A study of the paper Rui Rodrigues, João P

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Presentation transcript:

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

Introduction Modeling Applications

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)

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

Searching for the mirror plane

Geometric properties Geometric properties Linear Constraints

The setup

The linear equations

The algorithm

formula

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”, https://www.gamedev.net/forums/topic/670415-right-vs-left-handed-matrix-representation/ David Eberly , “Right-Handed Coordinates “, https://answers.unity.com/storage/temp/12048-lefthandedtorighthanded.pdf