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一、图像变形
假设原图像为f(u,v)，扭曲的目标图像是g(x,y)
1. forward warping
2. inverse warping
二、python图像变形
import cv2 import math import numpy as np #加载一个灰度图像 image = cv2.imread('F:/a.jpg',cv2.IMREAD_GRAYSCALE) #获取高、宽 rows,cols = image.shape ''' rows = height (y轴) cols = width (X轴) ''' #创建一个空图像 output = np.zeros(image.shape,dtype = image.dtype) #垂直方向变形 for i in range(rows): for j in range(cols): offset_x = int(50.0*math.cos(2*math.pi*i/180.0)) offset_y = 0 if j+offset_x < cols:#X轴方向 output[i,j] = image[i,(j+offset_x)%cols] else: output[i,j] = 255 #cv2.imshow('Original Image',image) cv2.imwrite("F:/b.jpg",output) #cv2.imshow('Vertical wave',output) #水平方向变形 for i in range(rows): for j in range(cols): offset_x = 0 offset_y = int(50.0*math.sin(2*math.pi*j/180.0)) if i+offset_y < rows:#Y轴方向 output[i,j] = image[(i+offset_y)%rows,j] else: output[i,j] = 255 #cv2.imshow('Horizontal wave',output) cv2.imwrite("F:/c.jpg",output) #垂直+水平方向变形 for i in range(rows): for j in range(cols): offset_x = int(50.0*math.cos(2*math.pi*i/180)) offset_y = int(50.0*math.sin(2*math.pi*j/180)) if j+offset_x < cols and i+offset_y < rows: output[i,j] = image[(i+offset_y)%rows,(j+offset_x)%cols] else: output[i,j] = 255 #cv2.imshow('Vertical & Horizontal wave',output) cv2.imwrite("F:/d.jpg",output) #凹形 for i in range(rows): for j in range(cols): offset_x = int(128.0*math.sin(2*math.pi*i/(2*cols))) offset_y = 0 if j+offset_x < cols: output[i,j] = image[i,(j+offset_x)%cols] else: output[i,j] = 255 #cv2.imshow('Concave wave',output) cv2.imwrite("F:/e.jpg",output) cv2.waitKey() 原图：
（1）垂直方向变形
（2）水平方向变形
（3）垂直+水平方向变形
（4）凹形
三、附：计算二维曲线长度
import numpy as np from mpl_toolkits.mplot3d import * import matplotlib.pyplot as plt ## 二维空间曲线，采用参数形式 def curve_param_2d(dt=0.0001,plot=True): dt = dt # 变化率 t = np.arange(0,2*np.pi, dt) x = t*np.cos(t) y = t*np.sin(t) # print(len(t)) area_list = [] # 存储每一微小步长的曲线长度 # 下面的方式是循环实现 # for i in range(1,len(t)): # # 计算每一微小步长的曲线长度，dx = x_{i}-x{i-1}，索引从1开始 # dl_i = np.sqrt( (x[i]-x[i-1])**2 + (y[i]-y[i-1])**2 ) # # 将计算结果存储起来 # area_list.append(dl_i) # 更加pythonic的写法 area_list = [np.sqrt( (x[i]-x[i-1])**2 + (y[i]-y[i-1])**2 ) for i in range(1,len(t))] area = sum(area_list)# 求和计算曲线在t:[0,2*pi]的长度 print("二维参数曲线长度：{:.4f}".format(area)) if plot: fig = plt.figure() ax = fig.add_subplot(111) ax.plot(x,y) plt.title("2-D Parameter Curve") plt.show() ## 二维空间曲线 def curve_2d(dt=0.0001,plot=True): dt = dt # 变化率 t = np.arange(-6,10, dt) x = t y = x**3/8 - 4*x + np.sin(3*x) # print(len(t)) area_list = [] # 存储每一微小步长的曲线长度 # for i in range(1,len(t)): # # 计算每一微小步长的曲线长度，dx = x_{i}-x{i-1}，索引从1开始 # dl_i = np.sqrt( (x[i]-x[i-1])**2 + (y[i]-y[i-1])**2 ) # # 将计算结果存储起来 # area_list.append(dl_i) area_list = [np.sqrt( (x[i]-x[i-1])**2 + (y[i]-y[i-1])**2 ) for i in range(1,len(t))] area = sum(area_list)# 求和计算曲线在t:[0,2*pi]的长度 print("二维曲线长度：{:.4f}".format(area)) if plot: fig = plt.figure() ax = fig.add_subplot(111) ax.plot(x,y) plt.title("2-D Curve") plt.show() if __name__ == '__main__': curve_param_2d(plot=True) curve_2d(plot=True) 
