Many image processing problems require the enhancement of coherent ow-like structures. This can be accomplished in a natural way by combining anisotropic diiusion ltering and texture analysis by means of the structure tensor (second-moment matrix). In this paper an extension of these ideas to vector-valued images is presented. A structure tensor for vector-valued images is constructed as the su...

This paper is the part II of a serious work about T-product tensors focusing at establishing new probability bounds for sums random, independent, tensors. These characterize large-deviation behavior extreme eigenvalue random We apply Laplace transform method and Lieb’s concavity theorem obtained from our I paper, these tools to generalize classical associated with names Chernoff, Bernstein scal...

We prove a theorem on scalar-valued functions of tensors, where ``scalar'' refers to absolute scalars as well relative weight $w$. The present work thereby generalizes an identity referred earlier by Rosenfeld in his publication ``On the energy-momentum tensor''. provides $(1,1)$-tensor which can be regarded tensor analogue following from Euler's homogeneous functions. remarkably simple is inde...

We characterize some variations of pseudoskeleton (also called CUR) decompositions for matrices and tensors over arbitrary fields. These characterizations extend previous results to fields which use generalized inverses the constituent matrices, in contrast Moore–Penrose pseudoinverses prior works are specific real or complex valued significantly more structured.

We propose a novel spectral decomposition of a 4th-order covariance tensor, S. Just as the variability of vector (i.e., a 1st-order tensor)-valued random variable is characterized by a covariance matrix (i.e., a 2nd-order tensor), S, the variability of a 2nd-order tensor-valued random variable, D, is characterized by a 4th-order covariance tensor, S. Accordingly, just as the spectral decomposit...

We show that the centraliser of the space of n-fold symmetric injective tensors, n ≥ 2, on a real Banach space is trivial. With a geometric condition on the set of extreme points of its dual, the space of integral polynomials we obtain the same result for complex Banach spaces. We give some applications of this results to centralisers of spaces of homogeneous polynomials and complex Banach spac...

The electromagnetic eld of the ultrarelativistic Reissner Nordstrrm Solution shows the physically highly unsatisfactory property of a vanishing eld tensor but a nonzero, i.e.-like, energy density. The aim of this work is to analyse this situation from a mathematical point of view, using the framework of Colombeau's theory of nonlinear generalized functions. It is shown that the physically unsat...

We propose a new extension of monogenic analysis to multi-valued signals like color images. This generalization is based on an analogy between the Riesz transform and structure tensors and takes advantage of the well defined vector differential geometry. Our color wavelet transform is non-marginal and its coefficients separated into amplitude, phase, orientation and local color axis have intere...

This work considers the problem of estimating the parameters of negative mixture models, i.e. mixture models that possibly involve negative weights. The contributions of this paper are as follows. (i) We show that every rational probability distributions on strings, a representation which occurs naturally in spectral learning, can be computed by a negative mixture of at most two probabilistic a...