Multiresolution volumetric medical data modeling based on Gaussian curvature by using weighted alpha shapes

This paper describes a method to achieve a different level of detail for the given volumetric data by assigning weight of each data point. Level of detail increases the efficiency of rendering by decreasing the workload. The relation between curvature and a weight of alpha shape was investigated to define a different level of resolution. In weighted α-shape, if a is chosen so that the α-shape produce a piecewise linear surface in sparse weight region, it will hide details in denser regions. If α is chosen so that the dense regions are nicely modeled, then the α-shape will develop holes and break apart in sparse regions. The assignment of large weights in sparse-weight regions and of small weight in dense region can be used to counteract this undesirable effect. The data point of sparse region requires a large circumsphere to connect each data point. A large circumsphere has a small curvature, because a curvature equals to the reciprocal of its radius. Curvature is inversed and assigned as a weight. It leads to assign a large weight in sparse region as it is desired. Conversely, a small weight value is assigned to data points of dense region. A large weight favors and a small weight discourages connections to neighboring points.