[英]render Voronoi diagram to numpy array
我想根据中心列表和图像大小生成 Voronoi 区域。
我尝试了下一个代码,基于https://rosettacode.org/wiki/Voronoi_diagram
def generate_voronoi_diagram(width, height, centers_x, centers_y):
image = Image.new("RGB", (width, height))
putpixel = image.putpixel
imgx, imgy = image.size
num_cells=len(centers_x)
nx = centers_x
ny = centers_y
nr,ng,nb=[],[],[]
for i in range (num_cells):
nr.append(randint(0, 255));ng.append(randint(0, 255));nb.append(randint(0, 255));
for y in range(imgy):
for x in range(imgx):
dmin = math.hypot(imgx-1, imgy-1)
j = -1
for i in range(num_cells):
d = math.hypot(nx[i]-x, ny[i]-y)
if d < dmin:
dmin = d
j = i
putpixel((x, y), (nr[j], ng[j], nb[j]))
image.save("VoronoiDiagram.png", "PNG")
image.show()
我有所需的输出:
但是生成输出需要太多时间。
我也试过https://stackoverflow.com/a/20678647它很快,但我没有找到将其转换为 img_width X img_height 的 numpy 数组的方法。 大多数情况下,因为我不知道如何为 scipy Voronoi class提供图像大小参数。
有没有更快的方法来获得这个输出? 不需要中心或多边形边
提前致谢
2018-12-11 编辑:使用@tel “快速解决方案”
代码执行速度更快,似乎中心已经转换。 可能这种方法是为图像添加边距
以下是如何将基于scipy.spatial.Voronoi
的快速解决方案的输出转换为任意宽度和高度的 Numpy 数组。 给定一组regions, vertices
您从链接代码中的voronoi_finite_polygons_2d
函数获得的regions, vertices
,这里有一个辅助函数,可以将该输出转换为数组:
import numpy as np
import matplotlib.pyplot as plt
from matplotlib.backends.backend_agg import FigureCanvasAgg as FigureCanvas
def vorarr(regions, vertices, width, height, dpi=100):
fig = plt.Figure(figsize=(width/dpi, height/dpi), dpi=dpi)
canvas = FigureCanvas(fig)
ax = fig.add_axes([0,0,1,1])
# colorize
for region in regions:
polygon = vertices[region]
ax.fill(*zip(*polygon), alpha=0.4)
ax.plot(points[:,0], points[:,1], 'ko')
ax.set_xlim(vor.min_bound[0] - 0.1, vor.max_bound[0] + 0.1)
ax.set_ylim(vor.min_bound[1] - 0.1, vor.max_bound[1] + 0.1)
canvas.draw()
return np.frombuffer(canvas.tostring_rgb(), dtype='uint8').reshape(height, width, 3)
这是一个完整的vorarr
示例:
from scipy.spatial import Voronoi
# get random points
np.random.seed(1234)
points = np.random.rand(15, 2)
# compute Voronoi tesselation
vor = Voronoi(points)
# voronoi_finite_polygons_2d function from https://stackoverflow.com/a/20678647/425458
regions, vertices = voronoi_finite_polygons_2d(vor)
# convert plotting data to numpy array
arr = vorarr(regions, vertices, width=1000, height=1000)
# plot the numpy array
plt.imshow(arr)
输出:
如您所见,生成的 Numpy 数组确实具有(1000, 1000)
的形状,如对vorarr
的调用中所指定。
以下是如何更改当前代码以使用/返回 Numpy 数组:
import math
import matplotlib.pyplot as plt
import numpy as np
def generate_voronoi_diagram(width, height, centers_x, centers_y):
arr = np.zeros((width, height, 3), dtype=int)
imgx,imgy = width, height
num_cells=len(centers_x)
nx = centers_x
ny = centers_y
randcolors = np.random.randint(0, 255, size=(num_cells, 3))
for y in range(imgy):
for x in range(imgx):
dmin = math.hypot(imgx-1, imgy-1)
j = -1
for i in range(num_cells):
d = math.hypot(nx[i]-x, ny[i]-y)
if d < dmin:
dmin = d
j = i
arr[x, y, :] = randcolors[j]
plt.imshow(arr.transpose(1, 0, 2))
plt.scatter(cx, cy, c='w', edgecolors='k')
plt.show()
return arr
用法示例:
np.random.seed(1234)
width = 500
cx = np.random.rand(15)*width
height = 300
cy = np.random.rand(15)*height
arr = generate_voronoi_diagram(width, height, cx, cy)
示例输出:
不使用 matplotlib 的快速解决方案也是可能的。 您的解决方案很慢,因为您要遍历所有像素,这会在 Python 中产生大量开销。 对此的一个简单解决方案是在单个 numpy 操作中计算所有距离,并在另一个单个操作中分配所有颜色。
def generate_voronoi_diagram_fast(width, height, centers_x, centers_y):
# Create grid containing all pixel locations in image
x, y = np.meshgrid(np.arange(width), np.arange(height))
# Find squared distance of each pixel location from each center: the (i, j, k)th
# entry in this array is the squared distance from pixel (i, j) to the kth center.
squared_dist = (x[:, :, np.newaxis] - centers_x[np.newaxis, np.newaxis, :]) ** 2 + \
(y[:, :, np.newaxis] - centers_y[np.newaxis, np.newaxis, :]) ** 2
# Find closest center to each pixel location
indices = np.argmin(squared_dist, axis=2) # Array containing index of closest center
# Convert the previous 2D array to a 3D array where the extra dimension is a one-hot
# encoding of the index
one_hot_indices = indices[:, :, np.newaxis, np.newaxis] == np.arange(centers_x.size)[np.newaxis, np.newaxis, :, np.newaxis]
# Create a random color for each center
colors = np.random.randint(0, 255, (centers_x.size, 3))
# Return an image where each pixel has a color chosen from `colors` by its
# closest center
return (one_hot_indices * colors[np.newaxis, np.newaxis, :, :]).sum(axis=2)
在我的机器上运行此函数可以获得相对于原始迭代解决方案的约 10 倍加速(不考虑绘图并将结果保存到磁盘)。 我确信还有很多其他的调整可以进一步加速我的解决方案。
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