KEYWORDS: Image segmentation, 3D image processing, 3D modeling, Ultrasonography, Optical spheres, Image processing algorithms and systems, Medical imaging, Systems modeling, Detection and tracking algorithms, Algorithm development
Active contour models have already been used succesfully for segmentation of organs from medical images in 3D. In implicit models, the contour is given as the isosurface of a scalar function, and therefore topology adaptations are handled naturally during a contour evolution. Nevertheless, explicit or parametric models are often preferred since user interaction and special geometric constraints are usually easier to incorporate. Although many researchers have studied topology adaptation algorithms in explicit mesh evolutions, no stable algorithm is known for interactive applications. In this paper, we present a topology adaptation system, which consists of two novel ingredients: A spatial hashing technique is used to detect self-colliding triangles of the mesh whose expected running time is linear with respect to the number of mesh vertices. For the topology change procedure, we have developed formulas by homology theory. During a contour evolution, we just have to choose between a few possible mesh retriangulations by local triangle-triangle intersection tests. Our algorithm has several advantages compared to existing ones: Since the new algorithm does not require any global mesh reparametrizations, it is very efficient. Since the topology adaptation system does not require constant sampling density of the mesh vertices nor especially smooth meshes, mesh evolution steps can be performed in a stable way with a rather coarse mesh. We apply our algorithm to 3D ultrasonic data, showing that accurate segmentation is obtained in some seconds.
We propose a two-step approach to segment closed surfaces
in 3D of arbitrary topology. First, a pre segmentation
step with an active contour method is performed.
This evolution process does not take into account
topology adaptions. Topologically correct segmentations
are derived with Kazhdan's algorithm in a
second step. Kazhdan's algorithm requires information
on the surface normals, which are obtained from the
active contour method. We show that the two-step algorithm
is computationally efficient. Moreover, we apply
the algorithms for segmentation of 3D ultrasound
data.
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