Image Analysis Using Multigrid Relaxation Methods
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Direct Analytical Methods for Solving Poisson Equations in Computer Vision Problems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape from shading
On active contour models and balloons
CVGIP: Image Understanding
International Journal of Computer Vision
Parametrization of closed surfaces for 3-D shape description
Computer Vision and Image Understanding
Journal of Computational Physics
Efficient Spectral-Galerkin Methods IV. Spherical Geometries
SIAM Journal on Scientific Computing
Double Fourier series on a sphere: applications to elliptic and vorticity equations
Journal of Computational Physics
Finite-Element Methods for Active Contour Models and Balloons for 2-D and 3-D Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Improved penalized likelihood reconstruction of anatomically correlated emission computed tomography data
IEEE Transactions on Image Processing
Snakes, shapes, and gradient vector flow
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Novel Quantitative Method for Spleen's Morphometry in Splenomegally
ICAISC '08 Proceedings of the 9th international conference on Artificial Intelligence and Soft Computing
ICDHM'07 Proceedings of the 1st international conference on Digital human modeling
ICAISC'06 Proceedings of the 8th international conference on Artificial Intelligence and Soft Computing
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Variational energy minimization techniques for surface reconstruction are implemented by evolving an active surface according to the solutions of a sequence of elliptic partial differential equations (PDE's). For these techniques, most current approaches to solving the elliptic PDE are iterative involving the implementation of costly finite element methods (FEM) or finite difference methods (FDM). The heavy computational cost of these methods makes practical application to 3D surface reconstruction burdensome. In this paper, we develop a fast spectral method which is applied to 3D active surface reconstruction of star-shaped surfaces parameterized in polar coordinates. For this parameterization the Euler-Lagrange equation is a Helmholtz-type PDE governing a diffusion on the unit sphere. After linearization, we implement a spectral non-iterative solution of the Helmholtz equation by representing the active surface as a double Fourier series over angles in spherical coordinates. We show how this approach can be extended to include region-based penalization. A number of 3D examples and simulation results are presented to illustrate the performance of our fast spectral active surface algorithms.