Python 实现任意多边形的最大内切圆算法_任意多边形最大内切圆算法

CSDN搬家失败，手动导出markdown后再导入博客园

参考 Matlab 计算轮廓内切圆

初衷是为了求裂缝的最大宽度

![[output/attachments/5ecf17abcb54aaa4fb35b00c3f243f32_MD5.png]]

直接上代码

import random
 
import cv2
import math
import numpy as np
from numpy.ma import cos, sin
import matplotlib.pyplot as plt
 
 
def max_circle(f):
    img = cv2.imread(f, cv2.IMREAD_COLOR)
    img_gray = cv2.cvtColor(img, cv2.COLOR_BGR2GRAY)
    # _, img_gray = cv2.threshold(img_gray, 0, 255, cv2.THRESH_BINARY + cv2.THRESH_OTSU)
    contous, hierarchy = cv2.findContours(img_gray, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
    """
    第二个参数表示轮廓的检索模式，有四种（本文介绍的都是新的cv2接口）：
    cv2.RETR_EXTERNAL表示只检测外轮廓
    cv2.RETR_LIST检测的轮廓不建立等级关系
    cv2.RETR_CCOMP建立两个等级的轮廓，上面的一层为外边界，里面的一层为内孔的边界信息。如果内孔内还有一个连通物体，这个物体的边界也在顶层。
    cv2.RETR_TREE建立一个等级树结构的轮廓。

    第三个参数method为轮廓的近似办法
    cv2.CHAIN_APPROX_NONE存储所有的轮廓点，相邻的两个点的像素位置差不超过1，即max（abs（x1-x2），abs（y2-y1））==1
    cv2.CHAIN_APPROX_SIMPLE压缩水平方向，垂直方向，对角线方向的元素，只保留该方向的终点坐标，例如一个矩形轮廓只需4个点来保存轮廓信息
    cv2.CHAIN_APPROX_TC89_L1，CV_CHAIN_APPROX_TC89_KCOS使用teh-Chinl chain 近似算法
    """
    for c in contous:
        left_x = min(c[:, 0, 0])
        right_x = max(c[:, 0, 0])
        down_y = max(c[:, 0, 1])
        up_y = min(c[:, 0, 1])
        upper_r = min(right_x - left_x, down_y - up_y) / 2
        # 定义相切二分精度
        precision = math.sqrt((right_x - left_x) ** 2 + (down_y - up_y) ** 2) / (2 ** 13)
        # 构造包含轮廓的矩形的所有像素点
        Nx = 2 ** 8
        Ny = 2 ** 8
        pixel_X = np.linspace(left_x, right_x, Nx)
        pixel_Y = np.linspace(up_y, down_y, Ny)
 
        # [pixel_X, pixel_Y] = ndgrid(pixel_X, pixel_Y);
        # pixel_X = reshape(pixel_X, numel(pixel_X), 1);
        # pixel_Y = reshape(pixel_Y, numel(pixel_Y), 1);
        xx, yy = np.meshgrid(pixel_X, pixel_Y)
        # % 筛选出轮廓内所有像素点
        in_list = []
        for c in contous:
            for i in range(pixel_X.shape[0]):
                for j in range(pixel_X.shape[0]):
                    if cv2.pointPolygonTest(c, (xx[i][j], yy[i][j]), False) > 0:
                        in_list.append((xx[i][j], yy[i][j]))
        in_point = np.array(in_list)
        pixel_X = in_point[:, 0]
        pixel_Y = in_point[:, 1]
        # 随机搜索百分之一像素提高内切圆半径下限
        N = len(in_point)
        rand_index = random.sample(range(N), N // 100)
        rand_index.sort()
        radius = 0
        big_r = upper_r
        center = None
        for id in rand_index:
            tr = iterated_optimal_incircle_radius_get(c, in_point[id][0], in_point[id][1], radius, big_r, precision)
            if tr > radius:
                radius = tr
                center = (in_point[id][0], in_point[id][1]) # 只有半径变大才允许位置变更，否则保持之前位置不变
        # 循环搜索剩余像素对应内切圆半径
        loops_index = [i for i in range(N) if i not in rand_index]
        for id in loops_index:
            tr = iterated_optimal_incircle_radius_get(c, in_point[id][0], in_point[id][1], radius, big_r, precision)
            if tr > radius:
                radius = tr
                center = (in_point[id][0], in_point[id][1])    # 只有半径变大才允许位置变更，否则保持之前位置不变
        # 效果测试
        plot_x = np.linspace(0, 2 * math.pi, 100)
        circle_X = center[0] + radius * cos(plot_x)
        circle_Y = center[1] + radius * sin(plot_x)
        print(radius * 2)
        plt.figure()
        plt.imshow(img_gray)
        plt.plot(circle_X, circle_Y)
        plt.show()
 
 
def iterated_optimal_incircle_radius_get(contous, pixelx, pixely, small_r, big_r, precision):
    radius = small_r
    L = np.linspace(0, 2 * math.pi, 360)  # 确定圆散点剖分数360, 720
    circle_X = pixelx + radius * cos(L)
    circle_Y = pixely + radius * sin(L)
    for i in range(len(circle_Y)):
        if cv2.pointPolygonTest(contous, (circle_X[i], circle_Y[i]), False) < 0:    # 如果圆散集有在轮廓之外的点
            return 0
    while big_r - small_r >= precision:   # 二分法寻找最大半径
        half_r = (small_r + big_r) / 2
        circle_X = pixelx + half_r * cos(L)
        circle_Y = pixely + half_r * sin(L)
        if_out = False
        for i in range(len(circle_Y)):
            if cv2.pointPolygonTest(contous, (circle_X[i], circle_Y[i]), False) < 0:  # 如果圆散集有在轮廓之外的点
                big_r = half_r
                if_out = True
        if not if_out:
            small_r = half_r
    radius = small_r
    return radius
 
 
if __name__ == '__main__':
    max_circle('thresh_crack.png')