1 - Looking for shapes in two-dimensional, cluttered point clouds.
A. Srivastava and I. H. Jermyn. IEEE Trans. Pattern Analysis and Machine Intelligence, 31(9): pages 1616-1629, September 2009.
Keywords : Shape, Bayesian, Point cloud, Diffeomorphism, Sampling, Fisher-Rao.
Copyright : ©2008 IEEE. Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
@ARTICLE{SrivastavaJermyn09,
|
| author |
= |
{Srivastava, A. and Jermyn, I. H.}, |
| title |
= |
{Looking for shapes in two-dimensional, cluttered point clouds}, |
| year |
= |
{2009}, |
| month |
= |
{September}, |
| journal |
= |
{IEEE Trans. Pattern Analysis and Machine Intelligence}, |
| volume |
= |
{31}, |
| number |
= |
{9}, |
| pages |
= |
{1616-1629}, |
| url |
= |
{http://dx.doi.org/10.1109/TPAMI.2008.223}, |
| pdf |
= |
{http://www-sop.inria.fr/members/Ian.Jermyn/publications/SrivastavaJermyn09.pdf}, |
| keyword |
= |
{Shape, Bayesian, Point cloud, Diffeomorphism, Sampling, Fisher-Rao} |
| } |
Abstract :
We study the problem of identifying shape classes in point clouds. These clouds contain sampled contours and are
corrupted by clutter and observation noise. Taking an analysis-by-synthesis approach, we simulate high-probability configurations of
sampled contours using models learnt from training data to evaluate the given test data. To facilitate simulations, we develop statistical
models for sources of (nuisance) variability: (i) shape variations within classes, (ii) variability in sampling continuous curves, (iii) pose
and scale variability, (iv) observation noise, and (v) points introduced by clutter. The variability in sampling closed curves into finite
points is represented by positive diffeomorphisms of a unit circle. We derive probability models on these functions using their squareroot
forms and the Fisher-Rao metric. Using a Monte Carlo approach, we simulate configurations from a joint prior on the shape-sample
space and compare them to the data using a likelihood function. Average likelihoods of simulated configurations lead to estimates of
posterior probabilities of different classes and, hence, Bayesian classification. |
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