Computation of Discrete Medial Axis Using Local Search in Domain Delaunay Triangulation of a Solid

A new method is proposed to determine the points on the medial axis transform (MAT) of an object from its surface mesh representation. Current art typically uses a Voronoi diagram-based approach to generate the medial axis of a given point cloud on the boundary of the object or a surface mesh representation as input. This approach defines the MAT points as a subset of the Voronoi vertices close to the medial axis, where the accuracy and density of the points on the medial axis depend on the sampling density of the input point cloud representation. Therefore, the set of medial axis points is incomplete and may lack various topological features of the MAT and its reconstruction property. Instead of filtering the Voronoi vertices that are not medial points, the method proposed in this paper searches for the correct MAT point in the vicinity of such Voronoi vertices and finds the pair of corresponding footpoints using the properties of the MAT point. Hence, the algorithm can determine points on the medial axis without being dependent on the given sampling density and even in the presence of inputs having non-manifold entities. As the MAT points are generated based on the definition of medial axis (MA), the result obtained is accurate to within a specified tolerance.

Area-Construction Algorithms Using Tangent Circles

Computer aided geometric design employs mathematical and computational methods for describing geometric objects, such as curves, areas in two dimensions (2D) and surfaces, and solids in 3D. An area can be represented using its boundary curves, and a solid can be represented using its boundary surfaces with intersection curves among these boundary surfaces. In addition, other methods, such as the medial-axis transform, can also be used to represent an area. Although most researchers have presented algorithms that find the medial-axis transform from an area, a algorithm using the contrasting approach is proposed; i.e., it finds an area using a medial-axis transform. The medial-axis transform is constructed using discrete points on a curve and referred to as the skeleton of the area. Subsequently, using the aforementioned discrete points, medial-axis circles are generated and referred to as the muscles of the area. Finally, these medial-axis circles are blended and referred to as the blended boundary curves skin of the area; consequently, the boundary of the area generated is smooth.

MAT-Net: Medial Axis Transform Network for 3D Object Recognition

3D deep learning performance depends on object representation and local feature extraction. In this work, we present MAT-Net, a neural network which captures local and global features from the Medial Axis Transform (MAT). Different from K-Nearest-Neighbor method which extracts local features by a fixed number of neighbors, our MAT-Net exploits effective modules Group-MAT and Edge-Net to process topological structure. Experimental results illustrate that MAT-Net demonstrates competitive or better performance on 3D shape recognition than state-of-the-art methods, and prove that MAT representation has excellent capacity in 3D deep learning, even in the case of low resolution.