Title :
A wide-sense estimation theory on the unit sphere
Author :
Chiuso, Alessandro ; Picci, Giorgio
Author_Institution :
Dipt. di Elettronica e Inf., Padova Univ., Italy
Abstract :
Online estimation of the direction of feature points moving in space from noisy projections on a plane is a classical problem occuring in computer vision which has traditionally been treated by ad hoc statistical methods in the literature. Picci (1997) formulated it as a Bayesian estimation problem on the unit sphere. A natural probabilistic structure which makes this estimation problem tractable has been introduced. Within this structure, exact recursive solutions can be given for sequential observations of a fixed target point, while for a moving object in general one has to resort to approximations. In this paper an approximate (“wide-sense”) solution is proposed which leads to very simple recursions similar to the Kalman filter. In certain situations this solution may provide a substantial improvement over the traditional EKF. As an example, we discuss estimation of the direction of points whose motion is described by a simple dynamic model of the random walk type. This model is of interest in practical situations when dealing with slowly time-varying observed feature points
Keywords :
Bayes methods; Markov processes; computer vision; estimation theory; filtering theory; probability; recursive estimation; statistical analysis; exact recursive solutions; feature points; fixed target point; moving object; natural probabilistic structure; noisy projections; random walk type model; sequential observations; simple dynamic model; slowly time-varying observed feature points; unit sphere; wide-sense estimation theory; Acoustic noise; Additive noise; Cameras; Computer vision; Estimation theory; Length measurement; Optical arrays; Optical filters; Optical noise; Statistical analysis;
Conference_Titel :
Decision and Control, 1998. Proceedings of the 37th IEEE Conference on
Conference_Location :
Tampa, FL
Print_ISBN :
0-7803-4394-8
DOI :
10.1109/CDC.1998.761800