19 April 2004 Visualization and modeling of 3D scattered volume data by using wavelet transformation and generalized asymptotic decider criterion
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Abstract
The common problem of volumetric image data is that the amount of data is too much. This paper proposes a method, which selects the important data and models it by using wavelet transformation and Generalized Asymptotic Decider Criterion. In the pre-processing stage, the important data are selected based on the coefficients of wavelet from the cuberille data. We interpret the scattered data interpolation as surface interpolation to the given data. To perform scattered data domain of definition of our 4-D surface is the union of tetrahedral. These geometric domains allow us to define surface interpolants for irregularly located points. In trivate surface interpolation, we need to define a tetrahedral domain decomposition. The initial tetrahedral domain is constructed by using Delaunay tetrahedrization. In the case of ambiguity, asymptotic decider criterion is used instead of sphere criterion. In this paper, asymptotic decider criterion is applied to tetrahedral domain instead of cubical domain. To apply this idea to tetrahedral instead of cubes, asymptotic decider criterion needs to be generalized. In the generalized asymptotic decider criterion, the intersection of two diagonal of quadrilateral does not necessary to be orthogonal. The value of oblique asymptotes is obtained instead of vertical and horizontal asymptotes. The value of oblique asymptotes is obtained from interpolation over quadrilateral instead of rectangle by using barycentric coordinates.
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Kun Lee, Kun Lee, Oubong Gwun, Oubong Gwun, } "Visualization and modeling of 3D scattered volume data by using wavelet transformation and generalized asymptotic decider criterion", Proc. SPIE 5300, Vision Geometry XII, (19 April 2004); doi: 10.1117/12.525274; https://doi.org/10.1117/12.525274
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