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Sherman-Morrison-Woodbury Formula-based Algorithms for the Surface Smoothing Problem
BibTeX
@MISC{Lai_sherman-morrison-woodburyformula-based,
author = {Shang-hong Lai and B. C. Vemuri},
title = {Sherman-Morrison-Woodbury Formula-based Algorithms for the Surface Smoothing Problem},
year = {}
}
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Abstract
Surface smoothing applied to range/elevation data acquired using a variety of sources has been a very active area of research in computational vision over the past decade. Generalized splines have emerged as the single most popular approximation tool to this end. In this paper we present a new and fast algorithm for solving the surface smoothing problem using a membrane, a thin-plate, or a thin-plate-membrane spline for data containing discontinuities. Our approach involves imbeding the surface smoothing problem specified on an irregular domain (in the sense of discontinuties and boundaries) in a rectangular region using the capacitance matrix method based on the Sherman-Morrison-Woodbury formula of matrix analysis. This formula is used in converting the problem of solving the original linear system resulting from a finite element discretization of the variational formulation of the surface smoothing problem to solving a Lyapunov matrix equation or a cascade of two Lyapunov matrix equ...
Keyphrases
surface smoothing problem sherman-morrison-woodbury formula-based algorithm elevation data active area fast algorithm original linear system computational vision past decade irregular domain rectangular region lyapunov matrix equation finite element discretization sherman-morrison-woodbury formula matrix analysis thin-plate-membrane spline capacitance matrix method variational formulation popular approximation tool lyapunov matrix equ
