Geometric surface information such as depth maps and surface normals can be acquired by various methods such as stereo light fields, shape from shading and photometric stereo techniques. We compare several algorithms which deal with the combination of depth with surface normal information in order to reconstruct a refined depth map. The reasons for performance differences are examined from the ...

Manifold learning has become a hot issue in the research fields of machine learning and data mining. Current manifold learning algorithms assume that the observed data set has the high density. But, how to evaluate the denseness of the high dimensional observed data set? This paper proposes an algorithm based on the average geodesic distance as the preprocessing step of manifold learning. Moreo...

Recent advances in 3D depth sensors have created many opportunities for security, surveillance, and entertainment. The 3D depth sensors provide more powerful monitoring systems for dangerous situations irrespective of lighting conditions in buildings or production facilities. To robustly recognize emergency actions or hazardous situations of workers at a production facility, we present human jo...

In this paper the regularity of optimal transportation potentials dened on round spheres is investigated. Speci cally, this research generalises the calculations done by Loeper, where he showed that the strong (A3) condition of Trudinger and Wang is satis ed on the round sphere, when the cost-function is the geodesic distance squared. In order to generalise Loeper's calculation to a broader cla...

In the study of neurons, morphology influences function. The complexity in the structure of neurons poses a challenge in the identification and analysis of similar and dissimilar neuronal cells. Existing methodologies carry out structural and geometrical simplifications, which substantially change the morphological statistics. Using digitally-reconstructed neurons, we extend the work of Path2Pa...

This paper explores the visualization of two-dimensional stable and unstable manifolds of the origin (a saddle point) in a four-dimensional Hamiltonian system arising from control theory. The manifolds are computed using an algorithm that finds sets of points that lie at the same geodesic distance from the origin. By coloring the manifolds according to this geodesic distance, one can gain insig...

This paper we proposes an extended geodesic distance for head pose estimation. In ISOMAP, two approaches are applied for neighborhood construction, called k-neighbor and -neighbor. For the kneighbor, the number of the neighbors is a const k. For the other one, all the distances between the neighbors is less than . Either the k-neighbor or the -neighbor neglects the difference of each point. Thi...

Shortest-path tractography (SPT) algorithms solve global optimization problems defined from local distance functions. As diffusion MRI data is inherently noisy, so are the voxelwise tensors from which local distances are derived. We extend Riemannian SPT by modeling the stochasticity of the diffusion tensor as a “random Riemannian metric”, where a geodesic is a distribution over tracts. We appr...

OBJECTS To introduce a new method for generating the clinical target volume (CTV) from gross tumor volume (GTV) using the geodesic distance calculation for glioma. METHODS One glioblastoma patient was enrolled. The GTV and natural barriers were contoured on each slice of the computer tomography (CT) simulation images. Then, a graphic processing unit based on a parallel Euclidean distance tran...

The watershed line is the basic tool for segmenting images in mathematical morphology. A rigorous definition is given in terms of a distance function called topographic distance. If the topographical function is itself a distance function, then the topographical distance becomes identical with the geodesic distance function and the watershed becomes identical with the skeleton by zone of influe...