Convolutional network are the de-facto standard for analysing spatio-temporal data such as images, videos, 3D shapes, etc. Whilst some of this data is naturally dense (for instance, photos), many other data sources are inherently sparse. Examples include penstrokes forming on a piece of paper, or (colored) 3D point clouds that were obtained using a LiDAR scanner or RGB-D camera. Standard “dense...

Abstract This paper provides a convenient and practical method to compute the homology intersection pairing of branched double cover 4-ball. To projections links in 3-ball, surfaces 4-ball into boundary sphere, we associate sequence groups, called disoriented homology. We show that is isomorphic link or surface. define on first group surface this equal cover. These results generalize work Gordo...

Despite the growing growth of technology, handwritten signature has been selected as the first option between biometrics by users. In this paper, a new methodology for offline handwritten signature verification and recognition based on the Shearlet transform and transfer learning is proposed. Since, a large percentage of handwritten signatures are composed of curves and the performance of a sig...

In [Ch1], Chern gives a generalization of projective geometry by considering foliations on the Grassman bundle of p-planes Gr(p, R) → R by p-dimensional submanifolds that are integrals of the canonical contact differential system. The equivalence method yields an sl(n + 1, R)valued Cartan connection whose curvature captures the geometry of such foliation. In the flat case, the space of leaves o...

Twenty years ago it was not obvious that subspace approximations would be such a successful representation for faces and other phenomena whose measurement-space manifolds exhibit clear nonlinearities. Now PCA is ubiquitous in computer vision and, although its globally linear view of the data manifold can be a liability as systems scale up, it is not obvious that one can reliably construct a bet...

Crofton formulas on simply connected Riemannian space forms allow the volumes, or more generally Lipschitz–Killing curvature integrals of a submanifold with corners, to be computed by integrating Euler characteristic its intersection all geodesic submanifolds. We develop framework distributions replacing measures, which has in core Alesker's Radon transform valuations. then apply this framework...

We consider a sequence of quantum states, $\rho_N$, associated with submanifold $\Lambda$ product two integral compact Kahler manifolds. show that, when is submanifold, then, in the semiclassical limit, these states are not entangled. discuss whether geometry (specifically being submanifold) has any relationship entanglement properties $\rho_N$.