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Reports (Research Report) Year : 1992

Large deformable splines, crest lines and matching


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 to segment fine anatomical structures. With respect to earlier approaches by Cinquin's team in Grenoble or Medioni's team in U.S.C. and also by Cohen et al. or Kass et al. 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 key following improvements : - we show that the Euler equations has a closed form solution in a quadratic potential field. Each approximation requires only one iteration, - 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, - with a regularly sampled potential field, each point in the same image voxel in 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 curvature and directions. We describe next an original algorithm that extracts lines of extremal curvature on the surface. We present experimental evidence with real medical images that illustrate all the previous points. Finally we give two marginal contributions. We outline the spherical topology for spline surfaces. We use Ostrogradsky's formula to compute the exact volume bounded by such a surface.We also give some hints about the tricky topic of avoiding self-intersections.


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Dates and versions

inria-00077022 , version 1 (29-05-2006)


  • HAL Id : inria-00077022 , version 1


André Gueziec. Large deformable splines, crest lines and matching. [Research Report] RR-1782, INRIA. 1992. ⟨inria-00077022⟩
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