Generalized Image Acquisition and Analysis

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

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 geo- metric 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 demon- strate the effectiveness of our algorithm on extensive simulations as well as in a challenging real-world calibration scenario.

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Intrinsic Shape Matching by Planned Landmark Sampling

Art Tevs, Alexander Berner, Michael Wand, Ivo Ihrke, Hans-Peter Seidel
In: Proceedings of EUROGRAPHICS 2011.



Abstract

Recently, the problem of intrinsic shape matching has received a lot of attention. A number of algorithms have been proposed, among which random-sampling-based techniques have been particularly successful due to their generality and efficiency. We introduce a new sampling-based shape matching algorithm that uses a planning step to find optimized "landmark" points. These points are matched first in order to maximize the information gained and thus minimize the sampling costs. Our approach makes three main contributions: First, the new technique leads to a significant improvement in performance, which we demonstrate on a number of benchmark scenarios. Second, our technique does not require any keypoint detection. This is often a significant limitation for models that do not show sufficient surface features. Third, we examine the actual numerical degrees of freedom of the matching problem for a given piece of geometry. In contrast to previous results, our estimates take into account unprecise geodesics and potentially numerically unfavorable geometry of general topology, giving a more realistic complexity estimate.
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Bibtex

@INPROCEEDINGS{Tevs11:plansac,
AUTHOR = {Art Tevs and Alexander Berner and Michael Wand and Ivo Ihrke and Hans-Peter Seidel},
EDITOR = {Deussen, Oliver and Chen, Min},
TITLE = {{Intrinsic Shape Matching by Planned Landmark Sampling}},
BOOKTITLE = {Computer Graphics Forum (Proc. EUROGRAPHICS)},
ORGANIZATION = {Eurographics},
PADDRESS = {Oxford, UK},
ADDRESS = {Llandudno, UK},
PUBLISHER = {Blackwell},
YEAR = {2011},
PAGES = {543--552},
}
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