We propose a natural Fedosov type quantization of generalized Lagrange models and gravity theories with metrics lifted on tangent bundle, or extended to higher dimension, following some stated geometric/ physical conditions (for instance, nonholonomic and/or conformal transforms to some physically important metrics or mapping into a gauge model). Such generalized Lagrange transforms define cano...

This paper presents a content-based image retrieval technique based on interest points matching and geometric hashing. We estimate points with significant luminance variations as interest points. A small region around the interest point is located as an image patch. Low-level features are extracted to describe each image patch. To provide geometric invariant image matching, we index the image p...

We study the Fourier-Mukai transform for holonomic D-modules on complex abelian varieties. Among other things, we show that the cohomology support loci of a holonomic D-module are finite unions of linear subvarieties, which go through points of finite order for objects of geometric origin; that the standard t-structure on the derived category of holonomic complexes corresponds, under the Fourie...

This paper proposes to adopt hierarchical tree construction of directional lapped orthogonal transforms (DirLOTs) to image denoising. The DirLOTs are 2-D non-separable lapped orthogonal transforms with directional characteristics. The bases are allowed to be anisotropic with the fixed-criticallysubsampling, overlapping, orthogonal, symmetric, real-valued and compact-support property. As well, i...

The present paper is concerned with the study of manifold-valued multiscale transforms with a focus on the Stiefel manifold. For this specific geometry we derive several formulas and algorithms for the computation of geometric means which will later enable us to construct multiscale transforms of wavelet type. As an application we study compression of piecewise smooth families of low-rank matri...

Curvelet transform is the new member of the evolving family of multiscale geometric transforms. It offers an effective solution to the problems associated with image denoising using wavelets. Finger prints possess the unique properties of distinctiveness and persistence. However, their image contrast is poor due to mixing of complex type of noise. In this paper an attempt has been made to prese...

In this paper, we consider a risk model with two independent classes of insurance risks and random incomes. We assume that the two independent claim counting processes are, respectively, the Poisson and the Erlang(2) process. When the individual premium sizes are exponentially distributed, the explicit expressions for the Laplace transforms of the expected discounted penalty functions are deriv...

We show that every non-trivial Sobolev bound for generalized Radon transforms which average functions over families of curves and surfaces yields an incidence theorem for suitably regular discrete sets of points and curves or surfaces in Euclidean space. This mechanism allows us to deduce geometric results not readily accessible by combinatorial methods.