Jolley Hall, Room 309
"Medial Axis Approximation and Regularization"
Adviser: Tao Ju
Medial axis is a classical shape descriptor. Among many good properties, medial axis is thin, centered in the shape, and topology preserving. Therefore, it is constantly sought after by researchers and practitioners in their respective domains. However, two barriers remain that hinder wide adoption of medial axis.
First, medial axis is easily disturbed by small noises on its defining shape. To tame instability, a majority of current works define a significance measure to prune noises on medial axis. Among them, local measures are widely available due to their efficiency, but can be either too aggressive or conservative. While global measures outperform local ones in differentiating noises from features, they are rarely well-defined or efficient to compute. Second, medial axis is too complex to compute exactly. Though abundant approximation methods exist, they are either limited in scalability, or susceptible to numerical issues.
In this dissertation, we attempt to address these issues with sound, robust and efficient solutions. In Chapter 2, we present Erosion Thickness (ET) to regularize instability. ET is the first global measure in 3D that is well-defined and efficient to compute. To demonstrate its usefulness, we utilize ET to generate a family of shape revealing and topology preserving skeletons. In Chapter 3, we propose a novel medial axis approximation called voxel core. We show voxel core is topologically and geometrically convergent to the true medial axis. We then describe a straightforward implementation as a result of our simple definition. In a variety of experiments, our method is shown to be efficient and robust in delivering topological promises on a wide range of shapes. Finally, we point out future directions, including a potential application of our works in a real world problem.