NDLI: A spectral method for solving elliptic equations for surface reconstruction and 3D active contours

Content Provider	IEEE Xplore Digital Library
Author	Jia Li Hero, A.O.
Copyright Year	2001
Description	Author affiliation: Dept. of Electr. Eng. & Comput. Sci., Michigan Univ., Ann Arbor, MI, USA (Jia Li)
Abstract	The solution of elliptic partial differential equations arises in 3D surface reconstruction and active contours. Most current approaches are iterative including finite element methods (FEM) and finite difference methods (FDM). We describe a fast spectral method for solving elliptic equations over the unit sphere. A double Fourier series expansion is applied to model convex or star-shaped 3D surfaces. The Helmholtz equation governing a diffusion on the unit sphere is solved by spectral methods using the double Fourier series as orthogonal basis functions. The optimization of the regularization parameter, which controls the tradeoff between denoising and matching high spatial frequencies, is studied for different 3D shapes and noise models. We show how the resultant solution can be combined with active contour methods to speed up 3D medical image segmentation. A number of examples and simulation results are presented to illustrate the algorithm.
Sponsorship	IEEE Signal Process. Soc
Starting Page	1067
Ending Page	1070
File Size	388349
Page Count	4
File Format	PDF
ISBN	0780367251
DOI	10.1109/ICIP.2001.958311
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2001-10-07
Publisher Place	Greece
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Surface reconstruction Active contours Finite difference methods Fourier series Shape control Partial differential equations Image reconstruction Iterative methods Finite element methods Noise reduction
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
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
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