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Model-based segmentation with volumetric conditions Disclosure Number: IPCOM000182878D
Publication Date: 2009-May-08
Document File: 3 page(s) / 206K

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Model-based segmentation with volumetric conditions

Model-based segmentation has numerous applications in interventions and follow-up studies, for instance in determining the motion of coronal arteries in a time-series of heart CT images. In model-based segmentation, deformable models, described by flexible surface meshes, for instance triangle meshes, are adapted to the corresponding image structures. Usually this adaptation is carried out by optimizing a weighted sum of two competing energies: an external energy driving the mesh triangles towards features in the image, and an internal energy preserving the form of the model [1].

An adaptation of surface meshes alone can not take spatial relations between several object parts into account and hence often results in wrong adaptation results as for instance self-intersecting meshes. First attempts to overcome such problems when adapting multiple meshes are described in [2-6]. There a collision detection is carried out [3,4], or additional edges connecting two meshes are introduced into the model. For these additional edges, the internal energy is extended to keep the spatial relationship of the two meshes [2], or a connection energy is defined to include prior knowledge of the spatial relationship between the connected meshes [5,6]. Such additional edges could also be introduced between different parts of one surface mesh. But they can not describe volumetric conditions as for instance volume preservation. When adapting a heart model, the heart muscle enclosed by the surfaces of the inner and outer walls of the heart chambers approximately preserves its volume: when it stretches in one direction, it contracts in the other spatial directions. Here we propose to introduce volumetric connection elements between such surfaces in order to describe volumetric connection conditions.

We introduce tetrahedral connecting elements between adjacent mesh surfaces. These tetrahedra consist of a base triangle out of the surface mesh and three additional edges connecting the base triangle to one mesh vertex of the adjacent surface. When adapting the surface mesh, the connecting tetrahedra change its shape. A connection energy is introduced, penalizing deviations of pre-defined conditions for the tetrahedra. For instance, when requiring a volume preservation, the current volume of any tetrahedron, described by the product of the area of the base triangle and the height, is compared with the volume of the corresponding tetrahedron in the model, and deviations will be penalized. Hence when the base area increases indicating, for instance, a stretching of the heart muscle in mesh surface direction, the height of the tetrahedron has to shrink which moves the adjacent mesh surfaces closer to each other and corresponds to a contraction of the heart muscle perpendicular to the surfaces....