NDLI: Generalized Newton methods for energy formulations in image procesing

Content Provider	IEEE Xplore Digital Library
Author	Bar, L. Sapiro, G.
Copyright Year	2008
Description	Author affiliation: Dept. of Electr. & Comput. Eng., Univ. of Minnesota, Minneapolis, MN (Bar, L.; Sapiro, G.)
Abstract	Many problems in image processing are solved via the minimization of a cost functional. The most widely used optimization technique is the gradient descent, often used due to its simplicity and applicability where other optimization techniques, e.g., those coming from discrete optimization, can not be used. Yet, gradient descent suffers from a slow convergence, and often to just local minima which highly depends on the condition number of the functional Hessian. Newton- type methods, on the other hand, are known to have a rapid (quadratic) convergence. In its classical form, the Newton method relies on the $L^{2}-type$ norm to define the descent direction. In this paper, we generalize and reformulate this very important optimization method by introducing a novel Newton method based on general norms. This generalization opens up new possibilities in the extraction of the Newton step, including benefits such as mathematical stability and smoothness constraints. We first present the derivation of the modified Newton step in the calculus of variation framework. Then we demonstrate the method with two common objective functionals: variational image deblurring and geodesic active contours. We show that in addition to the fast convergence, different selections norm yield different and superior results.
Starting Page	809
Ending Page	812
File Size	391409
Page Count	4
File Format	PDF
ISBN	9781424417650
ISSN	15224880
DOI	10.1109/ICIP.2008.4711878
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-12
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Newton method Convergence Cost function Optimization methods Calculus Image segmentation Image processing Active contours Image edge detection Shape Variational methods
Content Type	Text
Resource Type	Article

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1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
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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
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