With every real valued function, of a real argument, can be associated a matrix function mapping a linear space of symmetric matrices into itself. In this paper we study directional differentiability properties of such matrix functions associated with directionally differentiable real valued functions. In particular, we show that matrix valued functions inherit semismooth properties of the corr...

We introduce a certain integrability condition for the reciprocal of Jacobian determinant which guarantees local homeomorphism property quasiregular mappings with small inner dilatation. This turns out to be sharp in planar case. also show that every branch point mapping dilatation is Lebesgue differential matrix mapping.

In this paper, we present a deeper analysis of linear regression as an efficient method for face alignment. Linear regression for face alignment [2] consists of learning a mapping matrix between image features and shape parameters displacements. Typically, shape parameters are projections of a set of points which follow a Point Distribution Model onto the subspace generated by applying Principa...

According to the nonlinear characteristic of the speech signal, this paper presents a novel robust MFCC extraction method using sample-ISOMAP. ISOMAP is a nonlinear dimensionality reduction method based on the theory of manifold, it can reveal the meaningful low-dimensional structure hidden in the high-dimensional observations. In the proposed method, ISOMAP is first applied for calculating the...

This note is concerned with the following problem: For a given matrix A E C’Ix” and a vector a E C”, does there exist a mapping 2’ assigning to each manic polynomial f of degree n a vector X(f) E C” such that the matrix B := A a. X(f)’ is a companion matrix off, i.e., the characteristic polynomial of B is t l)“ftf’ The classes of suitable matrices A and vectors a are characterized, and some pro...

This paper presents a supervised learning algorithm for image deblurring. The task is addressed into the conceptual framework of matrix regression and gradient evolution. Specifically, given pairs of blurred image patches and their corresponding clear ones, an optimization framework of matrix regression is proposed to learn a matrix mapping. For an image to be deblurred, the learned matrix mapp...

In this paper, a new method for extracting primitives of a regular texture via wavelet transform is provided. Each primitive is restricted to be a parallelogram. The main work of the proposed method is to extract the two displacement vectors that form the primitive of a regular texture. A contrast-based criterion is used to select appropriate subimages obtained from wavelet transform for detect...

In this paper we study the algebraic structure of the space of compactly supported orthonormal wavelets over real numbers. Based on the parametrization of wavelet space, one can deene a parameter mapping from the wavelet space of rank 2 (or 2-band, scale factor of 2) and genus g to the (g ? 1) dimensional real torus (the products of unit circles). By the uniqueness and exactness of factorizatio...

1 This paper is dedicated to my colleague and friend Alexandru Mateescu, the first author of Parikh matrix mapping.