Rudi Penne

Configurations of few lines in 3-space: isotopy, chirality and planar layouts

We give a characterization of the planar layouts of configurations with at most five lines. From this we obtain a new proof of Viros theorem that the isotopy type of such configurations is completely determined by chirality. We extend this result to labelled configurations. We also give an infinite family of non-realizable line diagrams, called ‘alternatingC-angles’, not containing non-realizable subdiagrams.

Moves on pseudoline diagrams

Pseudoline diagrams are simple arrangements of pseudolines in the affine plane where at each vertex one indicates which pseudolinecrosses overthe other. They naturally appear as projections of configurations of lines in 3-space. Motivated by isotopies of these spatial configurations, we define an equivalence for diagrams, generated by two types of moves. We encode diagrams by words and consider the associated word problem. Furthermore, in this combinational framework we obtain two new results on thechiralityof triples of lines, which are useful in the study of isotopies of line configurations in 3-space.

Efficient RGB-D data processing for feature-based self-localization of mobile robots

Abstract The problem of position and orientation estimation for an active vision sensor that moves with respect to the full six degrees of freedom is considered. The proposed approach is based on point features extracted from RGB-D data. This work focuses on efficient point feature extraction algorithms and on methods for the management of a set of features in a single RGB-D data frame. While the fast, RGB-D-based visual odometry system described in this paper builds upon our previous results as to the general architecture, the important novel elements introduced here are aimed at improving the precision and robustness of the motion estimate computed from the matching point features of two RGB-D frames. Moreover, we demonstrate that the visual odometry system can serve as the front-end for a pose-based simultaneous localization and mapping solution. The proposed solutions are tested on publicly available data sets to ensure that the results are scientifically verifiable. The experimental results demonstrate gains due to the improved feature extraction and management mechanisms, whereas the performance of the whole navigation system compares favorably to results known from the literature.

Mobile Camera Localization Using Apollonius Circles and Virtual Landmarks

We investigate the localization of a camera subject to a planar motion with horizontal optical axis in the presence of known vertical landmarks. Under these assumptions, a calibrated camera can measure the distance to the viewed landmarks. We propose to replace the trilateration method by intersecting a pair of Chasles-Apollonius circles. In the case of square pixels but unknown focal length we introduce a new method to recover the camera position from one image with three vertical landmarks. To this end we consider virtual landmarks and Apollonius-like circles. We extend this method in order to deal with an unknown principal point by using four landmarks.

Mirror symmetry in perspective

We assume the presence of mirror symmetry in the viewed scene. In this scene we consider planar point sets and their mirror reflections. We observe the existence of a homology that maps the image of such a planar point set to the image of its mirror reflection. We show how to compute the vertex and the axis of this homology. Finally, the homology is used to reduce image noise by “symmetrization”.

An Incremental Procedure for the Lateral Calibration of a Time-of-Flight Camera by One Image of a Flat Surface

We present a simple and accurate procedure to calibrate the pinhole parameters of a Time-of-Flight camera: the principal point

Yang-Baxter invariants for line configurations

c=(u_0, v_0)

Fast Ground Detection for Range Cameras on Road Surfaces Using a Three-Step Segmentation

c=(u0,v0), the focal length