Learning on Lie Groups for Invariant Detection and Tracking
Oncel Tuzel (1,3) Fatih Porikli (3) and Peter Meer (1,2)
(1)Department of Computer Science
(2)Department of Electrical and Computer Engineering
Rutgers University, Piscataway, NJ 08854, USA
(3) Mitsubishi Electric Research Laboratories
Cambridge, MA 02139
This paper presents a novel learning based tracking model combined with
object detection. The existing techniques proceed by linearizing the motion,
which makes an implicit Euclidean space assumption. Most of the transformations
used in computer vision have matrix Lie group structure. We learn the motion
model on the Lie algebra and show that the formulation minimizes a first
order approximation to the geodesic error. The learning model is extended
to train a class specific tracking function, which is then integrated to an
existing pose dependent object detector to build a pose invariant object detection
algorithm. The proposed model can accurately detect objects in various poses,
where the size of the search space is only a fraction compared to the existing
object detection methods. The detection rate of the original detector is improved
by more than 90% for large transformations.
Accepted for publication in 2008 Computer Vision and Pattern Recognition Conference, Anchorage,
Alaska, June 2008.
