NDLI: A Riemannian Framework for Matching Point Clouds Represented by the Schrödinger Distance Transform

Content Provider	IEEE Xplore Digital Library
Author	Yan Deng Rangarajan, A. Eisenschenk, S. Vemuri, B.C.
Copyright Year	2014
Description	Author affiliation: Dept. of CISE, Univ. of Florida, Gainesville, FL, USA (Yan Deng; Rangarajan, A.; Vemuri, B.C.) \|\| Dept. of Neurology, Univ. of Florida, Gainesville, FL, USA (Eisenschenk, S.)
Abstract	In this paper, we cast the problem of point cloud matching as a shape matching problem by transforming each of the given point clouds into a shape representation called the Schrödinger distance transform (SDT) representation. This is achieved by solving a static Schrödinger equation instead of the corresponding static Hamilton-Jacobi equation in this setting. The SDT representation is an analytic expression and following the theoretical physics literature, can be normalized to have unit 2 norm - making it a square-root density, which is identified with a point on a unit Hilbert sphere, whose intrinsic geometry is fully known. The Fisher-Rao metric, a natural metric for the space of densities leads to analytic expressions for the geodesic distance between points on this sphere. In this paper, we use the well known Riemannian framework never before used for point cloud matching, and present a novel matching algorithm. We pose point set matching under rigid and non-rigid transformations in this framework and solve for the transformations using standard nonlinear optimization techniques. Finally, to evaluate the performance of our algorithm - dubbed SDTM - we present several synthetic and real data examples along with extensive comparisons to state-of-the-art techniques. The experiments show that our algorithm outperforms state-of the-art point set registration algorithms on many quantitative metrics.
Starting Page	3756
Ending Page	3761
File Size	346864
Page Count	6
File Format	PDF
ISBN	9781479951185
ISSN	10636919
DOI	10.1109/CVPR.2014.486
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2014-06-23
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Shape Three-dimensional displays Transforms Measurement Optimization Data models Equations Unit Hilbert Sphere Point clouds matching non-rigid registration Schrodinger Distance Transform Riemannian Manifold
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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