Python PIL中重叠的多边形

Question

我不想用绘制的最后一个多边形的值覆盖多个多边形的重叠区域，而是想绘制这些多边形的平均值。 这在Python PIL中是否可行？

示例中的重叠像素的值应为1.5。

在完整的工作程序中，我必须在一个非常大的网格上绘制大约100000个多边形（可能会或可能不会相交），这就是我使用PIL而不是Numpy的原因。

from PIL import Image, ImageDraw
import numpy as np
import matplotlib.pyplot as plt

img = Image.new('F', (50, 50), 0)

ImageDraw.Draw(img).polygon([(20, 20), (20, 40), (40, 30), (30, 20)],
                            fill=1., outline=None)
ImageDraw.Draw(img).polygon([(10, 5), (10, 25), (25, 25), (25, 10)],
                            fill=2., outline=None)

myimg = np.ma.masked_equal(np.array(img), 0.)
plt.imshow(myimg, interpolation="None")
plt.colorbar()
plt.show()

Answer 1

我建议scikit-image，skimage.draw.polygon()返回多边形中的坐标。这是一个例子。首先创建一些随机多边形数据：

import pylab as pl
from random import randint
import numpy as np
from skimage import draw

W, H = 800, 600

def make_poly(x0, y0, r, n):
    a = np.linspace(0, np.pi*2, n, endpoint=False)
    x = x0 + r * np.cos(a)
    y = y0 + r * np.sin(a)
    return y, x

count_buf = np.zeros((H, W))
sum_buf = np.zeros((H, W))

N = 2000

polys = []
for i in range(N):
    x0, y0, r, n = randint(10, W-10), randint(10, H-10), randint(10, 50), randint(3, 10)
    polys.append((make_poly(x0, y0, r, n), randint(1, 10)))

然后绘制多边形：

for (y, x), v in polys:
    rr, cc = draw.polygon(y, x, (H, W))
    count_buf[rr, cc] += 1
    sum_buf[rr, cc] += v

mean_buf = np.zeros_like(sum_buf)
mask = count_buf > 0
mean_buf[mask] = sum_buf[mask] / count_buf[mask]

我的电脑上的时间约为1.5秒，可以绘制平均半径为30像素的2000个多边形。

结果如下：

如果您需要更快的速度，可以在scikit-image中复制以下代码：

https://github.com/scikit-image/scikit-image/blob/master/skimage/draw/_draw.pyx#L189

https://github.com/scikit-image/scikit-image/blob/master/skimage/_shared/geometry.pyx#L7

如果count_buf返回True，则更改for循环中的sum_buf和point_in_polygon()。

修改

这是Cython代码：

%%cython
#cython: cdivision=True
#cython: boundscheck=False
#cython: wraparound=False

import numpy as np
cimport numpy as np
from libc.math cimport ceil

cdef unsigned char point_in_polygon(double[::1] xp, double[::1] yp,
                                           double x, double y):
    cdef Py_ssize_t i
    cdef unsigned char c = 0
    cdef Py_ssize_t j = xp.shape[0] - 1
    for i in range(xp.shape[0]):
        if (
            (((yp[i] <= y) and (y < yp[j])) or
            ((yp[j] <= y) and (y < yp[i])))
            and (x < (xp[j] - xp[i]) * (y - yp[i]) / (yp[j] - yp[i]) + xp[i])
        ):
            c = not c
        j = i
    return c


cdef class PolygonAccumulator:

    cdef int width, height
    cdef int[:, ::1] count_buf
    cdef double[:, ::1] sum_buf

    def __cinit__(self, width, height):
        self.width = width
        self.height = height
        shape = (height, width)
        self.count_buf = np.zeros(shape, dtype=int)
        self.sum_buf = np.zeros(shape, dtype=float)

    def reset(self):
        self.count_buf[:, :] = 0
        self.sum_buf[:, :] = 0

    def add_polygon(self, ya, xa, double value):
        cdef Py_ssize_t minr = int(max(0, np.min(ya)))
        cdef Py_ssize_t maxr = int(ceil(np.max(ya)))
        cdef Py_ssize_t minc = int(max(0, np.min(xa)))
        cdef Py_ssize_t maxc = int(ceil(np.max(xa)))

        cdef double[::1] x = xa
        cdef double[::1] y = ya

        cdef Py_ssize_t r, c

        maxr = min(self.height - 1, maxr)
        maxc = min(self.width  - 1, maxc)

        for r in range(minr, maxr+1):
            for c in range(minc, maxc+1):
                if point_in_polygon(x, y, c, r):
                    self.count_buf[r, c] += 1
                    self.sum_buf[r, c] += value

    def mean(self):
        count_buf = self.count_buf.base
        sum_buf = self.sum_buf.base
        mean_buf = np.zeros_like(sum_buf)
        mask = count_buf > 0
        mean_buf[mask] = sum_buf[mask] / count_buf[mask]
        return mean_buf

绘制多边形：

pa = PolygonAccumulator(800, 600)
for (y, x), value in polys:
    pa.add_polygon(y, x, value)
pl.imshow(pa.mean(), cmap="gray")

它比skimage.draw.polygon()

快约4.5倍