An autonomous robot able to navigate inside an unknown environment and reconstruct full 3D scene models using monocular video has been a long term goal in the field of Machine Vision. A key component of such a system is the reconstruction of surface models from estimated scene structure. Sparse 3D measurements of real scenes are readily estimated from N-view image sequences using structure-from-motion techniques. In this thesis we present a geometric theory for reconstruction of surface models from sparse 3D data captured from N camera views. Based on this theory we introduce a general N-view algorithm for reconstruction of 3D models of arbitrary scenes from sparse data. Using a hypothesise and verify strategy this algorithm reconstructs a surface model which interpolates the sparse data and is guaranteed to be consistent with the feature visibility in the N-views. To achieve efficient reconstruction independent of the number of views a simplified incremental algorithm is developed which integrates the feature visibility independently for each view. This approach is shown to converge to an approximation of the real scene structure and have a computational cost which is linear in the number of views. Surface hypothesis are generated based on a new incremental planar constrained Delaunay triangulation algorithm. We present a statistical geometric framework to explicitly consider noise inherent in estimates of 3D scene structure from any real vision system. This approach ensures that the reconstruction is reliable in the presence of noise and missing data. Results are presented for reconstruction of both real and synthetic scenes together with an evaluation of the reconstruction performance in the presence of noise.

Attributed Relational Graph (ARG) is a powerful representation for model based object recognition due to its inherent robustness in handling noisy and incomplete data. In the past few years, the availability of efficient ARG matching algorithms and their theoretical underpinnings have greatly contributed to many successful applications of ARG representation in tackling high level vision problems. During my past three year investigation into object recognition using ARG representation, we have developed a number of novel theories and techniques in the subject area. Some are image processing techniques which help to segment and generate primitive features for building ARG representation (Chapter 2 and 4). Some are about projective invariance in ARG representations (Chapter 3 and 5). Some are about new ARG matching algorithms (Chapter 6). This thesis serves as a summary document of these theories and techniques. The most important contributions of our work to the domain of computer vision, in my opinion, are in two areas: Firstly, in the area of projective invariant ARG representation for object recognition. Here, we demonstrated for the first time, a way to systematically derive ARG representation for objects under complex projective transform by exploiting the knowledge of invariance. The methodology developed by us is a sound strategy that generates ARG representations with a number of desirable and provable properties, amongst which, the most important one is the ability to capture global transformation constraint using binary relations only. The approach significantly reduces the heuristic nature of designing relational measurements and paves the way for wider application of ARG representation in 2D and 3D object recognition. Secondly, in the area of ARG matching. A new mathematical framework for deterministic relaxation algorithms was developed to overcome a number of problems appeared in the existing theories and practises of efficient ARG labelling. A novel labelling algorithm was proposed based on the new theoretical framework. The algorithm has a number of desirable properties compared to existing algorithms. In particular, the resulting algorithm delivers more consistent, faithful-to-observation results in the presence of ambiguities and multiple interpretations compared to other algorithms.

This thesis presents the development of a set of novel graphical tools Known as 'virtual primitives' that allow the user of a stereoscopic telepresence system to actively and intuitively model features in a remote environment. The virtual primitives provide visual feedback during the model creating process in the form of a dynamic wireframe of the primitive overlaid and registered with the real object. The operator can immediately see the effect of his decisions and if necessary make minor corrections to improve the fit of the primitive during its generation. Virtual primitives are a generic augmented reality (AR) tool and their applications extend past the modelling of a workspace for telerobot operation to other remote tasks such as visual inspection, surveying and collaborative design. An AR system has been developed and integrated with the existing Surrey Telepresence System. The graphical overlays are generated using virtual reality software and combined with the video images. To achieve a one-to-one correspondence between the real and virtual worlds the AR system is calibrated using a simple pinhole camera model and standard calibration algorithm. An average RMS registration error between the video and graphical images of less than one framegrabber pixel is achieved. An assessment of a virtual pointer confirms that this level of accuracy is acceptable for use with the virtual primitives. The concept of the virtual primitives has been evaluated in an experiment to model three test objects. The results show that using a virtual primitive was superior in accuracy and task completion time to using a pointer alone. Finally, a case study on the remote inspection of sewers demonstrates the advantages of virtual primitives in a real application. It confirms that the use of virtual primitives significantly reduces the subjective nature of the task, offers an increase in precision by an order of magnitude over conventional inspection methods, and provides additional useful data on the characteristics of the sewer features not previously available.

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This thesis describes a new technique, absolute distance contouring, and a phase unwrapping algorithm for phase maps with discontinuities. Absolute distance contouring, which is based on the shadow moire method, using the rotation of a grating, is a technique which can be used for the measurement of absolute distance from the grating to the object and the determination of an object's height. By the selection of suitable rotation angles, images are captured at different positions of the grating to obtain the required data. The technique is divided into three different methods, according to the number of images required for each measurement and the rotation angles. These are known as: the absolute distance contouring method, the four-image method, and the three-image method. Using these methods, the three-dimensional shape of the object can be obtained directly and it is not necessary to determine the absolute moire fringe order nor to judge the hills and valleys of the object's surface. Some of the problems of the previous shadow moire methods can be solved and some inconvenience can be overcome by the proposed methods. The techniques have been verified by experimental work which was carried out on a specially designed system. The results show that the methods are fast and the accuracy is better than 10μm. The maximum measurable range is related to the geometry of the optical system and the rotation angles. The phase unwrapping algorithm is a technique to obtain the correct phase distribution for a phase map with discontinuities. A crossed grating, which has two sets of lines in two different directions, is projected onto the surface to be measured. The modulated grating image, which is equal to the superposition of two separate modulated images, is captured and Fourier transformed. The two images are separated in the Fourier domain. After filtering and frequency shifting, they are inverse transformed to obtain two phase maps with different precisions. Phase unwrapping at each pixel is carried out independently and the correct phase values can be obtained in the presence of discontinuities caused by a surface with steps or noise. This fast algorithm has been verified experimentally by measuring the shapes of objects with height steps, and it only requires a single image for each measurement. The methods of absolute distance contouring and the new phase unwrapping algorithm are new techniques for the measurement of three-dimensional object profile, which will find application in many areas.

Fringe projection is an optical technique for three dimensional non-contact measurement of height distributions. A fringe pattern is projected onto an object's surface and, when viewed off-axis, it deforms to follow the shape of the object. The deformed fringe pattern is analysed to obtain its phase, information that is directly related to the height distribution of the surface by a proportionality constant. This thesis analyses some key problems in fringe projection analysis. Special attention is focused on the automatisation of the process with Fourier Fringe Analysis (FFA). Unwrapping, or elimination of 21t discontinuities in a phase map, is treated in detail. Two novel unwrapping techniques are proposed, analysed and demonstrated. A new method to reduce the number of wraps in the resulting phase distribution is developed. A number of problems related to FFA are discussed, and new techniques are presented for their resolution. In particular, a technique with better noise isolation is developed and a method to analyse non-fullfield images based on function mapping is suggested. The use of parallel computation in the context of fringe analysis is considered. The parallelisation of cellular automata in distributed memory machines is discussed and analysed. A comparison between occam 2 and HPF, two compilers based upon a very different philosophy, is given. A case study with implementations in occam 2 and high performance FORTRAN (HPF) is presented. The advantages and disadvantages of each solution are critically assessed.