1. A study of the paper Rui Rodrigues, João P
A study of the paper Rui Rodrigues, João P. Barreto,Urbano Nunes, “Camera Pose Estimation Using Images of Planar Mirror Reflections”, ECCV 2010
KH Wong

2. Introduction
Modeling
Applications

3. Modeling
Relating Rotation R and translation t and T, T=pose matrix (extrinsic parameter)
It projection is q through a camera intrinsic matrix K
A mirror is a plane ={n,d} with normal vector (n) and orthogonal distance (d). If X is point on  , relating n,d and X.
Q is a point in 3D (real), its mirrored point (virtual) is , see diagram (c )
Relating Q and its mirrored point
Rearrange becomes
S is a symmetry transformation induced by the plane 
(1)
(2)
(3)

4. The virtual camera
Q’s projection is q through a camera intrinsic matrix K
Based on (1) and (2)
You may consider the relation between the real transformation (S) and and virtual transformation (S’) as

5. Searching for the mirror plane

6. Geometric properties
Geometric properties
Linear Constraints

7. The setup

8. The linear equations

9. The algorithm

10. formula

11. Reference
Rui Rodrigues, João P. Barreto,Urbano Nunes, “Camera Pose Estimation Using Images of Planar Mirror Reflections”, ECCV 2010
Vincent_M, “Right vs Left-Handed Matrix representation”,  
David Eberly , “Right-Handed Coordinates “,