A Novel Dynamic System in the Space of SPD Matrices with Applications to Appearance Tracking
- 1 January 2013
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Imaging Sciences
- Vol. 6 (1), 592-615
- https://doi.org/10.1137/110853376
Abstract
In this paper, we address the problem of video tracking using covariance descriptors constructed from simple features extracted from the given image sequence. Theoretically, this can be posed as a tracking problem in the space of ($n \times n$) symmetric positive definite (SPD) matrices denoted by $P_n$. A novel probabilistic dynamic model in $P_n$ based on Riemannian geometry and probability theory is presented in conjunction with a geometric (intrinsic) recursive filter for tracking a time sequence of SPD matrix measurements in a Bayesian framework. This newly developed filtering method can be used for the covariance descriptor updating problem in covariance tracking, leading to new and efficient video tracking algorithms. To show the accuracy and efficiency of our tracker in comparison to the state-of-the-art, we present synthetic experiments on $P_n$ and several real data experiments for tracking in video sequences.
This publication has 18 references indexed in Scilit:
- Visual Tracking via Particle Filtering on the Affine GroupThe International Journal of Robotics Research, 2009
- Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric MeasurementsJournal of Mathematical Imaging and Vision, 2006
- State space models on special manifoldsJournal of Multivariate Analysis, 2006
- A Differential Geometric Approach to the Geometric Mean of Symmetric Positive-Definite MatricesSIAM Journal on Matrix Analysis and Applications, 2005
- Principal Geodesic Analysis for the Study of Nonlinear Statistics of ShapeIEEE Transactions on Medical Imaging, 2004
- Bayesian and geometric subspace trackingAdvances in Applied Probability, 2004
- A tutorial on particle filters for online nonlinear/non-Gaussian Bayesian trackingIEEE Transactions on Signal Processing, 2002
- Mean shift: a robust approach toward feature space analysisIEEE Transactions on Pattern Analysis and Machine Intelligence, 2002
- A central limit theorem on the space of positive definite symmetric matricesAnnales de l'institut Fourier, 1992
- Riemannian center of mass and mollifier smoothingCommunications on Pure and Applied Mathematics, 1977