Lie Group Motor EKF

Presenter: Eduardo Bayro-Corrochano, CINVESTAV, Campus Guadalajara, Mexico

Joint work with Rémi Megret, Guillaime Bourmaud

The aim of this work is to develop a new filtering methodfor the recursive estimation of spinors from the observation of uncertaingeometric entities. It relies on a way of representing uncertain geometricentities in a way that is compatible with their instrinsic manifold.

Geometric Entities Voting Schemes Using the Conformal Geometric Algebra Framework

Presenter: Eduardo Bayro-Corrochano, CINVESTAV, Campus Guadalajara, Mexico

Joint work with Gehová López-González, Gerardo E. Altamirano-Gómez

Traditional methods for geometric entities resort to the Hough Transform and Tensor Voting schemes for detect lines and circles. In this work, the authors extend these approaches using representations in terms of k-vectors of the conformal geometric algebra. Of interest is the detection of lines and circles in images and planes, circles, spheres in the 3D visual space for that we use the randomized Hough transform using k-blades coding such geometric entities. Motivated by Tensor Voting, we have generalized this approach for any kind of geometric entities or geometric flags formulating the perceptual saliency function involving k-vectors. The experiments using real images show the performance of the algorithms.

Geometric Perception of Pose and Tracking

Presenter: Eduardo Bayro-Corrochano, CINVESTAV, Campus Guadalajara, Mexico

Joint work with G. Osuna-González, O. Carbajal-Espinosa, A. Loukianov

Object tracking and manipulation is an important process for many application in robotics and computer vision. A novel 3D pose estimation of objects using reflectionally symmetry formulated in Conformal Geometric Algebra (CGA) is proposed in this work. The synthesis of the kinematical model for robots and a sliding mode controller using the CGA approach is described. Real time implementation results are presented for the pose estimation of object using a stereo vision system.