3D plane-based egomotion for SLAM on semi-structured environment

Several works deal with 3D data in SLAM problem. Data come from a 3D laser sweeping unit or a stereo camera, both providing a huge amount of data. In this paper, we detail an efficient method to extract planar patches from 3D raw data. Then, we use these patches in an ICP-like method in order to address the SLAM problem. Using ICP with planes is not a trivial task. It needs some adaptation from the original ICP. Some promising results are shown for outdoor environment.

Exact and analytic-numerical solutions of lagging models of heat transfer in a semi-infinite medium

Different non-Fourier models of heat conduction have been considered in recent years, in a growing area of applications, to model microscale and ultrafast, transient, nonequilibrium responses in heat and mass transfer. In this work, using Fourier transforms, we obtain exact solutions for different lagging models of heat conduction in a semi-infinite domain, which allow the construction of analytic-numerical solutions with prescribed accuracy. Examples of numerical computations, comparing the properties of the models considered, are presented.

Real-time 3D semi-local surface patch extraction using GPGPU

Feature vectors can be anything from simple surface normals to more complex feature descriptors. Feature extraction is important to solve various computer vision problems: e.g. registration, object recognition and scene understanding. Most of these techniques cannot be computed online due to their complexity and the context where they are applied. Therefore, computing these features in real-time for many points in the scene is impossible. In this work, a hardware-based implementation of 3D feature extraction and 3D object recognition is proposed to accelerate these methods and therefore the entire pipeline of RGBD based computer vision systems where such features are typically used. The use of a GPU as a general purpose processor can achieve considerable speed-ups compared with a CPU implementation. In this work, advantageous results are obtained using the GPU to accelerate the computation of a 3D descriptor based on the calculation of 3D semi-local surface patches of partial views. This allows descriptor computation at several points of a scene in real-time. Benefits of the accelerated descriptor have been demonstrated in object recognition tasks. Source code will be made publicly available as contribution to the Open Source Point Cloud Library.

On stable uniqueness in linear semi-infinite optimization

This paper is intended to provide conditions for the stability of the strong uniqueness of the optimal solution of a given linear semi-infinite optimization (LSIO) problem, in the sense of maintaining the strong uniqueness property under sufficiently small perturbations of all the data. We consider LSIO problems such that the family of gradients of all the constraints is unbounded, extending earlier results of Nürnberger for continuous LSIO problems, and of Helbig and Todorov for LSIO problems with bounded set of gradients. To do this we characterize the absolutely (affinely) stable problems, i.e., those LSIO problems whose feasible set (its affine hull, respectively) remains constant under sufficiently small perturbations.

Robust linear semi-infinite programming duality under uncertainty

In this paper, we propose a duality theory for semi-infinite linear programming problems under uncertainty in the constraint functions, the objective function, or both, within the framework of robust optimization. We present robust duality by establishing strong duality between the robust counterpart of an uncertain semi-infinite linear program and the optimistic counterpart of its uncertain Lagrangian dual. We show that robust duality holds whenever a robust moment cone is closed and convex. We then establish that the closed-convex robust moment cone condition in the case of constraint-wise uncertainty is in fact necessary and sufficient for robust duality. In other words, the robust moment cone is closed and convex if and only if robust duality holds for every linear objective function of the program. In the case of uncertain problems with affinely parameterized data uncertainty, we establish that robust duality is easily satisfied under a Slater type constraint qualification. Consequently, we derive robust forms of the Farkas lemma for systems of uncertain semi-infinite linear inequalities.