NDLI: Newton geodesic optimization on special linear group

Content Provider	IEEE Xplore Digital Library
Author	Guangwei Li Yunpeng Liu Jian Yin Zelin Shi
Copyright Year	2009
Description	Author affiliation: Research Institute on General Development and Argumentation of Air Force, Beijing, China (Jian Yin) \|\| Shenyang Institute of Automation, Chinese Academy of Sciences, China (Guangwei Li; Yunpeng Liu; Zelin Shi)
Abstract	The Riemannian exponential map on a noncompact Lie Group, which is determined by a Riemannian metric, is different from the Lie group exponential map determined by one-parameter subgroups. The Riemannian exponential map which represents the geodesic of the optimal transformation is obtained in terms of the minimal geodesic equation on SL(n, R). Generally, the Newton optimization method on Lie group is independent of the connection but with the one-parameter group. Based on the parameterization of the manifold with the Riemannian exponential map, we propose an intrinsic Newton optimization method on special linear group and prove its locally quadratic convergence to critical point of the cost function. Our approach is slightly superior to the counterpart based on Lie group exponential map. We demonstrate this by an image registration example.
Starting Page	4346
Ending Page	4351
File Size	531916
Page Count	6
File Format	PDF
ISBN	9781424438716
ISSN	01912216
DOI	10.1109/CDC.2009.5400115
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-12-15
Publisher Place	China
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Optimization methods Constraint optimization Convergence Geometry Quaternions Algebra Visual servoing Vectors Algorithm design and analysis Iterative algorithms
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