二维图像计盒维数计算，python实现

import numpy as np from matplotlib import pyplot as plt import cv2 def boxCounting_1(img): """ 计算二值图像计盒维数（像素点在盒子边缘） """ cv2.imshow("img", img) cv2.imshow('o', o) h, w = img.shape[:2] Nr = [] #盒子数列表 for i in range(1,min(h//2+1, w//2+1)): #盒子边长从1到图片最小尺寸的二分之一 box_num = 0 #初始化盒子数 for row in range(h//i): #（h//i）为盒子的行数，（w//i）为盒子的列数 for col in range(w//i): if np.any(img[row*i:(row+1)*i+1, col*i:(col+1)*i+1]!=0): box_num+=1 Nr.append(box_num) return Nr, 1 def boxCounting_2(img): """ 计算二值图像计盒维数（像素点在盒子内部） """ h, w = img.shape[:2] Nr = [] #盒子数列表 #移动图像像素点到奇数行和列 new_img = np.zeros((2*h,2*w),np.uint8) for x in range(h): for y in range(w): new_img[2*x+1,2*y+1] = img[x,y] cv2.imshow("new_img", new_img) cv2.imshow("img", img) cv2.imshow('o', o) for i in range(2,min(h+1, w+1),2): #盒子边长从2到图片最小尺寸的二分之一 box_num = 0 #初始化盒子数 for row in range(2*h//i): #（2h//i）为盒子的行数，（2w//i）为盒子的列数 for col in range(2*w//i): if np.any(new_img[row*i:(row+1)*i+1, col*i:(col+1)*i+1]!=0) : box_num+=1 Nr.append(box_num) return Nr, 2 def Least_squares(x,y): """ 输入x、y坐标集，用最小二乘法拟合曲线 输出拟合直线y = ax+b 的参数a,b，和相关系数r """ x_ = x.mean() y_ = y.mean() m = np.zeros(1) n = np.zeros(1) k = np.zeros(1) p = np.zeros(1) l1 = np.zeros(1) l2 = np.zeros(1) l1_ = np.zeros(1) l2_ = np.zeros(1) r = np.zeros(1) for i in np.arange(len(x)): k = (x[i]-x_)* (y[i]-y_) m += k p = np.square( x[i]-x_ ) n = n + p l1 = np.square(x[i] - x_) l1_ = l1_ + l1 l2 = np.square(y[i] - y_) l2_ = l2_ + l2 a = m/n b = y_ - a* x_ r = m/np.sqrt(l1_*l2_) return a,b,r if __name__ == "__main__": o = cv2.imread("./text_img/slow1.png",cv2.IMREAD_GRAYSCALE) thresh = cv2.threshold(o,100,255,cv2.THRESH_BINARY_INV)[1] # thresh = cv2.resize(thresh,None,fx=0.5,fy=0.5) # thresh = cv2.Canny(o,50,200) #计算二值图像计盒维数 Nr, interval = boxCounting_2(thresh) print(Nr) print(len(Nr)) x = np.log(range(interval, interval*len(Nr)+interval, interval)) y = np.log(Nr) #最小二乘法拟合直线 a,b,r = Least_squares(x,y) print (a,b,r*r) y1 = a * x + b #设置微软雅黑，支持中文显示 plt.rcParams['font.sans-serif']=['SimHei'] # 新建一个figure对象 plt.figure(figsize=(10, 5), facecolor='w') plt.plot(x, y, 'bo', lw=2, markersize=6,label='散点数据') plt.plot(x, y1, 'r-', lw=2, markersize=6,label='y = %.4fx+%.4f' % (a,b)) plt.grid(b=True, ls=':') plt.xlabel(u'Ln[r]', fontsize=16) plt.ylabel(u'Ln[N(r)]', fontsize=16) plt.legend() #用来显示标签 plt.text(0.1,0.9,'R^2 = %.4f' % float(r*r), fontsize=12, style = "italic", weight = "light", verticalalignment='center', horizontalalignment='right', rotation=0) plt.show() cv2.waitKey() cv2.destroyAllWindows()