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Proceedings Paper

Large deformable splines, crest lines, and matching
Author(s): Andre P. Gueziec; Nicholas Ayache
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Paper Abstract

We present new deformable spline surfaces for segmentation of 3-D medical images. We explore parametric surfaces of the form x(u, v) with two different topologies, planar and cylindrical, that permit us to segment fine anatomical structures. With respect to earlier approaches that minimize the `energy' of a deformable surface in a potential field, we perform this optimization with successive approximations of dense data, and propose the following key improvements. First, we show that the Euler equation has a closed form solution in a quadratic potential field. Each approximation requires only one iteration. Second, we use tensor products of splines to solve independently the system along parameters u and v. This enables us to work with large meshes of control vertices, e.g., 10,000 vertices and more. Third, with a regularly sampled potential field, each point in the same image voxel is processed in the same way. We use a continuous potential field defined with 3-D volumetric splines to avoid this problem. When the deformation process stops, we end up with a smooth differentiable surface where we measure principle curvatures and directions. We describe next an original algorithm that extracts lines of extremal curvature on the surface. These lines can be matched from different views with an algorithm such as in.GA92. We present experimental evidence with real medical images that illustrate all the previous points. Finally, we outline the spherical topology for spline surfaces. We use Ostrogradsky's formula to compute the exact volume bounded by such a surface.

Paper Details

Date Published: 23 June 1993
PDF: 12 pages
Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); doi: 10.1117/12.146636
Show Author Affiliations
Andre P. Gueziec, INRIA (France)
Nicholas Ayache, INRIA (France)


Published in SPIE Proceedings Vol. 2031:
Geometric Methods in Computer Vision II
Baba C. Vemuri, Editor(s)

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