Schur functions and their realizations in the slice hyperholomorphic setting

we start the study of Schur analysis in the quaternionic setting using the theory of slice hyperholomorphic functions. The novelty of our approach is that slice hyperholomorphic functions allows to write realizations in terms of a suitable resolvent, the so called S-resolvent operator and to extend several results that hold in the complex case to the quaternionic case. We discuss reproducing kernels, positive definite functions in this setting and we show how they can be obtained in our setting using the extension operator and the slice regular product. We define Schur multipliers, and find their co-isometric realization in terms of the associated de Branges-Rovnyak space

Fast Marching Method for Generic Shape from Shading

International audienceWe develop a fast numerical method to approximate the solutions of a wide class of equations associated to the Shape From Shading problem. Our method, which is based on the control theory and the interfaces propagation, is an extension of the ?Fast Marching Method? (FMM) [30,25]. In particular our method extends the FMM to some equations for which the solution is not systematically decreasing along the optimal trajectories. We apply with success our one-pass method to the Shape From Shading equations which are involved by the most relevant and recent modelings [22,21] and which cannot be handled by the most recent extensions of the FMM [26,8]

Motion from Color

The use of color images for motion estimation is investigated in this work. Beyond the straightforward approach of using the color components as separate images of the same scene, a new method, based on exploiting color invariance under motion, is discussed. Two different sets of color-related, locally computable motion `invariants' are analyzed and tested in this paper, and the results of motion estimation based on them are compared to the direct use of the RGB brightness functions. 1 Introduction Optical or image flow estimation is considered by many researches as an important low-level stage of spatial motion recovery from a sequence of images. It is supposed to yield an estimate of the 2D projection of the velocity field on the image plane, which is submitted to further analysis aimed at inferring high-level, 3D motion descriptions. It is well known that the image flow cannot be completely determined from a single sequence of black-and-white images without introducing additional a..

Regularization of positive definite matrix fields based on multiplicative calculus

Multiplicative calculus provides a natural framework in problems involving positive images and positivity preserving operators. In increasingly important, complex imaging frameworks, such as diffusion tensor imaging, it complements standard calculus in a nontrivial way. The purpose of this article is to illustrate the basics of multiplicative calculus and its application to the regularization of positive definite matrix fields