Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations

[EN] The purpose of this paper is to present a fixed point theorem for generalized contractions in partially ordered complete metric spaces. We also present an application to first-order ordinary differential equations.

3-D geometry reconstruction using a color image stereo pair and partial differential equations

[EN] In this work, we present a new model for a dense disparity estimation and the 3-D geometry reconstruction using a color image stereo pair. First, we present a brief introduction to the 3-D Geometry of a camera system. Next, we propose a new model for the disparity estimation based on an energy functional. We look for the local minima of the energy using the associate Euler-Langrage partial differential equations. This model is a generalization to color image of the model developed in, with some changes in the strategy to avoid the irrelevant local minima. We present some numerical experiences of 3-D reconstruction, using this method some real stereo pairs.

Existence and uniqueness of positive and nondecreasing solutions for a class of singular fractional boundary value problems

[EN] We establish the existence and uniqueness of a positive and nondecreasing solution to a singular boundary value problem of a class of nonlinear fractional differential equation. Our analysis relies on a fixed point theorem in partially ordered sets.

A variational approach to camera motion smoothing

[EN] In this paper we study a variational problem derived from a computer vision application: video camera calibration with smoothing constraint. By video camera calibration we meanto estimate the location, orientation and lens zoom-setting of the camera for each video frame taking into account image visible features. To simplify the problem we assume that the camera is mounted on a tripod, in such case, for each frame captured at time t , the calibration is provided by 3 parameters : (1) P(t) (PAN) which represents the tripod vertical axis rotation, (2) T(t) (TILT) which represents the tripod horizontal axis rotation and (3) Z(t) (CAMERA ZOOM) the camera lens zoom setting. The calibration function t -> u(t) = (P(t),T(t),Z(t)) is obtained as the minima of an energy function I[u] . In thIs paper we study the existence of minima of such energy function as well as the solutions of the associated Euler-Lagrange equations.