Non-central Catadioptric Cameras Research Articles

Parallel Lines for Calibration of Non-Central Conical Catadioptric Cameras

In this paper we propose a new calibration method for non-central catadioptric cameras that use a conical mirror. This method consists of using parallel lines, extracted from a single omnidirectional image, instead of using the typical checkerboard to obtain the calibration parameters of the system.

Fitting line projections in non-central catadioptric cameras with revolution symmetry

Line-images in non-central cameras contain much richer information of the original 3D line than line projections in central cameras. The projection surface of a 3D line in most catadioptric non-central cameras is a ruled surface, encapsulating the complete information of the 3D line. The resulting line-image is a curve which contains the 4 degrees of freedom of the 3D line. That means a qualitative advantage with respect to the central case, although extracting this curve is quite difficult. In this paper, we focus on the analytical description of the line-images in non-central catadioptric systems with symmetry of revolution. As a direct application we present a method for automatic line-image extraction for conical and spherical calibrated catadioptric cameras. For designing this method we have analytically solved the metric distance from point to line-image for non-central catadioptric systems. We also propose a distance we call effective baseline measuring the quality of the reconstruction of a 3D line from the minimum number of rays. This measure is used to evaluate the different random attempts of a robust scheme allowing to reduce the number of trials in the process. The proposal is tested and evaluated in simulations and with both synthetic and real images.

Catadioptric stereo-vision system using a spherical mirror

In the computer vision field, the reconstruction of target surfaces is usually achieved by using 3D optical scanners assembled integrating digital cameras and light emitters. However, these solutions are limited by the low field of view, which requires multiple acquisition from different views to reconstruct complex free-form geometries. The combination of mirrors and lenses (catadioptric systems) can be adopted to overcome this issue. In this work, a stereo catadioptric optical scanner has been developed by assembling two digital cameras, a spherical mirror and a multimedia white light projector. The adopted configuration defines a non-single viewpoint system, thus a non-central catadioptric camera model has been developed. An analytical solution to compute the projection of a scene point onto the image plane (forward projection) and vice-versa (backward projection) is presented. The proposed optical setup allows omnidirectional stereo vision thus allowing the reconstruction of target surfaces with a single acquisition. Preliminary results, obtained measuring a hollow specimen, demonstrated the effectiveness of the described approach.

Forward projection model of non-central catadioptric cameras with spherical mirrors

SUMMARYNon-central catadioptric vision is widely used in robotics and vision but suffers from the lack of an explicit closed-form forward projection model (FPM) that relates a 3D point with its 2D image. The search for the reflection point where the scene ray is projected is extremely slow and unpractical for real-time applications. Almost all methods thus rely on the assumption of a central projection model, even at the cost of an exact projection.Two recent methods are able to solve this FPM, presenting a quasi-closed form FPM. However, in the special case of spherical mirrors, further enhancements can be made. We compare these two methods for the computation of the FPM and discuss both approaches in terms of practicality and performance. We also derive new expressions for the FPM on spherical mirrors (extremely useful to robotics and graphics) which speed up its computation.

A Framework for Augmented Reality using Non-Central Catadioptric Cameras

This paper addresses the problem of augmented reality on images acquired from non-central catadioptric systems. We propose a solution which allows the projection of textured objects to images of these type of systems and, depending on the complexity of the objects, can run up to 20 fps, using a 1328?1048 image resolution. The main contributions are related with the image formation of the non-central catadioptric cameras: projection of the 3D segments onto the image of non-central catadioptric cameras; occlusions; and illumination/shading. To validate the proposed solution, we used a non-central catadioptric camera formed with a perspective camera and a spherical mirror. Also, to test the robustness of the proposed method, we used a regular object (a parallelepiped) and three well known irregular objects in computer graphics: "bunny", "happy buddha" and "dragon", from Stanford database.

Self-calibration for a non-central catadioptric camera with approximate epipolar geometry

In spite of wide usage of catadioptric cameras, self-calibration for a non-central catadioptric camera remains very challenging work. In this paper, a novel self-calibration method for a non-central catadioptric camera is proposed. First, an approximate central projection is introduced. With a freely movable virtual viewpoint, the approximate central projection is able to compensate well the bias caused by the misalignment. Then a derived approximate epipolar geometry (AEG) for the non-central camera under the two-view case is given. Based on the AEG, a full self-calibration method using only two images is designed. Combined with an automatic initialization algorithm, the non-central catadioptric camera can be calibrated robustly without any manual intervention. Experiments on both synthetic data and real images verify the effectiveness of the proposed method.

Visual servoing of mobile robots using non-central catadioptric cameras

This paper presents novel contributions on image-based control of a mobile robot using a general catadioptric camera model. A catadioptric camera is usually made up by a combination of a conventional camera and a curved mirror resulting in an omnidirectional sensor capable of providing 360° panoramic views of a scene. Modeling such cameras has been the subject of significant research interest in the computer vision community leading to a deeper understanding of the image properties and also to different models for different types of configurations. Visual servoing applications using catadioptric cameras have essentially been using central cameras and the corresponding unified projection model. So far only in a few cases more general models have been used. In this paper we address the problem of visual servoing using the so-called radial model. The radial model can be applied to many camera configurations and in particular to non-central catadioptric systems with mirrors that are symmetric around an axis coinciding with the optical axis. In this case, we show that the radial model can be used with a non-central catadioptric camera to allow effective image-based visual servoing (IBVS) of a mobile robot. Using this model, which is valid for a large set of catadioptric cameras (central or non-central), new visual features are proposed to control the degrees of freedom of a mobile robot moving on a plane. In addition to several simulation results, a set of experiments was carried out on Robot Operating System (ROS)-based platform which validates the applicability, effectiveness and robustness of the proposed method for image-based control of a non-holonomic robot.

Noncentral catadioptric camera calibration using a generalized unified model

This Letter proposes a generalized unified model (GUM) for the calibration of noncentral catadioptric cameras. Releasing the constraint on the projection center and the orientation of the imaging plane that the traditional unified projection model has, the new model is able to well compensate the misalignment between the mirror and the camera. Being a compact and approximate central model, the GUM inherits the flexibility and simplicity from the unified model while maintaining accuracy even under severe misalignment. The calibration algorithm to compute the describing parameters of the model is also given. With the GUM, the calibration of central or noncentral systems could be treated with equal simplicity (or complexity). Experiments on both synthetic data and real images proved our success.

The Camera Itself as a Calibration Pattern: A Novel Self-Calibration Method for Non-Central Catadioptric Cameras

A novel and practical self-calibration method for misaligned non-central catadioptric cameras is proposed in this paper. Without the aid of any special calibration patterns in the scene, the developed method is able to automatically estimate the pose parameters of the mirror with respect to the perspective camera. First it uses the ellipse corresponding to the mirror boundary in the image to compute the possible solutions for mirror postures. With two pose candidates, thereafter we propose a novel selection method to find the correct solution by using the image of the lens boundary. The whole calibration process is automatic and convenient to carry out since nothing more than a single image acquired from the catadioptric camera is needed. Experimental results both on synthesized and real images prove our success.

Line Localization from Single Catadioptric Images

Indoor environments often contain several line segments. The 3D reconstruction of such environments can thus be reduced to the localization of lines in the 3D space. Multi-view reconstruction requires the solution of the correspondence problem. The use of a single image to localize space lines is attractive, since the correspondence problem can be avoided. However, using a central camera the line localization from single image is an ill-posed problem, because there are infinitely many lines sharing the same image.In this work we relaxed the constraint on single viewpoint imaging and considered a wide class of non-central catadioptric cameras, constituted by an axial symmetric mirror and a perspective camera placed at a generic relative position. In the paper we report the results of our study on line localization for such cameras, reporting the conditions that allow a line to be localized from a single image. We show how the analysis can be extended to other classes of non-central devices sharing a similar imaging model. We also present a brief overview of the main algorithms for line localization from single image that have been proposed.

Calibration of Cameras with Radially Symmetric Distortion

We present algorithms for plane-based calibration of general radially distorted cameras. By this, we understand cameras that have a distortion center and an optical axis such that the projection rays of pixels lying on a circle centered on the distortion center form a right viewing cone centered on the optical axis. The camera is said to have a single viewpoint (SVP) if all such viewing cones have the same apex (the optical center); otherwise, we speak of NSVP cases. This model encompasses the classical radial distortion model [5], fisheyes, and most central or noncentral catadioptric cameras. Calibration consists in the estimation of the distortion center, the opening angles of all viewing cones, and their optical centers. We present two approaches of computing a full calibration from dense correspondences of a single or multiple planes with known euclidean structure. The first one is based on a geometric constraint linking viewing cones and their intersections with the calibration plane (conic sections). The second approach is a homography-based method. Experiments using simulated and a broad variety of real cameras show great stability. Furthermore, we provide a comparison with Hartley-Kang's algorithm [12], which, however, cannot handle such a broad variety of camera configurations, showing similar performance.