Geometrical analysis of the caustic surfaces - Application to catadioptric sensors

Omnidirectional vision makes use of optical systems that usually simplify the notion of caustic in order to preserve perpectively correct views. Caustic surfaces are in these cases degenerated and reduced to a single point. Such a property is called single view point constraint. Hence, most of the catadioptric cameras rely on the single viewpoint constraint that is hardly fullfilled since it requires highly precised components placement. There exists many works on non single viewpoint catadioptric sensors fullfilling specific resolutions. In such configurations, the computation of the caustic curve becomes essential. Existing solutions are unfortunately too specific to a class of curves and need heavy computation load. This paper presents a flexible geometric construction of the caustic curve of a 3D surface. This construction is an extension of a geometric construction designed for 2D plane curves. Tests and experimental results illustrate the possibilities of this approach.La vision omnidirectionnelle utilise des systèmes optiques pour lesquels la notion de caustique est souvent occultée par souci de simplification, afin de respecter une reconstruction perspective correcte. La surface caustique est ramenée à un cas de dégénérescence, appelé la contrainte du point focal unique. Une telle hypothèse implique un placement précis des composants la rendant difficile à satisfaire. De plus, afin d’exploiter des propriétés plus générales de résolutions, il est nécessaire d’examiner la surface caustique. Une étude de la caustique par réflexion (dite catacaustique) est abordée ici dans la mesure où les capteurs utilisés sont principalement à base de surfaces réfléchissantes. Les travaux existants sont malheureusement spécifiques à une famille de surfaces et nécessitent un prétraitement lourd en calcul. Nous proposons ici une méthode souple de construction géométrique de la caustique adaptée aux surfaces 3D, basée sur une méthode développée à l’origine pour les courbes planes 2D

Système de stéréovision panoramique

Pour obtenir une reconstruction complète de son environnement un robot mobile a besoin d'une vision globale. La vision panoramique contrairement à la vision classique répond pleinement à ce problème. Ce papier présente un aperçu général des capteurs optiques utilisés à ce jour en vision panoramique ainsi que notre solution à ce problème. Nous présentons un nouveau système de stéréovision panoramique passive basée sur la rotation de deux barrettes CCD. L'objectif est de déterminer la géométrie des scènes observées en utilisant des techniques d'appariements qui utilisent les simplifications introduites par l'architecture du système pour apparier les primitives et cela en respectant une contrainte de temps réel

Cylindrical Calibration for Hybrid Epipolar Configurations

This paper deals with the calibration of a cylindrical omnidirectional imaging system, based on a rotating 2048 pixels linear camera which provides high definition panoramas. The two-step algorithm relies on line segment projections as calibration features, which are sinusoidal curves. A cylindrical image line detection algorithm is proposed, based on the dual principle of the Hough transform. Moreover, the use of Plücker coordinates introduces some new characteristics in the calibration process. This kind of formalism allows a linearization of the cylindrical projection, which is non-linear in the usual way. Results obtained from this first step are used to evaluate one of the intrinsic parameters, the other one being determined by a linear criterion minimization in the dual space, ie the sine magnitude space.Cet article présente le calibrage d'un capteur cylindrique omnidirectionnel, qui fournit des panoramas Haute Résolution par la mise en rotation d'une caméra CCD linéaire. L'algorithme utilise les segments de droite pour primitives, dont les projections sont des composées de sinusoïdes, et est constitué de deux étapes. Un algorithme de détection et d'identification de l'image de droites est proposé, selon une méthode proche de la transformée de Hough. De plus, l'utilisation des coordonnées de Plücker permet la linéarisation de la projection cylindrique. Les résultats extraits de la première étape sont utilisés pour l'évaluation du premier paramètre intrinsèque. Le second est quant à lui déterminé par l'intermédiaire de la minimisation d'un critère linéaire dans l'espace d'accumulation

Complexity Analysis of Iterative Basis Transformations Applied to Event-Based Signals

This paper introduces an event-based methodology to perform arbitrary linear basis transformations that encompass a broad range of practically important signal transforms, such as the discrete Fourier transform (DFT) and the discrete wavelet transform (DWT). We present a complexity analysis of the proposed method, and show that the amount of required multiply-and-accumulate operations is reduced in comparison to frame-based method in natural video sequences, when the required temporal resolution is high enough. Experimental results on natural video sequences acquired by the asynchronous time-based neuromorphic image sensor (ATIS) are provided to support the feasibility of the method, and to illustrate the gain in computation resources

Peripheral vision by a real time 3D system for analysing dynamic scenes

Many applications in robotics need enhanced vision systems able to give a reliable 3D information of the focused objects in a dynamic scene context . In this paper we propose a complete system (including the conception of sensors, their disposition and th e information processing) for observing a scene in a peripheral way, this means that it will cover 360° of angle, and for evaluatin g the observed objects' distances .De nombreuses applications en robotique exigent des systèmes de vision de plus en plus performants permettant de restituer l'espace 3D observé le plus fidèlement possible et dans un contexte de scène dynamique. Dans cette contribution on propose un système complet temps réel (comprenant la conception des capteurs, leur disposition, et le traitement informatique de l'information) visant à observer une scène de façon périphérique, c'est à dire couvrant 360° d'angle, et à évaluer les distances des objets observés

Optical flow estimation using the Fisher-Rao metric

The optical flow in an event camera is estimated using measurements in the Address Event Representation (AER). Each measurement consists of a pixel address and the time at which a change in the pixel value equalled a given fixed threshold. The measurements in a small region of the pixel array and within a given window in time are approximated by a probability distribution defined on a finite set. The distributions obtained in this way form a three dimensional family parameterized by the pixel addresses and by time. Each parameter value has an associated Fisher-Rao matrix obtained from the Fisher-Rao metric for the parameterized family of distributions. The optical flow vector at a given pixel and at a given time is obtained from the eigenvector of the associated Fisher-Rao matrix with the least eigenvalue. The Fisher-Rao algorithm for estimating optical flow is tested on eight datasets, of which six have ground truth optical flow. It is shown that the Fisher-Rao algorithm performs well in comparison with two state of the art algorithms for estimating optical flow from AER measurements

A Fisher-Rao metric for paracatadioptric images of lines

In a central paracatadioptric imaging system a perspective camera takes an image of a scene reflected in a paraboloidal mirror. A 360° field of view is obtained, but the image is severely distorted. In particular, straight lines in the scene project to circles in the image. These distortions make it diffcult to detect projected lines using standard image processing algorithms. The distortions are removed using a Fisher-Rao metric which is defined on the space of projected lines in the paracatadioptric image. The space of projected lines is divided into subsets such that on each subset the Fisher-Rao metric is closely approximated by the Euclidean metric. Each subset is sampled at the vertices of a square grid and values are assigned to the sampled points using an adaptation of the trace transform. The result is a set of digital images to which standard image processing algorithms can be applied. The effectiveness of this approach to line detection is illustrated using two algorithms, both of which are based on the Sobel edge operator. The task of line detection is reduced to the task of finding isolated peaks in a Sobel image. An experimental comparison is made between these two algorithms and third algorithm taken from the literature and based on the Hough transform

Semi-Dense 3D Reconstruction with a Stereo Event Camera

Event cameras are bio-inspired sensors that offer several advantages, such as low latency, high-speed and high dynamic range, to tackle challenging scenarios in computer vision. This paper presents a solution to the problem of 3D reconstruction from data captured by a stereo event-camera rig moving in a static scene, such as in the context of stereo Simultaneous Localization and Mapping. The proposed method consists of the optimization of an energy function designed to exploit small-baseline spatio-temporal consistency of events triggered across both stereo image planes. To improve the density of the reconstruction and to reduce the uncertainty of the estimation, a probabilistic depth-fusion strategy is also developed. The resulting method has no special requirements on either the motion of the stereo event-camera rig or on prior knowledge about the scene. Experiments demonstrate our method can deal with both texture-rich scenes as well as sparse scenes, outperforming state-of-the-art stereo methods based on event data image representations.Comment: 19 pages, 8 figures, Video: https://youtu.be/Qrnpj2FD1e