [132, 141, 141, 142, 119, 132, 126, 115, 131, 122]], dtype=uint8)

b = skimage.measure.block_reduce(a, block_size = (2,2), func=np.mean)
b
Out[6]: 
array([[ 126.  ,  128.  ,  117.5 ,  122.75,  130.5 ],
       [ 123.25,  127.  ,  120.25,  124.  ,  124.  ],
       [ 132.  ,  123.25,  129.75,  132.5 ,  133.5 ],
       [ 132.75,  119.5 ,  132.  ,  124.75,  130.5 ],
       [ 136.  ,  126.75,  124.25,  126.25,  126.75]])

That might give you interesting side-effects in your own logic. It definitely screws with matplotlibs histogram function, because having floats makes it think differently about how to place the bin borders.

Check this out:

a = (10 * np.random.randn(200,200) + 127).astype(np.uint8)
b = skimage.measure.block_reduce(a, block_size = (2,2), func=np.mean)
hist(b.ravel(), bins=255)

The white bits are actually zero in the array that the hist function returns. It gets even worse if you force rounding in my toy example:

hist(b.ravel().astype(np.uint8), bins=255)

Giving it the bins and the range solves the problem. Even if you zoom close

 hist(b.ravel().astype(np.uint8), bins=255, range=(0,255))