问题描述
我正在使用Voronoi图进行图像处理（procedurally generated stippling）。 为此，我需要创建一个元组（x，y像素位置）列表（coords_within_cell）的列表（单元）。
我已经开发了几种蛮力算法来完成此任务（请参阅下文），但是它们太慢了，无法处理超过10分。 scipy空间实用程序的效率似乎高出1000倍以上。因此，我想使用scipy生成Voronoi图： https://docs.scipy.org/doc/scipy/reference/generated/scipy.spatial.Voronoi.html
使用scipy生成Voronoi图非常简单，但是不幸的是，我无法弄清楚如何将像元区域转换为像素坐标。最好的方法是什么？
我找到了一个相关的问题，但是没有答案，因此被删除：https://web.archive.org/web/20200120151304/https://stackoverflow.com/questions/57703129/converting-a-voronoi-diagram-into-bitmap
蛮力算法1（太慢）
import math
import random
from PIL import Image
def distance(x1,y1,x2,y2):
return math.hypot(x2 - x1,y2 - y1)
# define the size of the x and y bounds
screen_width = 1260
screen_height = 1260
# define the number of points that should be used
number_of_points = 16
# randomly generate a list of n points within the given x and y bounds
point_x_coordinates = random.sample(range(0,screen_width),number_of_points)
point_y_coordinates = random.sample(range(0,screen_height),number_of_points)
points = list(zip(point_x_coordinates,point_y_coordinates))
# each point needs to have a corresponding list of pixels
point_pixels = []
for i in range(len(points)):
point_pixels.append([])
# for each pixel within bounds,determine which point it is closest to and add it to the corresponding list in point_pixels
for pixel_y_coordinate in range(screen_height):
for pixel_x_coordinate in range(screen_width):
distance_to_closest_point = float('inf')
closest_point_index = 1
for point_index,point in enumerate(points):
distance_to_point = distance(pixel_x_coordinate,pixel_y_coordinate,point[0],point[1])
if(distance_to_point < distance_to_closest_point):
closest_point_index = point_index
distance_to_closest_point = distance_to_point
point_pixels[closest_point_index].append((pixel_x_coordinate,pixel_y_coordinate))
# each point needs to have a corresponding centroid
point_pixels_centroid = []
for pixel_group in point_pixels:
x_sum = 0
y_sum = 0
for pixel in pixel_group:
x_sum += pixel[0]
y_sum += pixel[1]
x_average = x_sum / len(pixel_group)
y_average = y_sum / len(pixel_group)
point_pixels_centroid.append((round(x_average),round(y_average)))
# display the resulting voronoi diagram
display_voronoi = Image.new("RGB",(screen_width,"white")
for pixel_group in point_pixels:
rgb = random.sample(range(0,255),3)
for pixel in pixel_group:
display_voronoi.putpixel( pixel,(rgb[0],rgb[1],rgb[2],255) )
for centroid in point_pixels_centroid:
print(centroid)
display_voronoi.putpixel( centroid,(1,1,255) )
display_voronoi.show()
蛮力算法2（也太慢了）： Based on this concept.
import math
import random
from PIL import Image
def distance(x1,y2 - y1)
# define the size of the x and y bounds
screen_width = 500
screen_height = 500
# define the number of points that should be used
number_of_points = 4
# randomly generate a list of n points within the given x and y bounds
point_x_coordinates = random.sample(range(0,determine which point it is closest to and add it to the corresponding list in point_pixels
# do this by continuously growing circles outwards from the points
# if circles overlap then whoever was their first claims the location
# keep track of whether pixels have been used or not
# this is done via a 2D list of booleans
is_drawn_on = []
for i in range(screen_width):
is_drawn_on.append([])
for j in range(screen_height):
is_drawn_on[i].append(False)
circles_are_growing = True
radius = 1
while(circles_are_growing):
circles_are_growing = False
for point_index,point in enumerate(points):
for i in range(point[0] - radius,point[0] + radius):
for j in range(point[1] - radius,point[1] + radius):
# print(str(i)+" vs "+str(len(is_drawn_on)))
if(i >= 0 and i < len(is_drawn_on)):
if(j >= 0 and j < len(is_drawn_on[i])):
if(not is_drawn_on[i][j] and distance(i,j,point[1]) <= radius):
point_pixels[point_index].append((i,j))
circles_are_growing = True
is_drawn_on[i][j] = True
radius += 1
# each point needs to have a corresponding centroid
point_pixels_centroid = []
for pixel_group in point_pixels:
x_sum = 0
y_sum = 0
for pixel in pixel_group:
x_sum += pixel[0]
y_sum += pixel[1]
x_average = x_sum / len(pixel_group)
y_average = y_sum / len(pixel_group)
point_pixels_centroid.append((round(x_average),255) )
display_voronoi.show()
解决方法
与其直接构建和询问Voronoi图，不如构建和查询标准搜索树。以下是我使用scipy.spatial.KDTree对代码进行的修改，以确定每个像素位置的最接近点，然后是结果图像（一个500x500图像，具有500个Voronoi点）。
代码仍然有些慢，但是现在可以在Voronoi点数上很好地扩展。如果您避免为每个Voronoi单元构建像素位置列表，而直接在图像中设置数据，则可能会更快。
最快的解决方案可能包括构建Voronoi diagam，一次遍历一个像素，并关联最接近的Voronoi单元，在需要时查看相邻的Voronoi单元（因为前一个像素为找到Voronoi单元提供了很好的猜测对于下一个像素）。但这将涉及编写更多这样的天真的使用KDTree的代码，并且可能不会产生巨大的收益：这时代码的慢部分是构建所有可以独立清理的按像素排列的数组/数据。 / p>
import math
import random
from PIL import Image
from scipy import spatial
import numpy as np
# define the size of the x and y bounds
screen_width = 500
screen_height = 500
# define the number of points that should be used
number_of_points = 500
# randomly generate a list of n points within the given x and y bounds
point_x_coordinates = random.sample(range(0,screen_width),number_of_points)
point_y_coordinates = random.sample(range(0,screen_height),number_of_points)
points = list(zip(point_x_coordinates,point_y_coordinates))
# each point needs to have a corresponding list of pixels
point_pixels = []
for i in range(len(points)):
point_pixels.append([])
# build a search tree
tree = spatial.KDTree(points)
# build a list of pixed coordinates to query
pixel_coordinates = np.zeros((screen_height*screen_width,2));
i = 0
for pixel_y_coordinate in range(screen_height):
for pixel_x_coordinate in range(screen_width):
pixel_coordinates[i] = np.array([pixel_x_coordinate,pixel_y_coordinate])
i = i+1
# for each pixel within bounds,determine which point it is closest to and add it to the corresponding list in point_pixels
[distances,indices] = tree.query(pixel_coordinates)
i = 0
for pixel_y_coordinate in range(screen_height):
for pixel_x_coordinate in range(screen_width):
point_pixels[indices[i]].append((pixel_x_coordinate,pixel_y_coordinate))
i = i+1
# each point needs to have a corresponding centroid
point_pixels_centroid = []
for pixel_group in point_pixels:
x_sum = 0
y_sum = 0
for pixel in pixel_group:
x_sum += pixel[0]
y_sum += pixel[1]
x_average = x_sum / max(len(pixel_group),1)
y_average = y_sum / max(len(pixel_group),1)
point_pixels_centroid.append((round(x_average),round(y_average)))
# display the resulting voronoi diagram
display_voronoi = Image.new("RGB",(screen_width,"white")
for pixel_group in point_pixels:
rgb = random.sample(range(0,255),3)
for pixel in pixel_group:
display_voronoi.putpixel( pixel,(rgb[0],rgb[1],rgb[2],255) )
for centroid in point_pixels_centroid:
#print(centroid)
display_voronoi.putpixel( centroid,(1,1,255) )
#display_voronoi.show()
display_voronoi.save("test.png")
