Visualization of multiresolution model for volumetric medical data by using weighted alpha shapes

Abstract

In real world applications, given data points are located arbitraily rather than in a regular distribution. The numerous applications of volumetric scattered data can be enumerated, such as computational fluid dynamics, medicine, terrain modeling and oil exploration. Multiresolution is desired to visualize volumetric scattered data, because the common problem of volumetric data is that the amount of data is too much. The modeling of such multiscale phenomena is computationally expensive. The mathematical model needs to reflect the different levels of details by approximating the mathematical object on multiple different scales, ranging from a coarse repesentation at a low resolution to a fine representation at a high resolution. The weighted alpha shapes method is defined for a finite set of weighted points. In other words, it is a polytope uniquely determined by the points, their weights, and a parameter α ∈ R that controls the desired level of detail. Therefore, we need to investigate the way to achieve different levels of detail in a single shape by assigning weights to the data points. In this paper, Gaussian curvature can be considered as the weight value of each data point.