Conventional video cameras have limited fields of view which make them restrictive for certain applications in computational vision. A catadioptric sensor uses a combination of lenses and mirrors placed in a carefully arranged configuration to capture a much wider field of view. One important design goal for catadioptric sensors is choosing the shapes of the mirrors in a way that ensures that the complete catadioptric system has a single effective viewpoint. The reason a single viewpoint is so desirable is that it is a requirement for the generation of pure perspective images from the sensed images. In this paper, we derive the complete class of single-lens single-mirror catadioptric sensors that have a single viewpoint. We describe all of the solutions in detail, including the degenerate ones, with reference to many of the catadioptric systems that have been proposed in the literature. In addition, we derive a simple expression for the spatial resolution of a catadioptric sensor in te...

This paper proposes a method for the visual-based navigation of a mobile robot in indoor environments, using a single omni-directional (catadioptric) camera. The geometry of the catadioptric sensor and the method used to obtain a bird's eye (orthographic) view of the ground plane are presented. This representation significantly simplifies the so to navigation protiok by eliminating any perspective effects. The nature of each navigation task is taken into account when designing the required navigation skills and environmental representation. We propose two main navigation mo dalities: Topological Navigation and Visual Path Following. To po lok Navigatio is used fo traveling lo distances and do es no require knowledge of the exact position of the robot but rather, a qualitative position of the took map. The navigation process combines appearance based methods and visual servorv up oso environmental features. Visual Path Following is required for local, very precise navigation fo e.g.do o traversal,do cking. The robot is contro to fo w a pre-specified p...

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Catadioptric sensors are devices which utilize mirrors and lenses to form a projection onto the image plane of a camera. Central catadioptric sensors are the class of these devices having a single effective viewpoint. In this paper, we propose a unifying model for the projective geometry induced by these devices and we study its properties as well as its practical implications. We show that a central catadioptric projection is equivalent to a two-step mapping via the sphere. The second step is equivalent to a stereographic projection in the case of parabolic mirrors. Conventional lens-based perspective cameras are also central catadioptric devices with a virtual planar mirror and are, thus, covered by the unifying model. We prove that for each catadioptric projection there exists a dual catadioptric projection based on the duality between points and line images (conics). It turns out that planar and parabolic mirrors build a dual catadioptric projection pair. As a practical example we describe a procedure to estimate focal length and image center from a single view of lines in arbitrary position for a parabolic catadioptric system.

. This paper presents fundamental theory and design of central panoramic cameras. Panoramic cameras combine a convex hyperbolic or parabolic mirror with a perspective camera to obtain a large field of view. We show how to design a panoramic camera with a tractable geometry and we propose a simple calibration method. We derive the image formation function for such a camera. The main contribution of the paper is the derivation of the epipolar geometry between a pair of panoramic cameras. We show that the mathematical model of a central panoramic camera can be decomposed into two central projections and therefore allows an epipolar geometry formulation. It is shown that epipolar curves are conics and their equations are derived. The theory is tested in experiments with real data. Keywords: omnidirectional vision, epipolar geometry, panoramic cameras, hyperbolic mirror, stereo, catadioptric sensors. 1 Introduction It is well known that egomotion estimation algorithms in some cases cannot ...

We describe a method for visual based robot navigation with a single omni-directional (catadioptric) camera. We show how omni-directional images can be used to generate the representations needed for two main navigation modalities: Topological Navigation and Visual Path Following. Topological Navigation relies on the robot’s qualitative global position, estimated from a set of omni-directional images obtained during a training stage (compressed using PCA). To deal with illumination changes, an eigenspace approximation to the Hausdorff measure is exploited. We present a method to transform omni-directional images to Bird’s Eye Views that correspond to scaled orthographic views of the ground plane. These images are used to locally control the orientation of the robot, through visual servoing. Visual Path Following is used to accurately control the robot along a prescribed trajectory, by using bird’s eye views to track landmarks on the ground plane. Due to the simplified geometry of these images, the robot’s pose can be estimated easily and used for accurate trajectory following. Omni-directional images facilitate landmark based navigation, since landmarks remain visible in all images, as opposed to a small field-of-view standard camera. Also, omni-directional images provide the means of having adequate representations to support both accurate or qualitative navigation. Results are described in the paper. 1.

In the past decade, a large number of robots has been built that explicitly implement biological navigation behaviours. We review these biomimetic approaches using a framework that allows for a common description of biological and technical navigation behaviour. The review shows that biomimetic systems make significant contributions to two fields of research: First, they provide a real world test of models of biological navigation behaviour; second, they make new navigation mechanisms available for technical applications, most notably in the field of indoor robot navigation. While simpler insect navigation behaviours have been implemented quite successfully, the more complicated way-finding capabilities of vertebrates still pose a challenge to current systems. ©2000 Elsevier Science B.V. All rights reserved.

Conventional vision systems and algorithms assume the camera to have a single viewpoint. However, sensors need not always maintain a single viewpoint. For instance, an incorrectly aligned system could cause non-single viewpoints. Also, systems could be designed to specifically deviate from a single viewpoint to trade-off image characteristics such as resolution and field of view. In these cases, the locus of viewpoints forms what is called a caustic. In this paper, we present an in-depth analysis of caustics of catadioptric cameras with conic reflectors. Properties of caustics with respect to field of view and resolution are presented. Finally, we present ways to calibrate conic catadioptric systems and estimate their caustics from known camera motion.

We present a family of reflective surfaces that will provide a wide field of view while preserving the geometry of a plane perpendicular to their axis of symmetry. Used in conjunction with a conventional imaging device, these surfaces act as computational sensors, capable of providing unwarped images automatically, eliminating the need for further processing. These surfaces arise as solutions to a differential equation that contain a function which controls the planar distortion. We demonstrate how the differential equation can be altered to accommodate different models of imaging devices with which the surfaces may be coupled. Such sensors could be potentially useful in mobile robotics, with applications such as control and range estimation. 1 Introduction Recently, many researchers in the robotics and vision community have begun to consider visual sensors that are able to obtain panoramic and omnidirectional views. 1 Such devices are the natural solution to various difficulties e...

This contribution gives the foundations of the useful panoramic cameras for stereo vision. The approach to a perspective camera-hyperbolic mirror system design is presented. The model of image formation by a central panoramic camera is defined. The analysis of epipolar geometry for panoramic cameras is the main growth of this paper. We show that the panoramic cameras with convex hyperbolic or parabolic mirrors, central panoramic cameras, allow the epipolar geometry as perspective cameras do. It is shown that the epipolar curves in central panoramic images are conics and their equation is derived. A simple adjustment procedure of a perspective camera and a hyperbolic mirror in order to form a proper central panoramic camera is proposed. This research was primarily motivated by looking for an improvement of the motion estimation from a pair of images but the results are also applicable for structure reconstruction from panoramic stereo images. The theory is demonstrated by a...