如何从OpenCV中的欧几里德变换中找到2x3矩阵的枢轴点

Question

我有两张图片：

使用cv2.findTransformECC (im1,im2,warp_matrix, warp_mode, criteria)我得到了这个转换矩阵：

[[   0.70637488    0.70783788  -86.60842133]
 [  -0.70783788    0.70637488  137.01171875]]

如何使用该矩阵找到图像转向的点？

以下是矩阵代表的内容：

我知道我可以使用X，Y平移的斜边以及旋转角来计算等腰三角形。但是我怎样才能使用等腰三角形（红色）来找到翻译中心的X和Y（绿色）？三角法是否是找到轴心点的唯一方法？

Answer 1

So you have a transformation matrix

/ a b  tx \
\ c d  ty /

And you want to convert this to a representation of a rotation about some pivot. A rotation about a pivot (px, py) can be expressed as

T = T(p) R T(-p)

If you expand this, you get

/ a b  tx \  =      / a b  px-apx-bpy \
\ c d  ty /         \ c d  py-cpx-dpy /

The first 2x2 matrix is already equal if you choose the same rotation. The last column gives you a linear system of equations. The general solution of this is (disregarding special cases):

px = (tx - d tx + b ty) / (a + b c + d - a d - 1)
py = (ty + c tx - a ty) / (a + b c + d - a d - 1)

For your matrix, this gives:

px = 121.842
py = 172.899