from __future__ import print_function, division """ COUNTLESS performance test in Python. python countless2d.py ./images/NAMEOFIMAGE """ import six from six.moves import range from collections import defaultdict from functools import reduce import operator import io import os from PIL import Image import math import numpy as np import random import sys import time from tqdm import tqdm from scipy import ndimage def simplest_countless(data): """ Vectorized implementation of downsampling a 2D image by 2 on each side using the COUNTLESS algorithm. data is a 2D numpy array with even dimensions. """ sections = [] # This loop splits the 2D array apart into four arrays that are # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), # and (1,1) representing the A, B, C, and D positions from Figure 1. factor = (2,2) for offset in np.ndindex(factor): part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) a, b, c, d = sections ab = a * (a == b) # PICK(A,B) ac = a * (a == c) # PICK(A,C) bc = b * (b == c) # PICK(B,C) a = ab | ac | bc # Bitwise OR, safe b/c non-matches are zeroed return a + (a == 0) * d # AB || AC || BC || D def quick_countless(data): """ Vectorized implementation of downsampling a 2D image by 2 on each side using the COUNTLESS algorithm. data is a 2D numpy array with even dimensions. """ sections = [] # This loop splits the 2D array apart into four arrays that are # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), # and (1,1) representing the A, B, C, and D positions from Figure 1. factor = (2,2) for offset in np.ndindex(factor): part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) a, b, c, d = sections ab_ac = a * ((a == b) | (a == c)) # PICK(A,B) || PICK(A,C) w/ optimization bc = b * (b == c) # PICK(B,C) a = ab_ac | bc # (PICK(A,B) || PICK(A,C)) or PICK(B,C) return a + (a == 0) * d # AB || AC || BC || D def quickest_countless(data): """ Vectorized implementation of downsampling a 2D image by 2 on each side using the COUNTLESS algorithm. data is a 2D numpy array with even dimensions. """ sections = [] # This loop splits the 2D array apart into four arrays that are # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), # and (1,1) representing the A, B, C, and D positions from Figure 1. factor = (2,2) for offset in np.ndindex(factor): part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) a, b, c, d = sections ab_ac = a * ((a == b) | (a == c)) # PICK(A,B) || PICK(A,C) w/ optimization ab_ac |= b * (b == c) # PICK(B,C) return ab_ac + (ab_ac == 0) * d # AB || AC || BC || D def quick_countless_xor(data): """ Vectorized implementation of downsampling a 2D image by 2 on each side using the COUNTLESS algorithm. data is a 2D numpy array with even dimensions. """ sections = [] # This loop splits the 2D array apart into four arrays that are # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), # and (1,1) representing the A, B, C, and D positions from Figure 1. factor = (2,2) for offset in np.ndindex(factor): part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) a, b, c, d = sections ab = a ^ (a ^ b) # a or b ab += (ab != a) * ((ab ^ (ab ^ c)) - b) # b or c ab += (ab == c) * ((ab ^ (ab ^ d)) - c) # c or d return ab def stippled_countless(data): """ Vectorized implementation of downsampling a 2D image by 2 on each side using the COUNTLESS algorithm that treats zero as "background" and inflates lone pixels. data is a 2D numpy array with even dimensions. """ sections = [] # This loop splits the 2D array apart into four arrays that are # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), # and (1,1) representing the A, B, C, and D positions from Figure 1. factor = (2,2) for offset in np.ndindex(factor): part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) a, b, c, d = sections ab_ac = a * ((a == b) | (a == c)) # PICK(A,B) || PICK(A,C) w/ optimization ab_ac |= b * (b == c) # PICK(B,C) nonzero = a + (a == 0) * (b + (b == 0) * c) return ab_ac + (ab_ac == 0) * (d + (d == 0) * nonzero) # AB || AC || BC || D def zero_corrected_countless(data): """ Vectorized implementation of downsampling a 2D image by 2 on each side using the COUNTLESS algorithm. data is a 2D numpy array with even dimensions. """ # allows us to prevent losing 1/2 a bit of information # at the top end by using a bigger type. Without this 255 is handled incorrectly. data, upgraded = upgrade_type(data) # offset from zero, raw countless doesn't handle 0 correctly # we'll remove the extra 1 at the end. data += 1 sections = [] # This loop splits the 2D array apart into four arrays that are # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), # and (1,1) representing the A, B, C, and D positions from Figure 1. factor = (2,2) for offset in np.ndindex(factor): part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) a, b, c, d = sections ab = a * (a == b) # PICK(A,B) ac = a * (a == c) # PICK(A,C) bc = b * (b == c) # PICK(B,C) a = ab | ac | bc # Bitwise OR, safe b/c non-matches are zeroed result = a + (a == 0) * d - 1 # a or d - 1 if upgraded: return downgrade_type(result) # only need to reset data if we weren't upgraded # b/c no copy was made in that case data -= 1 return result def countless_extreme(data): nonzeros = np.count_nonzero(data) # print("nonzeros", nonzeros) N = reduce(operator.mul, data.shape) if nonzeros == N: print("quick") return quick_countless(data) elif np.count_nonzero(data + 1) == N: print("quick") # print("upper", nonzeros) return quick_countless(data) else: return countless(data) def countless(data): """ Vectorized implementation of downsampling a 2D image by 2 on each side using the COUNTLESS algorithm. data is a 2D numpy array with even dimensions. """ # allows us to prevent losing 1/2 a bit of information # at the top end by using a bigger type. Without this 255 is handled incorrectly. data, upgraded = upgrade_type(data) # offset from zero, raw countless doesn't handle 0 correctly # we'll remove the extra 1 at the end. data += 1 sections = [] # This loop splits the 2D array apart into four arrays that are # all the result of striding by 2 and offset by (0,0), (0,1), (1,0), # and (1,1) representing the A, B, C, and D positions from Figure 1. factor = (2,2) for offset in np.ndindex(factor): part = data[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) a, b, c, d = sections ab_ac = a * ((a == b) | (a == c)) # PICK(A,B) || PICK(A,C) w/ optimization ab_ac |= b * (b == c) # PICK(B,C) result = ab_ac + (ab_ac == 0) * d - 1 # (matches or d) - 1 if upgraded: return downgrade_type(result) # only need to reset data if we weren't upgraded # b/c no copy was made in that case data -= 1 return result def upgrade_type(arr): dtype = arr.dtype if dtype == np.uint8: return arr.astype(np.uint16), True elif dtype == np.uint16: return arr.astype(np.uint32), True elif dtype == np.uint32: return arr.astype(np.uint64), True return arr, False def downgrade_type(arr): dtype = arr.dtype if dtype == np.uint64: return arr.astype(np.uint32) elif dtype == np.uint32: return arr.astype(np.uint16) elif dtype == np.uint16: return arr.astype(np.uint8) return arr def odd_to_even(image): """ To facilitate 2x2 downsampling segmentation, change an odd sized image into an even sized one. Works by mirroring the starting 1 pixel edge of the image on odd shaped sides. e.g. turn a 3x3x5 image into a 4x4x5 (the x and y are what are getting downsampled) For example: [ 3, 2, 4 ] => [ 3, 3, 2, 4 ] which is now easy to downsample. """ shape = np.array(image.shape) offset = (shape % 2)[:2] # x,y offset # detect if we're dealing with an even # image. if so it's fine, just return. if not np.any(offset): return image oddshape = image.shape[:2] + offset oddshape = np.append(oddshape, shape[2:]) oddshape = oddshape.astype(int) newimg = np.empty(shape=oddshape, dtype=image.dtype) ox,oy = offset sx,sy = oddshape newimg[0,0] = image[0,0] # corner newimg[ox:sx,0] = image[:,0] # x axis line newimg[0,oy:sy] = image[0,:] # y axis line return newimg def counting(array): factor = (2, 2, 1) shape = array.shape while len(shape) < 4: array = np.expand_dims(array, axis=-1) shape = array.shape output_shape = tuple(int(math.ceil(s / f)) for s, f in zip(shape, factor)) output = np.zeros(output_shape, dtype=array.dtype) for chan in range(0, shape[3]): for z in range(0, shape[2]): for x in range(0, shape[0], 2): for y in range(0, shape[1], 2): block = array[ x:x+2, y:y+2, z, chan ] # 2x2 block hashtable = defaultdict(int) for subx, suby in np.ndindex(block.shape[0], block.shape[1]): hashtable[block[subx, suby]] += 1 best = (0, 0) for segid, val in six.iteritems(hashtable): if best[1] < val: best = (segid, val) output[ x // 2, y // 2, chan ] = best[0] return output def ndzoom(array): if len(array.shape) == 3: ratio = ( 1 / 2.0, 1 / 2.0, 1.0 ) else: ratio = ( 1 / 2.0, 1 / 2.0) return ndimage.interpolation.zoom(array, ratio, order=1) def countless_if(array): factor = (2, 2, 1) shape = array.shape if len(shape) < 3: array = array[ :,:, np.newaxis ] shape = array.shape output_shape = tuple(int(math.ceil(s / f)) for s, f in zip(shape, factor)) output = np.zeros(output_shape, dtype=array.dtype) for chan in range(0, shape[2]): for x in range(0, shape[0], 2): for y in range(0, shape[1], 2): block = array[ x:x+2, y:y+2, chan ] # 2x2 block if block[0,0] == block[1,0]: pick = block[0,0] elif block[0,0] == block[0,1]: pick = block[0,0] elif block[1,0] == block[0,1]: pick = block[1,0] else: pick = block[1,1] output[ x // 2, y // 2, chan ] = pick return np.squeeze(output) def downsample_with_averaging(array): """ Downsample x by factor using averaging. @return: The downsampled array, of the same type as x. """ if len(array.shape) == 3: factor = (2,2,1) else: factor = (2,2) if np.array_equal(factor[:3], np.array([1,1,1])): return array output_shape = tuple(int(math.ceil(s / f)) for s, f in zip(array.shape, factor)) temp = np.zeros(output_shape, float) counts = np.zeros(output_shape, np.int) for offset in np.ndindex(factor): part = array[tuple(np.s_[o::f] for o, f in zip(offset, factor))] indexing_expr = tuple(np.s_[:s] for s in part.shape) temp[indexing_expr] += part counts[indexing_expr] += 1 return np.cast[array.dtype](temp / counts) def downsample_with_max_pooling(array): factor = (2,2) if np.all(np.array(factor, int) == 1): return array sections = [] for offset in np.ndindex(factor): part = array[tuple(np.s_[o::f] for o, f in zip(offset, factor))] sections.append(part) output = sections[0].copy() for section in sections[1:]: np.maximum(output, section, output) return output def striding(array): """Downsample x by factor using striding. @return: The downsampled array, of the same type as x. """ factor = (2,2) if np.all(np.array(factor, int) == 1): return array return array[tuple(np.s_[::f] for f in factor)] def benchmark(): filename = sys.argv[1] img = Image.open(filename) data = np.array(img.getdata(), dtype=np.uint8) if len(data.shape) == 1: n_channels = 1 reshape = (img.height, img.width) else: n_channels = min(data.shape[1], 3) data = data[:, :n_channels] reshape = (img.height, img.width, n_channels) data = data.reshape(reshape).astype(np.uint8) methods = [ simplest_countless, quick_countless, quick_countless_xor, quickest_countless, stippled_countless, zero_corrected_countless, countless, downsample_with_averaging, downsample_with_max_pooling, ndzoom, striding, # countless_if, # counting, ] formats = { 1: 'L', 3: 'RGB', 4: 'RGBA' } if not os.path.exists('./results'): os.mkdir('./results') N = 500 img_size = float(img.width * img.height) / 1024.0 / 1024.0 print("N = %d, %dx%d (%.2f MPx) %d chan, %s" % (N, img.width, img.height, img_size, n_channels, filename)) print("Algorithm\tMPx/sec\tMB/sec\tSec") for fn in methods: print(fn.__name__, end='') sys.stdout.flush() start = time.time() # tqdm is here to show you what's going on the first time you run it. # Feel free to remove it to get slightly more accurate timing results. for _ in tqdm(range(N), desc=fn.__name__, disable=True): result = fn(data) end = time.time() print("\r", end='') total_time = (end - start) mpx = N * img_size / total_time mbytes = N * img_size * n_channels / total_time # Output in tab separated format to enable copy-paste into excel/numbers print("%s\t%.3f\t%.3f\t%.2f" % (fn.__name__, mpx, mbytes, total_time)) outimg = Image.fromarray(np.squeeze(result), formats[n_channels]) outimg.save('./results/{}.png'.format(fn.__name__, "PNG")) if __name__ == '__main__': benchmark() # Example results: # N = 5, 1024x1024 (1.00 MPx) 1 chan, images/gray_segmentation.png # Function MPx/sec MB/sec Sec # simplest_countless 752.855 752.855 0.01 # quick_countless 920.328 920.328 0.01 # zero_corrected_countless 534.143 534.143 0.01 # countless 644.247 644.247 0.01 # downsample_with_averaging 372.575 372.575 0.01 # downsample_with_max_pooling 974.060 974.060 0.01 # ndzoom 137.517 137.517 0.04 # striding 38550.588 38550.588 0.00 # countless_if 4.377 4.377 1.14 # counting 0.117 0.117 42.85 # Run without non-numpy implementations: # N = 2000, 1024x1024 (1.00 MPx) 1 chan, images/gray_segmentation.png # Algorithm MPx/sec MB/sec Sec # simplest_countless 800.522 800.522 2.50 # quick_countless 945.420 945.420 2.12 # quickest_countless 947.256 947.256 2.11 # stippled_countless 544.049 544.049 3.68 # zero_corrected_countless 575.310 575.310 3.48 # countless 646.684 646.684 3.09 # downsample_with_averaging 385.132 385.132 5.19 # downsample_with_max_poolin 988.361 988.361 2.02 # ndzoom 163.104 163.104 12.26 # striding 81589.340 81589.340 0.02