NDLI: Uncertainty relations associated with motion analysis

Content Provider	IEEE Xplore Digital Library
Author	Leduc, J.-P.
Copyright Year	2001
Description	Author affiliation: Dept. of Math., Maryland Univ., College Park, MD, USA (Leduc, J.-P.)
Abstract	The purpose of this work is to describe the uncertainty relations which rule the estimation of motion parameters embedded in spatio-temporal digital signals defined in L/sup 2/(R/sup 2//spl times/R, dx/spl I.oarr/dt) as well as the estimation of motion parameters taking place in the exterior scene R/sup 3//spl times/R. This problem is central for optimal motion tracking applications since it determines how to design the sequence of motion parameters to estimate. This analysis extends to motion on smooth manifolds (i.e. curved surfaces) and/or to sensor arrays which are deployed on smooth manifolds. Signal analysis means motion detection, estimation and selective reconstructions. It is performed with template functions or wavelets taken as cross-correlation functions. In this context, both kinematics and geometry are described by Lie algebras. The Lie algebras characterize all the actual and physical models that can be observed in the exterior scenes as well as in scenes captured by the sensors. The local transformations are structured in Lie groups that are computed by exponentiation from the corresponding algebras. Eventually, group representations and continuous wavelets are derived in the functional space of the signals. The important issue is that the Lie algebra contains all the information on the estimation uncertainties. Indeed, any pair of generators in the algebra that fails to commute generates a Heisenberg-type inequality. The harmonic analysis associated with the uncertainty principle may then be derived in the functional space of interest from the construction of group representations. The example of motion estimation on flat surface is considered. In this case, the admissibility of multi-dimensional square-integrable templates moving at constant velocity (modeled by the Galilei group) require that velocity and translation (position) generators do not commute. The generalization of this motion is thereafter studied on manifolds and generates highly non-commutative cases.
Sponsorship	IEEE Inf. Theory Soc
File Size	129888
File Format	PDF
ISBN	0780371232
DOI	10.1109/ISIT.2001.936072
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-06-29
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Uncertainty Motion analysis Motion estimation Algebra Parameter estimation Layout Sensor arrays Sensor phenomena and characterization Tracking Surface reconstruction
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in