CGAL中凹多边形的直骨架

Question

我有一张图像，我从中提取轮廓并将其变成多边形，使用下面的代码见下图：

import os
from scipy import ndimage
from skimage import io, measure, img_as_bool, img_as_ubyte, filters
import skgeom as sg
from skgeom.draw import draw
from matplotlib import pyplot as plt

#Read in the image:
filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'traces.png')
traces = img_as_ubyte(io.imread(filename))

#Find contours in of the traces:
Alpha = traces[:,:,3]
bool = img_as_bool(Alpha)
filled = ndimage.binary_fill_holes(bool)
gaussian = filters.gaussian(filled)
countours = measure.find_contours(gaussian, 0.9)

#Display the image and plot all contours found as polygons:
fig, ax = plt.subplots(figsize=(32,16))

skels = []
for countour in countours:
    approximated_countour = measure.approximate_polygon(countour, 10)
    poly = sg.Polygon(approximated_countour)
    draw(poly)
    print(poly.is_simple())
    #skels.append(sg.skeleton.create_interior_straight_skeleton(poly)) #Causes error!

ax.axis('off')
ax.set_axis_off()
plt.show()

控制台输出：

False
False
False
False
False
False
False
False
False
False
False
False
False
False
False
False
False

我正在为 CGAL 使用一个名为 scikit-geometry 的 python 包装器。

CGAL 将所有多边形报告为 not-simple，但据我所知它们应该很简单。它们在任何地方都不相交，也没有任何重复点。

由于 CGAL 确信多边形是 not-simple，函数 create_interior_straight_skeleton 抛出错误并停止。

错误：

RuntimeError: CGAL ERROR: precondition violation!
Expr: aOutContour.is_simple() || !"The input polygon is not simple."
File: D:\bld\scikit-geometry_1602638892768\_h_env\Library\include\CGAL/create_straight_skeleton_2.h
Line: 133

那么，我是不是弄错了，多边形确实是 not-simple。如果是这样，我怎么还能骨架化？或者是其他地方的错误，我做错了什么？

编辑

根据要求多边形文件： Polygon Files

用于生成文件的代码：

import os
from scipy import ndimage
from skimage import io, measure, img_as_bool, img_as_ubyte, filters
import skgeom as sg

#Read in the image:
directory = os.path.dirname(os.path.abspath(__file__))
filename = os.path.join(directory, 'traces.png')
traces = img_as_ubyte(io.imread(filename))

#Find contours in of the traces:
Alpha = traces[:,:,3]
bool = img_as_bool(Alpha)
filled = ndimage.binary_fill_holes(bool)
gaussian = filters.gaussian(filled)
countours = measure.find_contours(gaussian, 0.9)

#Save the polygons to a text file:
for index, countour in enumerate(countours):
    approximated_countour = measure.approximate_polygon(countour, 10)
    poly = sg.Polygon(approximated_countour)

    file = open(os.path.join(directory, "polygons\poly_{}.txt".format(index)), "w")
    for vertice in poly.vertices:
        file.write("{}, {}\n".format(vertice.x(), vertice.y()))

编辑 2

感谢@sloriot，not-being 简单的问题已经解决。第一个点和最后一个点在每个多边形中都是重复的。

遗憾的是创建的骨骼非常变形：骷髅 骷髅放大

使用的代码：

import os
from scipy import ndimage
from skimage import io, measure, img_as_bool, img_as_ubyte, filters
import skgeom as sg
from skgeom.draw import draw
from matplotlib import pyplot as plt

#Read in the image:
filename = os.path.join(os.path.dirname(os.path.abspath(__file__)), 'traces.png')
traces = img_as_ubyte(io.imread(filename))

#Find contours in of the traces:
Alpha = traces[:,:,3]
bool = img_as_bool(Alpha)
filled = ndimage.binary_fill_holes(bool)
gaussian = filters.gaussian(filled)
countours = measure.find_contours(gaussian, 0.9)

def draw_skeleton(polygon, skeleton, show_time=False):
    draw(polygon)

    for h in skeleton.halfedges:
        if h.is_bisector:
            p1 = h.vertex.point
            p2 = h.opposite.vertex.point
            plt.plot([p1.x(), p2.x()], [p1.y(), p2.y()], 'r-', lw=2)

    if show_time:
        for v in skeleton.vertices:
            plt.gcf().gca().add_artist(plt.Circle(
                (v.point.x(), v.point.y()),
                v.time, color='blue', fill=False))

#Display the image and plot all contours found as polygons:

for countour in countours:
    approximated_countour = measure.approximate_polygon(countour, 10)

    if ((approximated_countour[0] == approximated_countour[-1]).all()):
        approximated_countour = approximated_countour[:-1]

    poly = sg.Polygon(approximated_countour)
    print(poly.is_simple())
    skel = sg.skeleton.create_interior_straight_skeleton(poly)

    draw_skeleton(poly, skel, True)

plt.show()

代码和 python 库似乎不是问题，因为它工作正常 here 而且我尝试时该代码也工作正常。同样，我的多边形是我担心的问题。请注意，如果我将 draw_skeleton() 限制为仅一个多边形，它也会变形。

最终编辑

直骨架失败了，因为我是按顺时针顺序创建顶点的多边形。在创建多边形之前颠倒点的顺序解决了最后一个问题。

Answer 1

尝试使用 create_interior_straight_skeleton() 时，确保多边形：

很简单 -> 没有相交线段或重复点
其顶点按逆时针顺序定义。

如果多边形不简单，您将收到这样的错误。

如果顶点不是逆时针顺序，你的直骨架看起来像恶魔产卵并且是不正确的。

感谢@Sloriot 的帮助！

CGAL中凹多边形的直骨架

Straight Skeleton from concave polygon in CGAL

python

cgal

编辑

编辑 2

最终编辑