<title>Visualization of volumetric scattered data based on weighted alpha shapes</title>

Abstract

Scattered data is defined as a collection of data that have little specified connectivity among data points. In this case, Marching Cubes algorithm is no longer applicable. In real world, many applicable data are available in a manner of scattered data rather than cuberille grid data. The alpha shapes of finite points set are a polytope that is uniquely determined by the set and a real number α. Alpha shapes express the intuitive notion of the shape of the point set, and α is a parameter that controls the level of detail reflected by the polytope. However, alpha-shapes give good results for points of roughly uniform density, it does not give for non-uniform point sets. In reconstructing a surface from scattered data it is rarely the case that the points are uniformly dense everywhere on the surface. In order to be effective in non-uniform point sets, it needs to change the value of alpha (radius of sphere) locally depending on the intensity of a point set. The weighted alpha shapes is defined for a finite set of weighted points. We need to investigate the way to achieve different levels of detail in a single shape by assigning weights to the data points. One of the ways to assign weight can be considered by using Inverse Distance Weighted methods. This paper describes how to assign the weight for each data points. The quality of interpolant of volumetric scattered data depend on the way of assigning weights. To achieve the reasonable way of assigning weights, we need to consider not only the positional information (inverse distance), but also intensity information.