We introduce and study certain deformation of Minkowski norms in [Formula: see text] determined by a set linearly independent 1-forms smooth positive function variables. In particular, the Euclidean norm produces defined our recent work; its indicatrix is rotation hypersurface with text]-dimensional axis passing through origin. For text], generalizes construction text]-norms which form rich cla...

The performance of modeltting feature detectors is critically dependent upon the function used to measure the degree of t between the feature model and the image data. In this paper, we consider the class of weighted L norms as potential tting functions and study the e ect which the choice of tting function has on one particular aspect of performance, namely parameter estimation accuracy. We rs...

We propose a new technique for direct visual matching of images for the purposes of face recognition and image retrieval, using a probabilistic measure of similarity, based primarily on a Bayesian (MAP) analysis of image di!erences. The performance advantage of this probabilistic matching technique over standard Euclidean nearest-neighbor eigenface matching was demonstrated using results from D...

The notion of regularization has been widely used as a tool to address a number of problems that are usually encountered in Machine Learning. Improving the performance of an estimator by shrinking the norm of the MVU estimator, guarding against overfitting, coping with ill-conditioning, providing a solution to an underdetermined set of equations, are some notable examples where regularization h...

In previous work [6, 9, 10], we advanced a new technique for direct visual matching of images for the purposes of face recognition and image retrieval, using a probabilistic measure of similarity based primarily on a Bayesian (MAP) analysis of image di erences, leading to a \dual" basis similar to eigenfaces [13]. The performance advantage of this probabilistic matching technique over standard ...

We study the asymptotic behavior of the diameter or maximum interpoint distance of a cloud of i.i.d. d-dimensional random vectors when the number of points in the cloud tends to infinity. This is a non standard extreme value problem since the diameter is a max U -statistic, hence the maximum of dependent random variables. Therefore, the limiting distributions may not be extreme value distributi...

In previous work 6, 9, 10], we advanced a new technique for direct visual matching of images for the purposes of face recognition and image retrieval, using a probabilistic measure of similarity based primarily on a Bayesian (MAP) analysis of image diier-ences, leading to a \dual" basis similar to eigenfaces 13]. The performance advantage of this probabilistic matching technique over standard E...

In this note, we study Luenberger-type full-state observers for nonlinear systems using contraction theory. We show that if the matrix measure of a suitably defined Jacobian matrix constructed from the dynamics of the system-observer interconnection is uniformly negative, then the state estimate converges exponentially to the actual state. This sufficient condition for convergence establishes t...

A square-root-free matrix QR decomposition (QRD) scheme was rederived in [1] based on [2] to simplify computations when solving least-squares (LS) problems on embedded systems. The scheme of [1] aims at eliminating both the square-root and division operations in the QRD normalization and backward substitution steps in the LS computations. It is claimed in [1] that the LS solution only requires ...

We study the Pareto frontier for two competing norms ‖ · ‖X and ‖ · ‖Y on a vector space. For a given vector c, the Pareto frontier describes the possible values of (‖a‖X , ‖b‖Y ) for a decomposition c = a + b. The singular value decomposition of a matrix is closely related to the Pareto frontier for the spectral and nuclear norm. We will develop a general theory that extends the notion of sing...