Study On Some Vision Geometry Problems In Multi-camera System

The research objective of computer vision is to provide the computer with theability to perceive the3D real-world environment through one or more2D images. Theresearch field of computer vision involves a large number of mathematical methods,among which the vision geometry is the basic mathematical theoretical basis for3Dcomputer vision. The studies on vision geometry have achieved abundant progress overthe past two decades. However, with the wide application of multi-camera system, thetraditional method can’t meet the demand any more. This paper aims at studying thecalibration problems in the multi-camera system in view of vision geometry and at thesame time exploring the polar geometry problems in the multi-camera system and the3D registration problem in the application of augmented reality. The main contributionsof this paper are as follows.1）Propose the calibration method of internal and external parameters based on sphereunder the constraints of rank-1. Camera calibration aims to obtain the internalparameters (which indicate the property of camera) and external parameters (whichindicate the relationship between the camera and scene position). Recently, with theoccurrence of multi-camera system, the traditional planar calibration object cannotmake the camera in different orientations simultaneously visible. So some researchersproposed calibration method based on sphere for multi-camera system. In this paper,based on the vision geometry properties of sphere, a new geometry interpretation of theconcentric relationship between the sphere image and IAC (the Image of AbsoluteConic) and another new geometry interpretation of the relationship between the sphereimage and the vanishing line are proposed. Based on the constraints of rank-1indouble-contact relationship, this paper put forward the method of solving camerainternal parameters under the constraints of rank-1as well as a simple method tocalculate camera external parameters. Besides, the constraints of rank-1is used to refinethe accuracy of solution, which further improves the calibration accuracy of externalparameters. Unlike that of the dual form of sphere image, our geometry interpretationsare established on the non-dual form of sphere image which is more direct and clear. Inaddition, the constraints of rank-1can improve the calibration accuracy of camerainternal and external parameters. 2） Propose one calibration method which replaces the traditional stick-like1Dcalibration object with the sphere. The stick-like1D calibration object usually realizesthe camera calibration through three collinear points with known position. Through theanalysis of the vision geometry property between two spheres, this paper proposed toregard the two spheres’ centers and the middle point between them as1D calibrationobject. Though the lengths of the1D calibration object are unfixed, the relative lengthsratio can be solved from the sphere projection property. Only with the images of asingle sphere at difference positions, the three collinear points can be precisely detectedand then the camera calibration can be accomplished.3）Propose one calibration method which applies sphere calibration object in thestructured light system. This paper analyzes the double-contact relationship between thesphere image and the image of the intersection circle (of the light plane and the sphere).Then, the sphere images and the intersection circle are used for solving the internalparameters and the light plane equation is established with the aids of the equation ofthe sphere. Experiments showed that this method could reach relatively highreconstruction accuracy.4）Propose one method and its geometry interpretation for solving fundamental matrixthrough6corresponding points under the constraints of four coplanar points. Thefundamental matrix indicates the polar geometry relationship of two images obtainedfrom the same3D scene. It’s widely used in camera calibration and3D reconstruction.For multi-camera system, it’s easy for the principal axes of two cameras to closelyparallel. However, the fundamental matrix solutions may not be stable. Throughanalysis, we found out that the reason for unstable fundamental matrix solutions withthe traditional method based on the polar lines and proposed a new method. In ourmethod, the projective matrix of the camera in projective space is solved by using theprojective transformations both in3D space and image plane. Then, with the help ofbifocal tensor which connects the fundamental matrix with the projective matrix, thefundamental matrix is established. This method can improve the stability and accuracyof fundamental matrix.5） Propose one camera calibration method in the augmented reality application insoccer video and3D registration method based on the nature scene feature of the fielddiagram. Generally the task of3D registration is to place the3D data into a common reference frame by estimating the transformations between the datasets. In suchaugmented reality application in soccer video,3D registration is to real-time detect therelative position and orientation of the camera with respect to a real world and thenplace a virtual3D object into the coordinate system of the real world and correctlyproject it on the image. The method in this paper takes advantage of the nature diagramof soccer field. The center circle is a conic and the center point and the vanishing line ispole-polar with respect to the center circle. As defined in the world coordinate system,the camera parameters are calibrated. Calculate the camera internal and externalparameters and obtain the camera projection matrix. In this way,3D registration ofvirtual object is projected on the image correctly. Compared with the traditionalmethods, this method based on the whole conic can improve the stability of registrationand be used in case of variable camera internal parameters.