Relating vanishing points to catadioptric camera calibration

This paper presents the analysis and derivation of the geometric relation between vanishing points and camera parameters of central catadioptric camera systems. These vanishing points correspond to the three mutually orthogonal directions of 3D real world coordinate system (i.e. X, Y and Z axes). Compared to vanishing points (VPs) in the perspective projection, the advantages of VPs under central catadioptric projection are that there are normally two vanishing points for each set of parallel lines, since lines are projected to conics in the catadioptric image plane. Also, their vanishing points are usually located inside the image frame. We show that knowledge of the VPs corresponding to XYZ axes from a single image can lead to simple derivation of both intrinsic and extrinsic parameters of the central catadioptric system. This derived novel theory is demonstrated and tested on both synthetic and real data with respect to noise sensitivity

Proyecciones cónicas de rectas en sistemas catadióptricos para percepción visual en entornos construidos por el hombre

Los sistemas de visión omnidireccional son dispositivos que permiten la adquisición de imágenes con un campo de vista de 360º en un eje y superior 180º en el otro. La necesidad de integrar estas cámaras en sistemas de visión por computador ha impulsado la investigación en este campo profundizando en los modelos matemáticos y la base teórica necesaria que permite la implementación de aplicaciones. Existen diversas tecnologías para obtener imágenes omnidireccionales. Los sistemas catadióptricos son aquellos que consiguen aumentar el campo de vista utilizando espejos. Entre estos, encontramos los sistemas hiper-catadióptricos que son aquellos que utilizan una cámara perspectiva y un espejo hiperbólico. La geometría hiperbólica del espejo garantiza que el sistema sea central. En estos sistemas adquieren una especial relevancia las rectas del espacio, en la medida en que, rectas largas son completamente visibles en única imagen. La recta es una forma geométrica abundante en entornos construidos por el hombre que además acostumbra a ordenarse según direcciones dominantes. Salvo construcciones singulares, la fuerza de la gravedad fija una dirección vertical que puede utilizarse como referencia en el cálculo de la orientación del sistema. Sin embargo el uso de rectas en sistemas catadióptricos implica la dificultad añadida de trabajar con un modelo proyectivo no lineal en el que las rectas 3d son proyectadas en cónicas. Este TFM recoge el trabajo que se presenta en el artículo "Significant Conics on Catadioptric Images for 3D Orientation and Image Rectification" que pretendemos enviar a "Robotics and Autonomous Systems". En él se presenta un método para calcular la orientación de un sistema hiper-catadióptrico utilizando las cónicas que son proyecciones de rectas 3D. El método calcula la orientación respecto del sistema de referencia absoluto definido por el conjunto de puntos de fuga en un entorno en que existan direcciones dominantes

Simultaneously calibrating catadioptric camera and detecting line features using Hough transform

Abstract- A line in space is projected to a conic in a central catadioptric image, and such a conic is called a line image. This paper proposes a novel approach to calibrating catadioptric camera and detecting line images simultaneously by using Hough transform. Previous approaches to catadioptric cameras calibration employ the traditional conic detecting or fitting methods for line images, and then use these recovered conics to estimate the intrinsic parameters based on some properties of line images. However, the type of a line image can be line, circle, ellipse, hyperbola or parabola, and in general only a small arc of the conic is visible in the image, which brings novel challenges for conic detection and fitting where traditional conic detecting and fitting methods may fail. As we know, the accuracy of the estimated intrinsic parameters highly depends on the accuracy of the extracted conics. The main contribution of this work is we show that all line images from catadioptric cameras with the same intrinsic parameters must belong to a family of conics with only two degree-of-freedom, and such a family is called a line image family. Therefore, we present a novel special Hough transform for line images detection which ensures that all detected conics must belong to a line image family related to certain intrinsic parameters. For all possible values of the unknown intrinsic parameters, the line image special Hough transform are performed. The one with the highest confidence is chosen as the estimated values for these unknown intrinsic parameters, and the corresponding results of line image detection are chosen as the estimated values for line images. In order to make the searching process more efficient, the hierarchical approaches are employed in this paper. The validity of our proposed approach is illustrated by experiments. Index Terms – Camera calibration, omnidirectional camera, Hough transform, feature extraction, line features

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