Jesus Bermudez-Cameo

Hypercatadioptric line images for 3D orientation and image rectification

In central catadioptric systems 3D lines are projected into conics. In this paper we present a new approach to extract conics in the raw catadioptric image, which correspond to projected straight lines in the scene. Using the internal calibration and two image points we are able to compute analytically these conics which we name hypercatadioptric line images. We obtain the error propagation from the image points to the 3D line projection in function of the calibration parameters. We also perform an exhaustive analysis on the elements that can affect the conic extraction accuracy. Besides that, we exploit the presence of parallel lines in man-made environments to compute the dominant vanishing points (VPs) in the omnidirectional image. In order to obtain the intersection of two of these conics we analyze the self-polar triangle common to this pair. With the information contained in the vanishing points we are able to obtain the 3D orientation of the catadioptric system. This method can be used either in a vertical stabilization system required by autonomous navigation or to rectify images required in applications where the vertical orientation of the catadioptric system is assumed. We use synthetic and real images to test the proposed method. We evaluate the 3D orientation accuracy with a ground truth given by a goniometer and with an inertial measurement unit (IMU). We also test our approach performing vertical and full rectifications in sequences of real images.

Automatic Line Extraction in Uncalibrated Omnidirectional Cameras with Revolution Symmetry

Revolution symmetry is a realistic assumption for modelling the majority of catadioptric and dioptric cameras. In central systems it can be described by a projection model based on radially symmetric distortion. In these systems straight lines are projected on curves called line-images. These curves have in general more than two degrees of freedom and their shape strongly depends on the particular camera configuration. Therefore, the existing line-extraction methods for this kind of omnidirectional cameras require the camera calibration by contrast with the perspective case where the calibration is not involved in the shape of the projected line-image. However, this drawback can be considered as an advantage because the shape of the line-images can be used for self-calibration. In this paper, we present a novel method to extract line-images in uncalibrated omnidirectional images which is valid for radially symmetric central systems. In this method we propose using the plumb-line constraint to find closed form solutions for different types of camera systems, dioptric or catadioptric. The inputs of the proposed method are points belonging to the line-images and their intensity gradient. The gradient information allows to reduce the number of points needed in the minimal solution improving the result and the robustness of the estimation. The scheme is used in a line-image extraction algorithm to obtain lines from uncalibrated omnidirectional images without any assumption about the scene. The algorithm is evaluated with synthetic and real images showing good performance. The results of this work have been implemented in an open source Matlab toolbox for evaluation and research purposes.

Line-Images in Cone Mirror Catadioptric Systems

The projection surface of a 3D line in a non-central camera is a ruled surface, containing 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. In this paper we investigate the properties of the line-image in conical catadioptric systems. This curve is a particular quartic that can be described by only six homogeneous parameters. We present the relation between the line-image description and the geometry of the mirror. This result reveals the coupling between the depth of the line and the distance from the camera to the mirror. If this distance is unknown the 3D information of a projected line can be recovered up to scale. Knowing this distance allows obtaining the 3D metric reconstruction. The proposed parametrization also allows to simultaneously reconstruct the 3D line and computing the aperture angle of the mirror from five projected points on the line-image. We analytically solve the metric distance from a point to a line-image and we evaluate the proposal with real images.

A unified framework for line extraction in dioptric and catadioptric cameras

Many of the omnidirectional visual systems have revolution symmetry and, consequently, they can be described by the radially symmetric distortion model. Following this projection model, straight lines are projected on curves called line-images. In this paper we present a novel unified framework to deal with these line-images directly on the image which is valid for any central system. In order to validate this framework we have developed a method to extract line-images with a 2-points RANSAC, which makes use of the camera calibration. The proposed method also gives the adjacent regions of line-images which can be used for matching purposes. The line-images extractor has been implemented and tested with simulated and real images.

Minimal Solution for Computing Pairs of Lines in Non-central Cameras

In non-central cameras, the complete geometry of a 3D line is mapped to each corresponding projection, therefore each line can be theoretically recovered from a single view. However, the solution of this problem is ill-conditioned due to the lack of effective baseline between rays. This limitation prevents from a practical implementation of the approach if lines are not close to the visual system. In this paper, we exploit additional geometric constraints to improve the results of line reconstruction from single images in non-central systems. In particular, we obtain the minimal solution for the case of a pair of intersecting orthogonal lines and for the case of a pair of parallel lines considering three rays from each line. The proposal has been evaluated with simulations and tested with real images.

Line extraction in uncalibrated central images with revolution symmetry.

In omnidirectional cameras, straight lines in the scene are projected onto curves called line-images. The shape of these curves is strongly dependent of the particular camera configuration. The great diversity of omnidirectional camera systems makes harder the line-image extraction in a general way. Therefore, it is difficult to design uncalibrated general approaches, and existing methods to extract lines in omnidirectional images require the camera calibration. In this paper, we present a novel method to extract lineimages in uncalibrated images which is valid for radially symmetric central systems. In our proposal, the distortion function is analytically solved for different types of camera systems, dioptric or catadioptric. We present the unified line-image constraints to extract the projection plane of each line and main calibration parameter of the camera from a single line-image. The use of gradient-based information allows computing both from a minimum of two image points. This scheme is used in a line-image extraction algorithm to obtain lines from uncalibrated omnidirectional images without any assumption about the scene. The algorithm is evaluated with synthetic and real images showing good performance.

Exploiting line metric reconstruction from non-central circular panoramas

Comparison among non-central systems for single-view line metric reconstruction.Non-Manhattan line metric reconstruction from single image in non-central panoramas.Automatic line-image extraction in non-central panoramas. In certain non-central imaging systems, straight lines are projected via a non-planar surface encapsulating the 4 degrees of freedom of the 3D line. Consequently the geometry of the 3D line can be recovered from a minimum of four image points. However, with classical non-central catadioptric systems there is not enough effective baseline for a practical implementation of the method. In this paper we propose a multi-camera system configuration resembling the circular panoramic model which results in a particular non-central projection allowing the stitching of a non-central panorama. From a single panorama we obtain well-conditioned 3D reconstruction of lines, which are specially interesting in texture-less scenarios. No previous information about the direction or arrangement of the lines in the scene is assumed. The proposed method is evaluated on both synthetic and real images.

RGB-D Computer Vision Techniques for Simulated Prosthetic Vision.

Recent research on visual prosthesis demonstrates the possibility of providing visual perception to people with certain blindness. Bypassing the damaged part of the visual path, electrical stimulation provokes spot percepts known as phosphenes. Due to physiological and technological limitations the information received by patients has very low resolution and reduced dynamic range. In this context, the inclusion of new computer vision techniques to improve the semantic content in this information channel is an active and open key topic. In this paper, we present a system for Simulated Prosthetic Vision based on a head-mounted display with an RGB-D camera, and two tools, one focused on human interaction and the other oriented to navigation, exploring different proposals of phosphenic representations.

Line reconstruction using prior knowledge in single non-central view

Line projections in non-central systems contain more geometric information than in central systems. The four degrees of freedom of the 3D line are mapped to the line-image and the 3D line can be theoretically recovered from 4 projecting rays (i.e. line-image points) from a single non-central view. In practice, extraction of line-images is consid- erably more difficult and the resulting reconstruction is imprecise and sensitive to noise. In this paper we present a minimal solution to recover the geometry of the 3D line from only three line-image points when the line is parallel to a given plane. A second minimal solution allows to recover the 3D line from two points when the direction of the 3D line is known. Both cases can exploit the prior knowledge of the vertical direction in man-made environments to reduce the complexity in line-image extraction and line reconstruction. The formulation based on Plucker lines is integrated in a line-extraction pipeline, which is tested with synthetic and real non-central circular panoramas. In addition, we evaluate the performance of the robust extractor and the accuracy of the proposal in comparison with the unconstrained method.

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

Abstract 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.