opencv 实现任意角度的透视变换

opencv中提供了getPerspectiveTransform函数来获取由四对点间的转换矩阵，输出矩阵为3*3， 同时也提供了warpPerspective函数来对通过变换矩阵来对图像进行透视变换的操作，同时还提供了perspectiveTransform来提供对点的转换：

getPerspectiveTransform：

Calculates a perspective transform from four pairs of the corresponding points.
C++: Mat getPerspectiveTransform(InputArray src, InputArray dst)
C++: Mat getPerspectiveTransform(const Point2f src[], const Point2f dst[])
Python: cv2.getPerspectiveTransform(src, dst) → retval

perspectiveTransform：

Performs the perspective matrix transformation of vectors.


C++: void perspectiveTransform(InputArray src, OutputArray dst, InputArray m)
Python: cv2.perspectiveTransform(src, m[, dst]) → dst
C: void cvPerspectiveTransform(const CvArr* src, CvArr* dst, const CvMat* mat)
Parameters:
src – input two-channel or three-channel floating-point array; each element is a 2D/3D vector to be transformed.
dst – output array of the same size and type as src.
m – 3x3 or 4x4 floating-point transformation matrix.

warpPerspective：

Applies a perspective transformation to an image.


C++: void warpPerspective(InputArray src, OutputArray dst, InputArray M, Size dsize, int flags=INTER_LINEAR, int borderMode=BORDER_CONSTANT, const Scalar&borderValue=Scalar())
Python: cv2.warpPerspective(src, M, dsize[, dst[, flags[, borderMode[, borderValue]]]]) → dst
C: void cvWarpPerspective(const CvArr* src, CvArr* dst, const CvMat* map_matrix, int flags=CV_INTER_LINEAR+CV_WARP_FILL_OUTLIERS, CvScalarfillval=cvScalarAll(0) )
Parameters:
src – input image.
dst – output image that has the size dsize and the same type as src .
M – 3\times 3 transformation matrix.
dsize – size of the output image.
flags – combination of interpolation methods (INTER_LINEAR or INTER_NEAREST) and the optional flag WARP_INVERSE_MAP, that sets M as the inversetransformation ( \texttt{dst}\rightarrow\texttt{src} ).
borderMode – pixel extrapolation method (BORDER_CONSTANT or BORDER_REPLICATE).
borderValue – value used in case of a constant border; by default, it equals 0.

本文为方便，采用的python + opencv 实现，代码及效果如下

#-*- coding:utf-8 -*-import cv2import numpy as npdef rad(x):    return x*np.pi/180img = cv2.imread("b.jpg")cv2.imshow("original", img)#扩展图像，保证内容不超出可视范围img = cv2.copyMakeBorder(img,200,200,200,200,cv2.BORDER_CONSTANT,0)w,h=img.shape[0:2]anglex=45angley = 45anglez = 0fov = 42while 1:    #镜头与图像间的距离，21为半可视角，算z的距离是为了保证在此可视角度下恰好显示整幅图像    z=np.sqrt(w**2 + h**2)/2/np.tan(rad(fov/2))    #齐次变换矩阵    rx = np.array([[1,                  0,                          0,                          0],                   [0,                  np.cos(rad(anglex)),        -np.sin(rad(anglex)),       0],                   [0,                 -np.sin(rad(anglex)),        np.cos(rad(anglex)),        0,],                   [0,                  0,                          0,                          1]], np.float32)    ry = np.array([[np.cos(rad(angley)), 0,                         np.sin(rad(angley)),       0],                   [0,                   1,                         0,                          0],                   [-np.sin(rad(angley)),0,                         np.cos(rad(angley)),        0,],                   [0,                   0,                         0,                          1]], np.float32)    rz = np.array([[np.cos(rad(anglez)), np.sin(rad(anglez)),      0,                          0],                   [-np.sin(rad(anglez)), np.cos(rad(anglez)),      0,                          0],                   [0,                  0,                          1,                          0],                   [0,                  0,                          0,                          1]], np.float32)    r = rx.dot(ry).dot(rz)    #四对点的生成    pcenter = np.array([h/2, w/2, 0, 0], np.float32)        p1 = np.array([0,0,  0,0], np.float32) - pcenter    p2 = np.array([w,0,  0,0], np.float32) - pcenter    p3 = np.array([0,h,  0,0], np.float32) - pcenter    p4 = np.array([w,h,  0,0], np.float32) - pcenter        dst1 = r.dot(p1)    dst2 = r.dot(p2)    dst3 = r.dot(p3)    dst4 = r.dot(p4)    list_dst = [dst1, dst2, dst3, dst4]    org = np.array([[0,0],                    [w,0],                    [0,h],                    [w,h]], np.float32)        dst = np.zeros((4,2), np.float32)    #投影至成像平面    for i in range(4):        dst[i,0] = list_dst[i][0]*z/(z-list_dst[i][2]) + pcenter[0]        dst[i,1] = list_dst[i][1]*z/(z-list_dst[i][2]) + pcenter[1]    warpR = cv2.getPerspectiveTransform(org, dst)    result = cv2.warpPerspective(img, warpR, (h,w))    cv2.imshow("result", result)    c=cv2.waitKey(30)        #anglex += 3            #auto rotate    #anglez += 1             #auto rotate    #angley += 2            #auto rotate    #键盘控制    if 27 == c:             #Esc quit        break;    if c == ord('w'):        anglex += 1    if c == ord('s'):        anglex -= 1    if c == ord('a'):        angley += 1        #dx=0    if c == ord('d'):        angley -= 1    if c == ord('u'):        anglez += 1    if c == ord('p'):        anglez -= 1    if c == ord('t'):        fov +=1    if c == ord('r'):        fov -=1    if c == ord(' '):        anglex=angley=anglez=0    if c == ord('q'):        print("======================================")        print( '旋转矩阵：\n',r)        print("angle alpha: ",anglex, 'angle beta: ',angley, "dz: ",anglez, ": ",z)cv2.destroyAllWindows()

效果图：

原图：