NDLI: Enforcing integrability by error correction using ℓ1-minimization

Content Provider	IEEE Xplore Digital Library
Author	Reddy, D. Agrawal, A. Chellappa, R.
Copyright Year	2009
Description	Author affiliation: University of Maryland, College Park, 20742, USA (Reddy, D.; Chellappa, R.) \|\| Mitsubishi Electric Research Labs, Cambridge, MA, 02139, USA (Agrawal, A.)
Abstract	Surface reconstruction from gradient fields is an important final step in several applications involving gradient manipulations and estimation. Typically, the resulting gradient field is non-integrable due to linear/non-linear gradient manipulations, or due to presence of noise/outliers in gradient estimation. In this paper, we analyze integrability as error correction, inspired from recent work in compressed sensing, particulary ℓ0 - ℓ1 equivalence. We propose to obtain the surface by finding the gradient field which best fits the corrupted gradient field in ℓ1 sense. We present an exhaustive analysis of the properties of ℓ1 solution for gradient field integration using linear algebra and graph analogy. We consider three cases: (a) noise, but no outliers (b) no-noise but outliers and (c) presence of both noise and outliers in the given gradient field. We show that ℓ1 solution performs as well as least squares in the absence of outliers. While previous ℓ0 - ℓ1 equivalence work has focused on the number of errors (outliers), we show that the location of errors is equally important for gradient field integration. We characterize the ℓ1 solution both in terms of location and number of outliers, and outline scenarios where ℓ1 solution is equivalent to ℓ0 solution. We also show that when ℓ1 solution is not able to remove outliers, the property of local error confinement holds: i.e., the errors do not propagate to the entire surface as in least squares. We compare with previous techniques and show that ℓ1 solution performs well across all scenarios without the need for any tunable parameter adjustments.
Starting Page	2350
Ending Page	2357
File Size	1483801
Page Count	8
File Format	PDF
ISBN	9781424439928
ISSN	10636919
DOI	10.1109/CVPR.2009.5206603
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2009-06-20
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Error correction Surface reconstruction Cost function Least squares methods Noise robustness Educational institutions Compressed sensing Linear algebra Image reconstruction Least squares approximation
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

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