Helder Araújo

Geometric properties of central catadioptric line images and their application in calibration

In central catadioptric systems lines in a scene are projected to conic curves in the image. This work studies the geometry of the central catadioptric projection of lines and its use in calibration. It is shown that the conic curves where the lines are mapped possess several projective invariant properties. From these properties, it follows that any central catadioptric system can be fully calibrated from an image of three or more lines. The image of the absolute conic, the relative pose between the camera and the mirror, and the shape of the reflective surface can be recovered using a geometric construction based on the conic loci where the lines are projected. This result is valid for any central catadioptric system and generalizes previous results for paracatadioptric sensors. Moreover, it is proven that systems with a hyperbolic/elliptical mirror can be calibrated from the image of two lines. If both the shape and the pose of the mirror are known, then two line images are enough to determine the image of the absolute conic encoding the cameras intrinsic parameters. The sensitivity to errors is evaluated and the approach is used to calibrate a real camera.

Issues on the geometry of central catadioptric image formation

An imaging system with a single effective viewpoint is called a central projection system. The conventional perspective camera is an example of a central projection system. Systems using mirrors to enhance the field of view while keeping a unique center of projection are also examples of central projection systems. Perspective image formation can be described by a linear model with well known properties. In general central catadioptric imaging, the mapping between points in the world and in the image is highly nonlinear. The paper establishes a general model for central catadioptric image formation made up of three functions: a linear function mapping the world into an oriented projective plane, a nonlinear transformation between two oriented projective planes, and a collineation in the plane. The model is used to study issues in the projection of lines. The equations and geometric properties of general catadioptric imaging of lines are derived. The application of the results in auto-calibration of central catadioptric systems and reconstruction are discussed. A method to calibrate the system using three line images is presented.

Geometric Properties of Central Catadioptric Line Images

It is highly desirable that an imaging system has a single effective viewpoint. Central catadioptric systems are imaging systems that use mirrors to enhance the field of view while keeping a unique center of projection. A general model for central catadioptric image formation has already been established. The present paper exploits this model to study the catadioptric projection of lines. The equations and geometric properties of general catadioptric line imaging are derived. We show that it is possible to determine the position of both the effective viewpoint and the absolute conic in the catadioptric image plane from the images of three lines. It is also proved that it is possible to identify the type of catadioptric system and the position of the line at infinity without further information. A methodology for central catadioptric system calibration is proposed. Reconstruction aspects are discussed. Experimental results are presented. All the results presented are original and completely new.

A Fully Projective Formulation to Improve the Accuracy of Lowe's Pose-Estimation Algorithm

Both the original version of David Lowes influential and classic algorithm for tracking known objects and a reformulation of it implemented by Ishiiet al. rely on (different) approximated imaging models. Removing their simplifying assumptions yields a fully projective solution with significantly improved accuracy and convergence, and arguably better computation-time properties.

Simulating pursuit with machines. Experiments with robots and artificial vision

This article describes one solution for the problem of pursuit of objects moving on a plane by using a mobile robot and an active vision system. The solution deals with the interaction of different control systems using visual feedback and it is accomplished by the implementation of a visual gaze holding process interacting cooperatively with the control of the trajectory of a mobile robot. These two systems are integrated to follow a moving object at constant distance and orientation with respect to the mobile robot. The orientation and the position of the active vision system running a gaze holding process give the feedback signals to the control used to pursuit the target in real-time. The paper addresses the problems of visual fixation, visual smooth pursuit, navigation using visual feedback and compensation for systems movements. The algorithms for visual processing and control are described in the article. The mechanisms of cooperation between the different control and visual algorithms are also described. The final solution is a system able to operate at approximately human walking rates as the experimental results show in the paper.

A review on egomotion by means of differential epipolar geometry applied to the movement of a mobile robot

The estimation of camera egomotion is an old problem in computer vision. Since the 1980s, manyapproaches based on both the discrete and the di#erential epipolar constraint have been proposed. The discrete case is used mainlyin self-calibrated stereoscopic systems, whereas the di#erential case deals with a single moving camera. This article surveys several methods for 3D motion estimation unifying the mathematics convention which are then adapted to the common case of a mobile robot moving on a plane. Experimental results are given on synthetic data covering more than 0.5 million estimations. These surveyed algorithms have been programmed and are available on the Internet.

A Stereovision Method for Obstacle Detection and Tracking in Non-Flat Urban Environments

Obstacle detection is an essential capability for the safe guidance of autonomous vehicles, especially in urban environments. This paper presents an efficient method to integrate spatial and temporal constraints for detecting and tracking obstacles in urban environments. In order to enhance the reliability of the obstacle detection task, we do not consider the urban roads as rigid planes, but as quasi-planes, whose normal vectors have orientation constraints. Under this flexible road model, we propose a fast, robust stereovision based obstacle detection method. A watershed transformation is employed for obstacle segmentation in dense traffic conditions, even with partial occlusions, in urban environments. Finally a UKF (Unscented Kalman filter) is applied to estimate the obstacles parameters under a nonlinear observation model. To avoid the difficulty of the computation in metric space, the whole detection process is performed in the disparity image. Various experimental results are presented, showing the advantages of this method.

Real-time active visual surveillance by integrating peripheral motion detection with foveated tracking

In this paper we describe an active binocular tracking system integrating peripheral motion detection. The system is made up of a binocular active system used to track the objects and a fixed camera providing wide angle images of the environment. The system can cope with changes in lighting conditions by adjusting aperture and focus. Binocular flow enables tracking of nonrigid objects even when partial occlusion occurs.

Iterative multi-step explicit camera calibration

Perspective camera calibration has been in the last decades a research subject for a large group of researchers and as a result several camera calibration methodologies can be found in the literature. However only a small number of those methods base their approaches on the use of monoplane calibration points. This paper describes one of those methodologies that uses monoplane calibration points to realize an explicit 3D camera calibration. To avoid the singularity obtained with the calibration equations when monoplane calibration points are used, this method computes the calibration parameters in a multi-step procedure and requires a first-guess solution for the intrinsic parameters. These parameters are updated and their accuracy increased through an iterative procedure. A stability analysis as a function of the pose of the camera is presented. Camera pose view strategies for accurate camera orientation computation can be extracted from the pose view stability analysis.

Fitting conics to paracatadioptric projections of lines

The paracatadioptric camera is one of the most popular panoramic systems currently available in the market. It provides a wide field of view by combining a parabolic shaped mirror with a camera inducing an orthographic projection. Previous work proved that the para-catadioptric projection of a line is a conic curve, and that the sensor can be fully calibrated from the image of three or more lines. Howover, the estimation of the conic curves where the lines are projected is hard to accomplish because of the partial occlusion. In general only a small arc of the conic is visible in the image, and conventional conic fitting techniques are unable to accurately estimate the curve. The present work provides methods to overcome this problem. We show that in uncalibrated paracatadioptric views a set of conic curves is a set of line projections if and only if certain properties are verified. These properties are used to constrain the search space and correctly estimate the curves. The conic fitting is solved naturally by an eigensystem whenever the camera is skewless and the aspect ratio is known. For the general situation the line projections are estimated using non-linear optimization. The set of paracatadioptric lines is used in a geometric construction to determine the camera parameters and calibrate the system. We also propose an algorithm to estimate the conic locus corresponding to a line projection in a calibrated paracatadioptric image. It is proved that the set of all line projections is a hyperplane in the space of conic curves. Since the position of the hyperplane depends only on the sensor parameters, the accuracy of the estimation can be improved by constraining the search to conics lying in this subspace. We show that the fitting problem can be solved by an eigensystem, which leads to a robust and computationally efficient method for paracatadioptric line estimation.