原始图片数据如下（共100张）：
如何求每个界面的最大内圆？求每幅图片中阴影各点到阴影边界的最小距离中的最大距离即为最大内圆的半径，通过这种思路可得到内圆圆心位置和半径，代码实现：
#coding=utf-8 import matplotlib.pyplot as plt from skimage import io import math import numpy as np from mpl_toolkits.mplot3d import Axes3D # 在画3D的时候需要 def transfer_data(image_path): # get center points img = io.imread(image_path) points = [] # 存放图片中阴影的点信息 bound = [] # 存放图片中阴影的边界点信息 for x in range(img.shape[0]): for y in range(img.shape[1]): if img[x, y] == 0: points.append([x, y]) # 阴影点 # 判断是否为阴影的边界 if img[x - 1, y] > 0 or img[x + 1, y] > 0 or img[x, y - 1] > 0 or img[x, y + 1] > 0: bound.append([x, y]) # 阴影边界 return points, bound def get_center_radius(image_path): points, bound = transfer_data(image_path) radius_list = [] for point in points: min_radius = 1000 for bound_point in bound: if min_radius <= 0: min_radius = 0 break # 求阴影点到阴影边界的最小距离 distance = math.sqrt((bound_point[0] - point[0]) ** 2 + (bound_point[1] - point[1]) ** 2) if distance < min_radius: min_radius = distance radius_list.append([point[0], point[1], min_radius]) max_radius = [0, 0, 0] # 在所有阴影点离边界的最小距离中求取最大距离，即为内圆半径 for ele in radius_list: if ele[2] > max_radius[2]: max_radius = ele return max_radius def parse_images(): center_radius = [] for i in range(100): image_path = 'images/'+str(i)+'.bmp' temp = get_center_radius(image_path) center_radius.append({'index': i, 'data': temp}) print(image_path, temp) return center_radius # 求出了100个离散的中心点 center_radius = parse_images() print(center_radius)
求出结果为：
center_radius = [{'index': 0, 'data': [95, 256, 29.0]}, {'index': 1, 'data': [95, 256, 29.0]}, {'index': 2, 'data': [95, 256, 29.0]}, {'index': 3, 'data': [95, 256, 29.0]}, {'index': 4, 'data': [95, 256, 29.0]}, {'index': 5, 'data': [95, 256, 29.0]}, {'index': 6, 'data': [95, 256, 28.861739379323623]}, {'index': 7, 'data': [95, 257, 29.0]}, {'index': 8, 'data': [95, 257, 29.0]}, {'index': 9, 'data': [95, 257, 29.0]}, {'index': 10, 'data': [95, 257, 29.0]}, {'index': 11, 'data': [95, 258, 29.0]}, {'index': 12, 'data': [95, 258, 29.0]}, {'index': 13, 'data': [95, 258, 29.0]}, {'index': 14, 'data': [95, 259, 29.0]}, {'index': 15, 'data': [95, 260, 29.0]}, {'index': 16, 'data': [95, 260, 29.0]}, {'index': 17, 'data': [95, 261, 29.0]}, {'index': 18, 'data': [95, 262, 29.0]}, {'index': 19, 'data': [95, 263, 29.0]}, {'index': 20, 'data': [94, 266, 29.0]}, {'index': 21, 'data': [94, 267, 29.0]}, {'index': 22, 'data': [94, 268, 29.0]}, {'index': 23, 'data': [95, 267, 29.0]}, {'index': 24, 'data': [95, 276, 29.017236257093817]}, {'index': 25, 'data': [95, 275, 29.017236257093817]}, {'index': 26, 'data': [95, 275, 29.017236257093817]}, {'index': 27, 'data': [96, 285, 29.068883707497267]}, {'index': 28, 'data': [96, 285, 29.068883707497267]}, {'index': 29, 'data': [96, 284, 29.068883707497267]}, {'index': 30, 'data': [97, 291, 29.120439557122072]}, {'index': 31, 'data': [97, 291, 29.154759474226502]}, {'index': 32, 'data': [97, 291, 29.120439557122072]}, {'index': 33, 'data': [97, 291, 29.120439557122072]}, {'index': 34, 'data': [98, 296, 29.120439557122072]}, {'index': 35, 'data': [98, 296, 29.120439557122072]}, {'index': 36, 'data': [99, 300, 29.120439557122072]}, {'index': 37, 'data': [100, 304, 29.120439557122072]}, {'index': 38, 'data': [104, 316, 29.154759474226502]}, {'index': 39, 'data': [104, 316, 29.154759474226502]}, {'index': 40, 'data': [106, 321, 29.154759474226502]}, {'index': 41, 'data': [118, 344, 29.154759474226502]}, {'index': 42, 'data': [115, 339, 29.154759474226502]}, {'index': 43, 'data': [115, 339, 29.154759474226502]}, {'index': 44, 'data': [120, 347, 29.410882339705484]}, {'index': 45, 'data': [120, 347, 29.410882339705484]}, {'index': 46, 'data': [120, 347, 29.410882339705484]}, {'index': 47, 'data': [137, 368, 29.698484809834994]}, {'index': 48, 'data': [136, 367, 29.698484809834994]}, {'index': 49, 'data': [136, 367, 29.698484809834994]}, {'index': 50, 'data': [137, 368, 29.698484809834994]}, {'index': 51, 'data': [137, 368, 29.698484809834994]}, {'index': 52, 'data': [138, 369, 29.698484809834994]}, {'index': 53, 'data': [140, 371, 29.698484809834994]}, {'index': 54, 'data': [144, 375, 29.410882339705484]}, {'index': 55, 'data': [152, 382, 29.206163733020468]}, {'index': 56, 'data': [156, 385, 29.206163733020468]}, {'index': 57, 'data': [183, 402, 29.410882339705484]}, {'index': 58, 'data': [183, 402, 29.410882339705484]}, {'index': 59, 'data': [185, 403, 29.154759474226502]}, {'index': 60, 'data': [196, 408, 29.154759474226502]}, {'index': 61, 'data': [199, 409, 29.120439557122072]}, {'index': 62, 'data': [204, 411, 29.120439557122072]}, {'index': 63, 'data': [236, 419, 29.154759474226502]}, {'index': 64, 'data': [236, 419, 29.154759474226502]}, {'index': 65, 'data': [236, 419, 29.154759474226502]}, {'index': 66, 'data': [230, 418, 29.120439557122072]}, {'index': 67, 'data': [236, 419, 29.068883707497267]}, {'index': 68, 'data': [294, 419, 29.068883707497267]}, {'index': 69, 'data': [286, 420, 29.068883707497267]}, {'index': 70, 'data': [299, 418, 29.120439557122072]}, {'index': 71, 'data': [294, 419, 29.154759474226502]}, {'index': 72, 'data': [299, 418, 29.120439557122072]}, {'index': 73, 'data': [299, 418, 29.120439557122072]}, {'index': 74, 'data': [299, 418, 29.120439557122072]}, {'index': 75, 'data': [331, 409, 29.154759474226502]}, {'index': 76, 'data': [331, 409, 29.154759474226502]}, {'index': 77, 'data': [343, 404, 29.154759474226502]}, {'index': 78, 'data': [343, 404, 29.154759474226502]}, {'index': 79, 'data': [372, 387, 29.206163733020468]}, {'index': 80, 'data': [372, 387, 29.206163733020468]}, {'index': 81, 'data': [387, 375, 29.410882339705484]}, {'index': 82, 'data': [387, 375, 29.68164415931166]}, {'index': 83, 'data': [387, 375, 29.68164415931166]}, {'index': 84, 'data': [388, 374, 29.68164415931166]}, {'index': 85, 'data': [400, 362, 29.68164415931166]}, {'index': 86, 'data': [401, 361, 29.68164415931166]}, {'index': 87, 'data': [401, 361, 29.410882339705484]}, {'index': 88, 'data': [401, 361, 29.206163733020468]}, {'index': 89, 'data': [407, 354, 29.206163733020468]}, {'index': 90, 'data': [413, 346, 29.154759474226502]}, {'index': 91, 'data': [413, 346, 29.154759474226502]}, {'index': 92, 'data': [431, 314, 29.154759474226502]}, {'index': 93, 'data': [431, 314, 29.154759474226502]}, {'index': 94, 'data': [433, 309, 29.154759474226502]}, {'index': 95, 'data': [433, 309, 29.120439557122072]}, {'index': 96, 'data': [436, 301, 29.120439557122072]}, {'index': 97, 'data': [437, 298, 29.120439557122072]}, {'index': 98, 'data': [439, 291, 29.120439557122072]}, {'index': 99, 'data': [440, 287, 29.120439557122072]}]
说明：在结果中的index表示原始图片的序号，data表示图片内圆的圆心坐标和圆半径
{'index': 0, 'data': [95, 256, 29.0]}
表示图片0.bmp的圆心坐标为(95, 256) 半径为29.0
#coding=utf-8 import matplotlib.pyplot as plt from skimage import io import math import numpy as np from mpl_toolkits.mplot3d import Axes3D # 在画3D的时候需要 # 使用100个离散的中心点，采用曲线拟合方式，得出x(z)与y(z)的曲线 center_radius = [{'index': 0, 'data': [95, 256, 29.0]}, {'index': 1, 'data': [95, 256, 29.0]}, {'index': 2, 'data': [95, 256, 29.0]}, {'index': 3, 'data': [95, 256, 29.0]}, {'index': 4, 'data': [95, 256, 29.0]}, {'index': 5, 'data': [95, 256, 29.0]}, {'index': 6, 'data': [95, 256, 28.861739379323623]}, {'index': 7, 'data': [95, 257, 29.0]}, {'index': 8, 'data': [95, 257, 29.0]}, {'index': 9, 'data': [95, 257, 29.0]}, {'index': 10, 'data': [95, 257, 29.0]}, {'index': 11, 'data': [95, 258, 29.0]}, {'index': 12, 'data': [95, 258, 29.0]}, {'index': 13, 'data': [95, 258, 29.0]}, {'index': 14, 'data': [95, 259, 29.0]}, {'index': 15, 'data': [95, 260, 29.0]}, {'index': 16, 'data': [95, 260, 29.0]}, {'index': 17, 'data': [95, 261, 29.0]}, {'index': 18, 'data': [95, 262, 29.0]}, {'index': 19, 'data': [95, 263, 29.0]}, {'index': 20, 'data': [94, 266, 29.0]}, {'index': 21, 'data': [94, 267, 29.0]}, {'index': 22, 'data': [94, 268, 29.0]}, {'index': 23, 'data': [95, 267, 29.0]}, {'index': 24, 'data': [95, 276, 29.017236257093817]}, {'index': 25, 'data': [95, 275, 29.017236257093817]}, {'index': 26, 'data': [95, 275, 29.017236257093817]}, {'index': 27, 'data': [96, 285, 29.068883707497267]}, {'index': 28, 'data': [96, 285, 29.068883707497267]}, {'index': 29, 'data': [96, 284, 29.068883707497267]}, {'index': 30, 'data': [97, 291, 29.120439557122072]}, {'index': 31, 'data': [97, 291, 29.154759474226502]}, {'index': 32, 'data': [97, 291, 29.120439557122072]}, {'index': 33, 'data': [97, 291, 29.120439557122072]}, {'index': 34, 'data': [98, 296, 29.120439557122072]}, {'index': 35, 'data': [98, 296, 29.120439557122072]}, {'index': 36, 'data': [99, 300, 29.120439557122072]}, {'index': 37, 'data': [100, 304, 29.120439557122072]}, {'index': 38, 'data': [104, 316, 29.154759474226502]}, {'index': 39, 'data': [104, 316, 29.154759474226502]}, {'index': 40, 'data': [106, 321, 29.154759474226502]}, {'index': 41, 'data': [118, 344, 29.154759474226502]}, {'index': 42, 'data': [115, 339, 29.154759474226502]}, {'index': 43, 'data': [115, 339, 29.154759474226502]}, {'index': 44, 'data': [120, 347, 29.410882339705484]}, {'index': 45, 'data': [120, 347, 29.410882339705484]}, {'index': 46, 'data': [120, 347, 29.410882339705484]}, {'index': 47, 'data': [137, 368, 29.698484809834994]}, {'index': 48, 'data': [136, 367, 29.698484809834994]}, {'index': 49, 'data': [136, 367, 29.698484809834994]}, {'index': 50, 'data': [137, 368, 29.698484809834994]}, {'index': 51, 'data': [137, 368, 29.698484809834994]}, {'index': 52, 'data': [138, 369, 29.698484809834994]}, {'index': 53, 'data': [140, 371, 29.698484809834994]}, {'index': 54, 'data': [144, 375, 29.410882339705484]}, {'index': 55, 'data': [152, 382, 29.206163733020468]}, {'index': 56, 'data': [156, 385, 29.206163733020468]}, {'index': 57, 'data': [183, 402, 29.410882339705484]}, {'index': 58, 'data': [183, 402, 29.410882339705484]}, {'index': 59, 'data': [185, 403, 29.154759474226502]}, {'index': 60, 'data': [196, 408, 29.154759474226502]}, {'index': 61, 'data': [199, 409, 29.120439557122072]}, {'index': 62, 'data': [204, 411, 29.120439557122072]}, {'index': 63, 'data': [236, 419, 29.154759474226502]}, {'index': 64, 'data': [236, 419, 29.154759474226502]}, {'index': 65, 'data': [236, 419, 29.154759474226502]}, {'index': 66, 'data': [230, 418, 29.120439557122072]}, {'index': 67, 'data': [236, 419, 29.068883707497267]}, {'index': 68, 'data': [294, 419, 29.068883707497267]}, {'index': 69, 'data': [286, 420, 29.068883707497267]}, {'index': 70, 'data': [299, 418, 29.120439557122072]}, {'index': 71, 'data': [294, 419, 29.154759474226502]}, {'index': 72, 'data': [299, 418, 29.120439557122072]}, {'index': 73, 'data': [299, 418, 29.120439557122072]}, {'index': 74, 'data': [299, 418, 29.120439557122072]}, {'index': 75, 'data': [331, 409, 29.154759474226502]}, {'index': 76, 'data': [331, 409, 29.154759474226502]}, {'index': 77, 'data': [343, 404, 29.154759474226502]}, {'index': 78, 'data': [343, 404, 29.154759474226502]}, {'index': 79, 'data': [372, 387, 29.206163733020468]}, {'index': 80, 'data': [372, 387, 29.206163733020468]}, {'index': 81, 'data': [387, 375, 29.410882339705484]}, {'index': 82, 'data': [387, 375, 29.68164415931166]}, {'index': 83, 'data': [387, 375, 29.68164415931166]}, {'index': 84, 'data': [388, 374, 29.68164415931166]}, {'index': 85, 'data': [400, 362, 29.68164415931166]}, {'index': 86, 'data': [401, 361, 29.68164415931166]}, {'index': 87, 'data': [401, 361, 29.410882339705484]}, {'index': 88, 'data': [401, 361, 29.206163733020468]}, {'index': 89, 'data': [407, 354, 29.206163733020468]}, {'index': 90, 'data': [413, 346, 29.154759474226502]}, {'index': 91, 'data': [413, 346, 29.154759474226502]}, {'index': 92, 'data': [431, 314, 29.154759474226502]}, {'index': 93, 'data': [431, 314, 29.154759474226502]}, {'index': 94, 'data': [433, 309, 29.154759474226502]}, {'index': 95, 'data': [433, 309, 29.120439557122072]}, {'index': 96, 'data': [436, 301, 29.120439557122072]}, {'index': 97, 'data': [437, 298, 29.120439557122072]}, {'index': 98, 'data': [439, 291, 29.120439557122072]}, {'index': 99, 'data': [440, 287, 29.120439557122072]}] z_index = [] x_index = [] y_index = [] r_list = [] for item in center_radius: z_index.append(item['index']) x_index.append(item['data'][0]) y_index.append(item['data'][1]) r_list.append(item['data'][2]) radius = sum(r_list) / len(r_list) # 采用多项式进行拟合x(z)与y(z) z_array = np.array(z_index) x_array = np.array(x_index) y_array = np.array(y_index) times = 3 x_z_p = np.polyfit(z_array, x_array, times) # 用3次多项式拟合 y_z_p = np.polyfit(z_array, y_array, times) # 用3次多项式拟合 x_z_func = np.poly1d(x_z_p) y_z_func = np.poly1d(y_z_p) fig = plt.figure() ax = fig.add_subplot(1, 1, 1, projection='3d') ax.plot(x_array, y_array, z_array) # 画三维曲线 z_array = np.arange(0, 100, 0.01) xvals = x_z_func(z_array) yvals = y_z_func(z_array) ax.plot(xvals, yvals, z_array, 'r.', markersize=2) # 画三维曲线 plt.show()
采用拟合结果如图所示
最终选择7次方，绘制如图（将上面代码中的 markersize=2 改为 markersize=radius 即可）
