A study of the paper Rui Rodrigues João P BarretoUrbano Nunes Camera Pose Estimation Using Images of Planar Mirror Reflections ECCV 2010 KH Wong Introduction Modeling Applications Modeling ID: 772469
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A study of the paperRui Rodrigues, João P. Barreto,Urbano Nunes, “Camera Pose Estimation Using Images of Planar Mirror Reflections”, ECCV 2010 KH Wong
IntroductionModelingApplications
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 pointRearrange becomesS is a symmetry transformation induced by the plane (2) (3) (1)
The virtual cameraQ’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
ReferenceRui 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