This video presents an application of geodesic computation on 3D meshes to surface remeshing. The farthest point paradigm [1] is a powerful greedy algorithm that allows fast and accurate sampling of the underlying surface. The use of a varying speed function for front propagation enables an adaptive placement of the seed points. The connectivity of the resulting mesh is computed using a geodesi...

In order to identify maize purity rapidly and efficiently, the image processing technology and clustering algorithm were studied and explored in depth focused on the maize seed and characteristics of the seed images. An improved DBSCAN on the basis of farthest first traversal algorithm (FFT) adapting to maize seeds purity identification was proposed in the paper. The color features parameters o...

We present linear-time algorithms to construct tree-structured Voronoi diagrams, after the sequence of their regions at infinity or along a given boundary is known. We focus on Voronoi diagrams of line segments, including the farthest-segment Voronoi diagram, the order-(k+1) subdivision within a given order-k Voronoi region, and deleting a segment from a nearest-neighbor diagram. Although tree-...

Shape deformations preserving the intrinsic properties of a surface are called isometries. An isometry deforms a surface without tearing or stretching it, and preserves geodesic distances. We present a technique for matching point set surfaces, which is invariant with respect to isometries. A set of reference points, evenly distributed on the point set surface, is sampled by farthest point samp...

We present a simple, first-order approximation algorithm for the support vector classification problem. Given a pair of linearly separable data sets and ∈ (0, 1), the proposed algorithm computes a separating hyperplane whose margin is within a factor of (1 − ) of that of the maximum-margin separating hyperplane. We discuss how our algorithm can be extended to nonlinearly separable and inseparab...

We present linear-time algorithms to construct tree-like Voronoi diagrams with disconnected regions after the sequence of their faces along an enclosing boundary (or at infinity) is known. We focus on the farthest-segment Voronoi diagram, however, our techniques are also applicable to constructing the order-(k+1) subdivision within an order-k Voronoi region of segments and updating a nearest-ne...

For any two points in a simple polygon P , the geodesic distance between them is the length of the shortest path contained in P that connects them. A geodesic center of a set S of sites (points) with respect to P is a point in P that minimizes the geodesic distance to its farthest site. In many realistic facility location problems, however, the facilities are constrained to lie in feasible regi...

The traditional K-means clustering algorithm is difficult to initialize the number of clusters K, and the initial cluster centers are selected randomly, this makes the clustering results very unstable. Meanwhile, algorithms are susceptible to noise points. To solve the problems, the traditional K-means algorithm is improved. The improved method is divided into the same grid in space, according ...

Pareto-optimal objects are favored as each of such objects has at least one competitive edge against all other objects, or “not dominated.” Recently, in the database literature, skyline queries have gained attention as an effective way to identify such pareto-optimal objects. In particular, this paper studies the pareto-optimal objects in perspective of facility or business locations. More spec...

The farthest line segment Voronoi diagram shows properties different from both the closest-segment Voronoi diagram and the farthest-point Voronoi diagram. Surprisingly, this structure did not receive attention in the computational geometry literature. We analyze its combinatorial and topological properties and outline an O(n log n) time construction algorithm that is easy to implement. No restr...