Let P be a simple polygon of n vertices and let S be a set of N points lying in the interior of P . A geodesic disk GD(p, r) with center p and radius r is the set of points in P that have a geodesic distance ≤ r from p (where the geodesic distance is the length of the shortest polygonal path connection that lies in P ). In this paper we present an output sensitive algorithm for finding all N ge...

Hashing is a popular solution to Approximate Nearest Neighbor (ANN) problems. Many hashing schemes aim at preserving the Euclidean distance of the original data. However, it is the geodesic distance rather than the Euclidean distance that more accurately characterizes the semantic similarity of data, especially in a high dimensional space. Consequently, manifold based hashing methods have achie...

Spectral clustering is a method of subspace clustering which is suitable for the data of any shape and converges to global optimal solution. By combining concepts of shared nearest neighbors and geodesic distance with spectral clustering, a self-adaptive spectral clustering based on geodesic distance and shared nearest neighbors was proposed. Experiments show that the improved spectral clusteri...

In this paper, we present the geodesic-like algorithm for the computation of the shortest path between two objects on NURBS surfaces and periodic surfaces. This method can improve the distance problem not only on surfaces but in R. Moreover, the geodesic-like algorithm also provides an efficient approach to simulate the minimal geodesic between two holes on a NURBS surfaces.

When dealing with pattern recognition problems one encounters different types of prior knowledge. It is important to incorporate such knowledge into the classification method at hand. A common prior knowledge is that many datasets are on some kinds of manifolds. Distance-based classification methods can make use of this by a modified distance measure called geodesic distance. We introduce a new...

Isomap [4] is a manifold learning algorithm, which extends classical multidimensional scaling (MDS) by considering approximate geodesic distance instead of Euclidean distance. The approximate geodesic distance matrix can be interpreted as a kernel matrix, which implies that Isomap can be solved by a kernel eigenvalue problem. However, the geodesic distance kernel matrix is not guaranteed to be ...

Given a polygon P , for two points s and t contained in the polygon, their geodesic distance is the length of the shortest st-path within P . A geodesic disk of radius r centered at a point v ∈ P is the set of points in P whose geodesic distance to v is at most r. We present a polynomial time 2-approximation algorithm for finding a densest geodesic unit disk packing in P . Allowing arbitrary ra...

We present an algorithm for the efficient and accurate computation of geodesic distance fields on triangle meshes. We generalize the algorithm originally proposed by Surazhsky et al. [1]. While the original algorithm is able to compute geodesic distances to isolated points on the mesh only, our generalization can handle arbitrary, possibly open, polygons on the mesh to define the zero set of th...

The geodesic distance is commonly used when solving image processing problems. In noisy images, unfortunately, it often gives unsatisfactory results. In this paper, we propose a new k-max geodesic distance. The length of path is defined as the sum of the k maximum edge weights along the path. The distance is defined as the length of the path that is the shortest one in this sense. With an appro...

We study a distance between shapes defined by minimizing the integral of kinetic energy along transport paths constrained to measures with characteristic-function densities. The formal geodesic equations for this shape distance are Euler equations for incompressible, inviscid potential flow of fluid with zero pressure and surface tension on the free boundary. The minimization problem exhibits a...