NDLI: An O(N) iterative solution to the Poisson equation in low-level vision problems

Content Provider	IEEE Xplore Digital Library
Author	Lai, S.H. Vemuri, B.C.
Copyright Year	1994
Description	Author affiliation: Dept. of Electr. Eng., Florida Univ., Gainesville, FL, USA (Lai, S.H.)
Abstract	In this paper, we present a novel iterative numerical solution to the Poisson equation whose solution is needed in a variety of low-level vision problems. Our algorithm is an O(N) (N being the number of discretization points) iterative technique and does not make any assumptions on the shape of the input domain unlike the polyhedral domain assumption in the proof of convergence of multigrid techniques. We present two major results namely, a generalized version of the capacitance matrix theorem and a theorem on O(N) convergence of the alternating direction implicit method (ADI) used in our algorithm. Using this generalized theorem, we express the linear system corresponding to the discretized Poisson equation as a Lyapunov and a capacitance matrix equation. The former is solved using the ADI method while the solution to the later is obtained using a modified bi-conjugate gradient algorithm. We demonstrate the algorithm performance on synthesized data for the surface reconstruction and the SFS problems.<>
Starting Page	9
Ending Page	14
File Size	692577
Page Count	6
File Format	PDF
ISBN	0818658258
ISSN	10636919
DOI	10.1109/CVPR.1994.323804
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	1994-06-21
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Machine vision Iterative methods Image reconstruction
Content Type	Text
Resource Type	Article
Subject	Computer Vision and Pattern Recognition Software

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