Generation of Unit-Width Curve Skeletons Based on Valence Driven Spatial Median (VDSM)
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing
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The curve-skeleton is a one-dimensional (1D) abstraction of a three-dimensional (3D) object, consisting of a set of curves embedded in 3D space. As a reduced representation, it is useful in many visualization, computer graphics and computer vision tasks, such as: virtual navigation, reduced-model formulation, visualization improvement, mesh repair, animation, matching, etc. In spite its simplicity and proven usefulness, there is still no rigorous definition of the curve-skeleton. Recent attempts at providing such a definition are based on specific algorithms that extract some curve-skeleton.In the first part of this thesis, we attempt to bring formalism to the concept of a curve-skeleton. First, we survey numerous applications and algorithms designed to compute curve-skeletons and distill the desirable properties of a curve-skeleton from these applications. Our analysis suggests that a rigorous definition cannot be developed without compromising some of the desirable properties. Instead, we adopt a general definition and we strive to provide the end user with the flexibility of choosing from a variety of possible curve-skeletons, the one that best fits a given application requirements. To this end, we provide an extensive qualitative discussion of each of the surveyed algorithm classes with respect to the properties, and develop algorithms that quantitatively evaluate these properties for a given curve-skeleton.We also present a robust vector field based hierarchical curve-skeletonization framework and we investigate two types of vector fields: one based on the repulsive force generated by a generalized Newtonian potential function, the other based on a normal front propagation technique, we term a normal diffusion field. We provide a comparative study of two types of vector fields, with respect to the properties of the resulting curve-skeleton.In the second part of the thesis, we exemplify the utility of the curve-skeleton representation in general as shape abstraction and of our curve-skeletonization framework in particular, in several areas of visualization, computer graphics and computer vision. We investigate volume decomposition and several applications derived from it such as volume animation, texture mapping, focus and context rendering, and compression/packing of volumetric data for hardware accelerated volume rendering and manipulation. We present a robust method for 3D object retrieval based on matching curve-skeletons, and we investigate an extension of our matching and curve-skeletonization framework to four dimensions (4D) and its application in indexing and retrieval of fMRI time series by content.