(IJACSA) International Journal of Advanced Computer Science and Applications, Vol. 7, No. 9, 2016 Camera Self-Calibration with Varying Intrinsic Parameters by an Unknown Three-Dimensional Scene B. SATOURI LIIAN, Department of Mathematics and informatics Faculty of Sciences Dhar-Mahraz P.O.Box 1796 Atlas- Fes, Morocco A. EL ABDERRAHMANI LIIAN, Department of Mathematics and informatics Larache Poly disciplinary School, LARACHE, Morocco H. TAIRI LIIAN, Department of Mathematics and informaticsFaculty of Sciences Dhar-Mahraz P.O.Box 1796 Atlas- Fes, Morocco K. SATORI LIIAN, Department of Mathematics and informatics Faculty of Sciences Dhar-Mahraz P.O.Box 1796 Atlas- Fes, Morocco Abstract—In the present paper, we will propose a new and robust method of camera self-calibration having varying intrinsic parameters from a sequence of images of an unknown 3D object. The projection of two points of the 3D scene in the image planes is used to determine the projection matrices. The present method is based on the formulation of a non linear cost function from the determination of a relationship between two points of the scene with their opposite relative to the axis of abscise and their projections in the image planes. The resolution of this function with genetic algorithm enables us to estimate the intrinsic parameters of different cameras. The important of our approach reside in the use of a single pair of images which provides fewer equations, simplifies the mathematical complexities and minimizes the execution time of the application, the use of the data of the first image only without the use of the data of the second image, the use of any camera which makes the intrinsic parameters variable not constant and the use of a 3D scene reduces the planarity constraints. The experimental results on synthetic and real data prove the performance and robustness of our approach. Keywords—Self-calibration; varying intrinsic parameters; non linear optimization; Interests points; Matching; Fundamental matrix I. INTRODUCTION Computer vision is the science of vision machines. It is a scientist discipline who is interested in building artificial systems that obtain information from images. The input data can take many forms: photographs, video footage, multiple camera images or multidimensional data medical scanner. Subdomains of computer vision are for example the Reconstruction of scenes, detection of events, object recognition, learning and image restoration. The Reconstruction of 3D scenes is a research path which became very important and active with the advent of visualization by computer. As a matter of fact this technique will be found in various fields almost all of them situated on the crossroads of IT(data processing), mathematics and some of robotics related disciplines. The major objectif is always to extract information on the three-dimensional scene from a set of images gathered by numerical cameras with or without a priori knowledge of the scene. Therefore it will become clear and necessary to begin by modeling the camera. The parameters of the cameras can be estimated by two major methods: calibration [1, 2, 3, 4] and self-calibration. In this paper, we are interested in the self-calibration methods that can calibrate the cameras without any prior knowledge about the scene. The standard process of most of these methods is to search for equations according to intrinsic parameters and the invariants in the images, whose aim generally is to solve a nonlinear equation system. The algorithm used to solve this system requires two steps, initialization and optimization of a cost function. Self-calibration of the cameras is the main step to obtain three-dimensional coordinates of points from matches between pairs of images. Several methods of camera self-calibration with constant intrinsic parameters [5–14] and those with varying intrinsic parameters [15–25] are treated in this area. Our approach is a new and robust method for camera self- calibration having the varying intrinsic parameters by the use of an unknown three-dimensional scene. After the detection of interests points in the images by the Harris method [26] and the matching of these points in each pair of images by the correlation measure ZNCC [27], the fundamental matrix can be estimated from eight matches by the RANSAC algorithm [28]. This matrix is used with the projection of four points of the 3D scene in images taken by different views in order to formulate linear equations. Solving these equations allows the estimation of the projection matrices. The determination of a relationship between the four points of the 3D scene and their projections in the planes of the images g and d and the relationships between the images of the absolute conic allow the formulation of a nonlinear cost function. The minimization of this function by the genetic algorithms [29]allows the estimation of the intrinsic parameters of the cameras used. Our method presents a novelty: two images only are sufficient to estimate the cameras’ intrinsic parameters, the use of the data of the first image only, the use of any camera (with varying intrinsic parameters) and the use of an unknown 3D scene. These advantages allow us, on the one hand, to solve some problems related to the self-calibration system and, on the other hand, to work freely in the domain of self- calibration with fewer constraints. 77 | Page www.ijacsa.thesai.org