Considering the biological or artificial trajectory generation problem, we propose a biologically plausible model of the link between the (i) local "where-to-go-next" local mechanism in a locus map and the (ii) global trajectory generation problem. This explains how the well known hippocampal related areas containing place fields with local mechanisms are also very likely able to solve the global problem, providing the neural map activity is related to harmonic potentials. Such representation assume that obstacles to avoid (or constraints not to violate) correspond to maxima of a so-called potential, while the goal corresponds to its minimum. The corresponding algorithm thus behaves as if one throws a sheet onto this state space, this hyper-surface relief being elevated on obstacles, with a hole at the goal location. Finding a trajectory thus reduces to "roll down" along this relief, in the direction of the potential gradient. The originality of the present work is to build an harmonic potential (thus without local minimum) from a sparse adaptive combination of elementary place fields, as inspired by the biological modelization of the hippocampal structures. This leads to an internal representation of the problem as a non-topographical map, incrementally built during the system exploration. As such, it provides a key element for a biologically plausible model of the related hippocampus mechanisms in coherence with usual biological assumptions about such behavior.

High-level specification of how the brain represents and categorizes the causes of its sensory input allows to link "what is to be done" (perceptual task) with "how to do it" (neural network calculation). More precisely, a general class of cortical map computations can be specified representing what is to be done as an optimization problem, in order to derive the related neural network parameters considering regularization mechanisms (implemented using so-called partial-differential-equations). The present contribution revisits this framework with three add-ons. It is generalized to a larger class of (non-linear) map computations, including winner-take-all mechanisms. The capability to represent standard "analog" neural network and guaranty their convergence, providing their weights are local and unbiased, is made explicit. The fact that not only one but several cortical maps can interact, with feed-backs, in a stable way is shown. Two experiments are provided as an illustration of this general framework.

The purpose of this article is to provide potential neuroscientists and computer scientists with an artificial retina model, delivering spikes to higher-level visual tasks simulations. The architecture of our retina model is based on recent physiological studies, so that each feature is related to real retina characteristics. The model includes a linear filtering process, followed by a static non-linearity, and then a spike generation process. Two series of tests were performed: firstly on single cells for which ground truth is available, secondly on realistic visual scenes. This retina model can be further extended and we describe some possible additional features. It is our conviction that building such a bio-inspired model will help in better understanding how the retina performs and also in relating observations to biological mechanisms.

This study is aimed at developing a method for analysing 3D structure of a scene considering a monocular image sequence, with an uncalibrated camera-as for an active visual system-and using a continuous model of motion, considering that the scene is static.

In the present paper we address the problem of computing structure and motion, given a set point correspondences in a monocular image sequence, considering small motions when the camera is not calibrated. We first set the equations defining the calibration, rigid motion and scene structure. We then review the motion equation, the structure from equation and the depth evolution equation, including the particular case of planar structures, considering a discrete displacement between two frames. A step further, we develop the first order expansion of these equations and analyse the observability of the related infinitesimal quantities. It is shown that we obtain a complete correspondence between these equations and the equation derived in the discrete case. However, in the case of infinitesimal displacements, the projection of the translation (focus of expansion or epipole) is clearly separated from the rotational component of the motion. This is an important advantage of the present approach. Using this last property, we propose a mechanism of image stabilization in which the rotational disparity is iteratively canceled. This allows a better estimation of the focus of expansion, and simplifies different aspects of the analysis of the equations: structure from motion equation, analysis of ambiguity, geometrical interpretation of the motion equation.>

In this paper, we present a method to detect moving objects in a scene modelled as a set of line segments and using the measure of their 2D motion through a monocular sequence of images. These measures are supplied by a segment tracker using a Kalman filtering approach. In order to perform such a detection task, we have to determine and sort the rigid structures; we work with structures of five segments and declare that they are rigid if they verify several rigidity conditions. Using these constraints, we sort them into "classes" according to their associated 2D affine motion fields.

We attempt to build a vision system that will allow dynamic 3D-perception of objects of interest. More specifically, we discuss the idea of using 3D visual cues when tracking a visual target, in order to recover some of its 3D characteristics. The experimentation reported corresponds to an implementation of these general ideas by considering a calibrated robotic head. We analyse how to make use of such a system for: (1) detecting 3D-objects of interest, (2) recovering the average depth and size of the tracked objects, and (3) fixating and tracing such objects to facilitate their observation.

This paper proposes an algebraic method to generalize the usual equations of structure from motion, when calibration is not available. Contrary to previous approaches, the construction is made without any geometry and does not require a deep understanding of complex abstract objects. The construction being well formalized, an effective algorithm is easily derived, and experimental results are shown.

Addresses the well-known problem of estimating the motion and structure of a plane, but in the case where the visual system is not calibrated and in an unbounded monocular image sequence. The authors first define plane collineations and analyse some of their properties when utilized to analyse the retinal motion in an uncalibrated image sequence. The authors show how to relate them to the Euclidian parameters of the scene. In particular, the authors discuss how to detect and estimate the collineation of the plane at infinity and use this quantity for auto-calibration.

The authors consider the problem of recovering the relative displacements of a camera by using line matches in three views. In particular, they try to find whether there exist sets of 3-D lines such that irrespective of how many lines are observed there will always be several solutions to the relative displacement estimation problem. Recently, T. Buchanan (1992) provided a first analysis of the problem in which he gave a positive answer. Here, an attempt is made to build on his work and extend it in several directions. First, his purely projective analysis is cast in a more Euclidean framework better suited to applications. Second, his critical set is related to those of previously published algorithms. Third, the algebraic equations are introduced and an effective, i.e., computational, approach is provided for describing these critical sets in terms of simple geometric properties. This has allowed analysis of the structure of the critical sets.>

The authors develop a method of recovery of some aspects of the 3-D structure and motion of a scene in the case of a virtual moving observer with visual and odometric sensors. This observer attempts to build a 3-D depth and kinematic map of its environment, which can obtain fixed or moving objects. The development and implementation of some layers of a line-segment based module are described to recover ego-motion while building a 3-D map of the environment in which the absolute vertical is taken into account. Given a monocular sequence of images and 2-D-line-segments in this sequence, the goal is to reduce the disparity between two frames in such a way that 3-D vision is simplified, while an initial value for the 3-D rotation is provided. Using the vertical as a basic cue for 3-D-orientation tremendously simplifies and enrichs the structure from motion paradigm, but the usual equations have to be worked out in a different way.>

This paper describes the development and implementation of a reactive visual module utilized on an autonomous mobile robot to automatically correct in trajectory. The authors use a multisensorial mechanism based on inertial and visual cues. The authors report only on the implementation and the experimentation of this module, whereas the main theoretical aspects have been developed elsewhere.

A description is given of the development and implementation of a line segments based module of recovery of self-motion and 3-D structure. Given a monocular sequence of time-varying images and 2-D-lines matches in this sequence, the goal is to recover the camera motion and the 3-D-lines structure. A feedforward approach which combines prediction and correction is presented, and the equations are given and discussed in the case of small rigid motions. Algorithms, based on the minimization of the Mahalanobis distance between two estimates, are given and their implementations carefully discussed. The efficiency of the proposed approach is illustrated through experimental tests carried out considering noisy synthetic data and a real indoor scene.>