Decompose a homography matrix to rotation(s), translation(s) and plane normal(s)

[motions, nsols] = cv.decomposeHomographyMat(H, K)

Input

• H The input homography matrix between two images, 3x3.
• K The input intrinsic camera calibration matrix, 3x3.

Output

• motions Decomposed H. A scalar struct with the following fields:
  • R Array of rotation matrices. Cell array of 3x3 rotations.
  • t Array of translation matrices. Cell array of 3x1 translations.
  • n Array of plane normal matrices. Cell array of 3x1 normals.
• nsols number of solutions.

This function extracts relative camera motion between two views observing a planar object from the homography H induced by the plane. The intrinsic camera matrix K must also be provided. The function may return up to four mathematical solution sets. At least two of the solutions may further be invalidated if point correspondences are available by applying positive depth constraint (all points must be in front of the camera). The decomposition method is described in detail in [Malis]:

H = s * K * (R{i} + t{i} * n{i}') * inv(K),  for i=1:nsols

s is a scaling factor approximated as:

s = median(svd(inv(K) * H * K))

References

[Malis]:

Ezio Malis, Manuel Vargas, and others. "Deeper understanding of the homography decomposition for vision-based control". 2007.