Multiple View Geometry And 3D Reconstruction From Uncalibrated Images

One of the challenging problems of Computer Vision is to reconstruct a three-dimensional model of the scene from a single moving camera, with unconstrained motion and unknown constant parameters. Possible applications include: navigation of autonomous vehicles, object recognition, reverses engineering and IBMR (Image-Based Modeling and Rendering). The techniques for Euclidean reconstruction from multiple images of the same scene is studied profoundly and broadly in this thesis.Multiple view geometry focuses on the geometric interpretation of the different image relationships, but also presents a concise mathematical formalism that allows to derive the algebraic expressions explicitly in an elementary and uniform manner. The epipolar geometry is the intrinsic projective geometry between two views of a static scene. It is independent of scene structure, and only depends on the camera's internal parameters and relative pose. The fundamental matrix encapsulates the whole epipolar geometry and accurate and robust estimation of the fundamental matrix is very important in many applications such as scene modeling and camera self-calibration. The trifocal tensor plays an analogous role in three views to that played by the fundamental matrix in two. The tensor only depends on the motion between views and the internal parameters of the cameras and is defined uniquely by the camera matrices of the views.First, A random sampling algorithm for fundamental matrix robust estimation is examined, and is used to solve the displacement between real time and reference image in scene matching. The main geometric and algebraic properties of the trifocal tensor are introduced.The problem of camera self-calibration has attracted the attention of researchers in the computer vision community for providing a powerful method for the recovery of 3D models from a sequence of uncalibrated images. This thesis develops a self-calibration algorithm that use fundamental matrices and the Nelder-Mead Simplex Method to estimating the parameters: one based on properties of the essential matrix, and the second based on Kruppa's equations. Thus, constraints on the essential matrix and Kruppa's equations can be translated into constraints on the intrinsic parameters of camera. In both cases, the problem can be formulated as the minimization of a cost function related to the constraints.Next, 3D reconstruction from the uncalibrated two-views and single-view is addressed. The reconstruction methods employ geometric constraints available from geometric relationships that are plentiful in manmade structure-such as parallelism and orthogonality of lines and planes, these constraints lead to simple method to calibrate the intrinsic parameters of the camera.The single-view 3D reconstruction method has two components to the reconstruction process. First stage, the camera calibration and metric structure of each plane is computed, that is to calibrate a square pixel camera from three vanishing points of orthogonal directions and metric rectify each plane by computing the imaged circular points and the vanishing line. The second stage involves stitching the individually rectified planes together, accounting for the arbitrary scale factors in the rectification of each plane and the relative orientation of planes not known to be orthogonal.The two-views reconstruction process has two stages: the first to recover the camera positions and motions, the second step involves triangulation to recover the 3D points.Finally, An optimized factorization method for recovering both the 3D geometry of a scene and the camera parameters from multiple uncalibrated images is presented. In a first step, a projective approximation is recovered using a iterative approach. Then, be able to upgrade from projective to euclidean structure by estimating the absolute quadric.