Large deformable splines, crest lines, and matching

Andre P. Gueziec; Nicholas Ayache

doi:10.1117/12.146636

23 June 1993 Large deformable splines, crest lines, and matching

Andre P. Gueziec, Nicholas Ayache

Proceedings Volume 2031, Geometric Methods in Computer Vision II; (1993) https://doi.org/10.1117/12.146636
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

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.

Citation Download Citation

Andre P. Gueziec and Nicholas Ayache "Large deformable splines, crest lines, and matching", Proc. SPIE 2031, Geometric Methods in Computer Vision II, (23 June 1993); https://doi.org/10.1117/12.146636

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