Discovering the Structure of a Planar Mirror System from Multiple Observations of a Single Point

Ilya Reshetouski, Alkhazur Manakov, Ayush Bandhari, Ramesh Raskar, Hans-Peter Seidel, Ivo Ihrke; The IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 2013, pp. 89-96

Abstract


We investigate the problem of identifying the position of a viewer inside a room of planar mirrors with unknown geometry in conjunction with the room's shape parameters. We consider the observations to consist of angularly resolved depth measurements of a single scene point that is being observed via many multi-bounce interactions with the specular room geometry. Applications of this problem statement include areas such as calibration, acoustic echo cancelation and time-of-flight imaging. We theoretically analyze the problem and derive sufficient conditions for a combination of convex room geometry, observer, and scene point to be reconstructable. The resulting constructive algorithm is exponential in nature and, therefore, not directly applicable to practical scenarios. To counter the situation, we propose theoretically devised geometric constraints that enable an efficient pruning of the solution space and develop a heuristic randomized search algorithm that uses these constraints to obtain an effective solution. We demonstrate the effectiveness of our algorithm on extensive simulations as well as in a challenging real-world calibration scenario.

Related Material


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[bibtex]
@InProceedings{Reshetouski_2013_CVPR,
author = {Reshetouski, Ilya and Manakov, Alkhazur and Bandhari, Ayush and Raskar, Ramesh and Seidel, Hans-Peter and Ihrke, Ivo},
title = {Discovering the Structure of a Planar Mirror System from Multiple Observations of a Single Point},
booktitle = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
month = {June},
year = {2013}
}