Optimize the calculation of horizontal and vertical adjacency using numpy

Question

I have following cells:

cells = np.array([[1, 1, 1],
                  [1, 1, 0],
                  [1, 0, 0],
                  [1, 0, 1],
                  [1, 0, 0],
                  [1, 1, 1]])

and I want to calculate horizontal and vertical adjacencies to come to this result:

# horizontal adjacency 
array([[3, 2, 1],
       [2, 1, 0],
       [1, 0, 0],
       [1, 0, 1],
       [1, 0, 0],
       [3, 2, 1]])

# vertical adjacency 
array([[6, 2, 1],
       [5, 1, 0],
       [4, 0, 0],
       [3, 0, 1],
       [2, 0, 0],
       [1, 1, 1]])

The actual sollution looks like this:

def get_horizontal_adjacency(cells):
    adjacency_horizontal = np.zeros(cells.shape, dtype=int)
    for y in range(cells.shape[0]):
        span = 0
        for x in reversed(range(cells.shape[1])):
            if cells[y, x] > 0:
                span += 1
            else:
                span = 0
            adjacency_horizontal[y, x] = span
    return adjacency_horizontal

def get_vertical_adjacency(cells):
    adjacency_vertical = np.zeros(cells.shape, dtype=int)
    for x in range(cells.shape[1]):
        span = 0
        for y in reversed(range(cells.shape[0])):
            if cells[y, x] > 0:
                span += 1
            else:
                span = 0
            adjacency_vertical[y, x] = span
    return adjacency_vertical

The Algorithm is basically (for horizontal adjacency):

loop throgh rows
loop backward throgh columns
if the x, y value of cells is not zero, add 1 to the actual span
if the x, y value of cells is zero, reset actual span to zero
set the span as new x, y value of the resulting array

Since I need to loop two times over all array elements this is slow for bigger arrays (e.g. images).

Is there a way to improve the algorithm using vectorization or some other numpy magic?

Summary:

Great suggestions have been made by joni and Mark Setchell!

I created a small Repo with a sample image and a python file with the comparisons. The results are astonishing:

Original Approach: 3.675 s
Using Numba: 0.002 s
Using Cython: 0.005 s

user_2836621 · Answer

I had a really quick attempt at this with Numba but have not checked it too thoroughly though the results seem about right:

#!/usr/bin/env python3

# https://stackoverflow.com/q/69854335/2836621
# magick -size 1920x1080 xc:black -fill white -draw "circle 960,540 960,1040" -fill black -draw "circle 960,540 960,800" a.png

import cv2
import numpy as np
import numba as nb

def get_horizontal_adjacency(cells):
    adjacency_horizontal = np.zeros(cells.shape, dtype=int)
    for y in range(cells.shape[0]):
        span = 0
        for x in reversed(range(cells.shape[1])):
            if cells[y, x] > 0:
                span += 1
            else:
                span = 0
            adjacency_horizontal[y, x] = span
    return adjacency_horizontal

@nb.jit('void(uint8[:,::1], int32[:,::1])',parallel=True)
def nb_get_horizontal_adjacency(cells, result):
    for y in nb.prange(cells.shape[0]):
        span = 0
        for x in range(cells.shape[1]-1,-1,-1):
            if cells[y, x] > 0:
                span += 1
            else:
                span = 0
            result[y, x] = span
    return 

# Load image
im = cv2.imread('a.png', cv2.IMREAD_GRAYSCALE)

%timeit get_horizontal_adjacency(im)

result = np.zeros((im.shape[0],im.shape[1]),dtype=np.int32)
%timeit nb_get_horizontal_adjacency(im, result)

The timings are good, showing 4000x speed-up, if it works correctly:

In [15]: %timeit nb_get_horizontal_adjacency(im, result)
695 µs ± 9.12 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

In [17]: %timeit get_horizontal_adjacency(im)
2.78 s ± 44.2 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

Input

Input image was created in 1080p dimensions, i.e. 1920x1080, with ImageMagick using:

magick -size 1920x1080 xc:black -fill white -draw "circle 960,540 960,1040" -fill black -draw "circle 960,540 960,800" a.png

Output (contrast adjusted)

user_4745529 · Answer

As already stated in the comments, this is a perfect example where it's easier to just rewrite the function by means of Cython or Numba. Since Mark already provided a Numba solution, let me provide a Cython solution. First, let's time his solution on my machine for a fair comparison:

In [5]: %timeit nb_get_horizontal_adjacency(im, result)
836 µs ± 36 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Assuming the image im is a np.ndarray with dtype=np.uint8, a parallelised Cython solution looks like this:

In [6]: %%cython -f -a -c=-O3 -c=-march=native -c=-fopenmp --link-args=-fopenmp

from cython import boundscheck, wraparound, initializedcheck
from libc.stdint cimport uint8_t, uint32_t
from cython.parallel cimport prange
import numpy as np

@boundscheck(False)
@wraparound(False)
@initializedcheck(False)
def cy_get_horizontal_adjacency(uint8_t[:, ::1] cells):
    cdef int nrows = cells.shape[0]
    cdef int ncols = cells.shape[1]
    cdef uint32_t[:, ::1] adjacency_horizontal = np.zeros((nrows, ncols), dtype=np.uint32)
    cdef int x, y, span
    for y in prange(nrows, nogil=True, schedule="static"):
        span = 0
        for x in reversed(range(ncols)):
            if cells[y, x] > 0:
                span += 1
            else:
                span = 0
            adjacency_horizontal[y, x] = span
    return np.array(adjacency_horizontal, copy=False)

On my machine, this is nearly two times faster:

In [7]: %timeit cy_get_horizontal_adjacency(im)
431 µs ± 4.38 µs per loop (mean ± std. dev. of 7 runs, 1000 loops each)

Optimize the calculation of horizontal and vertical adjacency using numpy

2 Answers