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Recursive Motion Estimation on the Essential Manifold

Soatto, Stefano and Frezza, Ruggero and Perona, Pietro (1993) Recursive Motion Estimation on the Essential Manifold. California Institute of Technology , Pasadena, CA. (Unpublished) http://resolver.caltech.edu/CaltechCDSTR:1993.021

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Abstract

Visual motion estimation can be regarded as estimation of the state of a system of difference equations with unknown inputs defined on a manifold. Such a system happens to be "linear", but it is defined on a space (the so called "Essential manifold") which is not a linear (vector) space. In this paper we will introduce a novel perspective for viewing the motion estimation problem which results in three original schemes for solving it. The first consists in "flattening the space" and solving a nonlinear estimation problem on the flat (euclidean) space. The second approach consists in viewing the system as embedded in a larger euclidean space (the smallest of the embedding spaces), and solving at each step a linear estimation problem on a linear space, followed by a "projection" on the manifold (see fig. 5). A third "algebraic" formulation of motion estimation is inspired by the structure of the problem in local coordinates (flattened space), and consists in a double iteration for solving an "adaptive fixed-point" problem (see fig. 6). Each one of these three schemes outputs motion estimates together with the joint second order statistics of the estimation error, which can be used by any structure from motion module which incorporates motion error [20, 23] in order to estimate 3D scene structure. The original contribution of this paper involves both the problem formulation, which gives new insight into the differential geometric structure of visual motion estimation, and the ideas generating the three schemes. These are viewed within a unified framework. All the schemes have a strong theoretical motivation and exhibit accuracy, speed of convergence, real time operation and flexibility which are superior to other existing schemes [1, 20, 23]. Simulations are presented for real and synthetic image sequences to compare the three schemes against each other and highlight the peculiarities of each one.


Item Type:Report or Paper (Technical Report)
Additional Information:Research founded by the California Institute of Technology, an AT&T Foundation Special Purpose grant and grant ASI-RS-103 from the Italian Space Agency.
Group:Control and Dynamical Systems Technical Reports
Record Number:CaltechCDSTR:1993.021
Persistent URL:http://resolver.caltech.edu/CaltechCDSTR:1993.021
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:28064
Collection:CaltechCDSTR
Deposited By: Imported from CaltechCDSTR
Deposited On:01 Sep 2006
Last Modified:26 Dec 2012 14:29

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