Visualization of volumetric scattered data based on weighted alpha shapes

Kun Lee; Oubong Gwun; Minsan Lim

doi:10.1117/12.585949

17 January 2005 Visualization of volumetric scattered data based on weighted alpha shapes

Kun Lee, Oubong Gwun, Minsan Lim

Proceedings Volume 5675, Vision Geometry XIII; (2005) https://doi.org/10.1117/12.585949
Event: Electronic Imaging 2005, 2005, San Jose, California, United States

Abstract

This paper describes a method to achieve different level of detail for the given volumetric data by assigning weight for the given data points. The relation between wavelet transformation and alpha shape was investigated to define the different level of resolution. Wavelets are mathematical tool for hierarchically decomposing functions. We apply this feature for describing the ranking of importance for each data point. We treat a volumetric scattered data as the coefficients corresponding to a three-dimensional piecewise constant basis functions of wavelet transformation. We assign weight value based on wavelet coefficient. The given volumetric scattered data points, with a real weight, is connected by using the concept of weighted alpha shapes. Scattered data is defined as a collection of data that have little specified connectivity between data points. The quality of interpolant in volumetric trivariate space depends not only on the distribution of the data points in R³, but also on the data value (intensity). Wavelet coefficients can provide the description in terms of a coarse overall shape, plus details that range from broad to narrow with an approximation coefficients and detail coefficients, respectively. We can improve the quality of an approximation by using wavelet coefficient as weight for the corresponding data points.

Citation Download Citation

Kun Lee, Oubong Gwun, and Minsan Lim "Visualization of volumetric scattered data based on weighted alpha shapes", Proc. SPIE 5675, Vision Geometry XIII, (17 January 2005); https://doi.org/10.1117/12.585949

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