Abstract
This thesis treats one fundamental problem in computer vision which is image-based object reconstruction. It concentrates on the problem of improving the geometric accuracy of the reconstructed three-dimensional (3D) models. We define two principal lines of research which are: i) improving camera calibration accuracy, and ii) improving reconstruction accuracy based on Helmholtz Stereopsis (HS). Starting by improving the accuracy of camera calibration is a natural idea, because it is a preliminary stage to most reconstruction techniques. HS is a relatively recent reconstruction technique (2002), based on the principle of Helmholtz reciprocity, and which is remarkable for its ability to reconstruct a wide range of surfaces, regardless of their surface properties. In camera calibration, we present a collection of methods based on invariants, which can be used to improve calibration accuracy of the camera. Two main classes of methods are presented. The first one is based on Points at Infinity (PI), and applies to a translating camera. The second one is based on a novel entity called the Normalised Image of the Absolute Conic (NIAC). The NIAC generalises the invariance properties of the Image of the Absolute Conic (IAC), and we demonstrate its application for zooming camera calibration. In both situations, experiments with synthetic and real data showed some improvement over standard camera calibration methods which do not consider such invariance properties. In object reconstruction using HS, we present two main contributions. Firstly, we improve the intrinsic accuracy of the standard HS technique, by formulating an optimum normal reconstruction method, which gives a Maximum Likelihood (ML) estimate under standard Gaussian noise assumption. Secondly, we look at HS in a broader perspective, and observe that the standard pixel based implementation is biased in the case of rough and/or strongly textured surfaces. We propose a novel formulation, supported by recent research in the field of Physics, which does not suffer from such limitations. Results are given with a variety of objects presenting diverse surface properties and whose reconstruction with conventional reconstruction techniques is challenging. We show that HS is able to produce realistic and visually accurate 3D models.