This thesis discusses matching of 3D surfaces, in particular, their registration in a common coordinate system. This differs from object recognition in the sense that the surfaces are generally close to registration, sometimes so close that the mismatch cannot be detected on visual inspection. The surface matching algorithm, based on least squares theory, is therefore an estimation of the matching parameters, sometimes very small, which provides the most statistically accurate registration. High redundancy is achieved with the algorithm, as each point of one surface can potentially participate in the formation of an observation equation for the least squares adjustment. The algorithm minimises the separation between the surfaces. The surfaces are defined by sets of points represented by their cartesian coordinates in 3D space, without restrictions on the mode of sampling used in the capture of the data. The registration is executed without control points. Modern non-thematic sampling methods, for instance airborne laser scanning, can benefit from such an algorithm. Other applications include processes where permanent control markers cannot be used, for example, medical applications or coastal erosion. Surface matching has been used previously by a small number of people. The particular interest of this thesis, however, has been to test the accuracy and other characteristics of the matching, especially when weighting is used with the surface separations. This thesis presents and compares several weighting techniques including one technique based on the covariance function. In addition, a statistical method to model matching accuracy as a function of the density of the control surface is formulated. The method is useful to ascertain the interpolation component of the matching error. The remaining component of the error can be deducted and analysed according to the project under consideration. Examples of project might be filtering in data fusion assessment, or volume displacement in landslide analysis. The theory is developed using artificial data. This helps to isolate and analyse in turn the various characteristics of the surface matching. The thesis is then illustrated with examples involving real data sampled in Newcastle, NSW, Australia, using methods such as ALS, photogrammetry and GPS. / PhD Doctorate

Computer vision tasks such as three dimensional (3D) registration, 3D modelling, and 3D object recognition are becoming more and more useful in industry, and have application such as reverse CAD engineering, and robot navigation. Each of these applications use correspondence algorithms as part of their processes. Correspondence algorithms are required to compute accurate mappings between artificial surfaces that represent actual objects or scenes. In industry, inaccurate correspondence is related to factors such as expenses in time and labour, and also safety. Therefore, it is essential to select an appropriate correspondence algorithm for a given surface matching task. However, current research in the area of surface correspondence is hampered by an abundance of applications specific algorithms, and no uniform terminology of consistent model for selecting and/or comparing algorithms. This dissertation presents a correspondence framework for surface matching algorithms. The framework is a conceptual model that is implementable. It is designed to assist in the analysis, comparison, development, and implementation of correspondence algorithms, which are essential tasks when selecting or creating an algorithm for a particular application. The primary contribution of the thesis is the correspondence framework presented as a conceptual model for surface matching algorithms. The model provides a systematic method for analysing, comparing, and developing algorithms. The dissertation demonstrates that by dividing correspondence computation into five stages: region definition, feature extraction, feature representation, local matching, and global matching, the task becomes smaller and more manageable. It also shows that the same stages of different algorithms are directly comparable. Furthermore, novel algorithms can be created by simply connecting compatible stages of different algorithms. Finally, new ideas can be synthesised by creating only the stages to be tested, without developing a while new correspondence algorithm. The secondary contribution that is outlined is the correspondence framework presented as a software design tool for surface matching algorithms. The framework is shown to reduce the complexity of implementing existing algorithms within the framework. This is done by encoding algorithms in a stage-wise procedure, whereby an algorithm is separated into the five stages of the framework. The software design tool is shown to validate the integrity of restructuring existing algorithms within it, and also provide an efficient basis for creating new algorithms. The third contribution that is made is the specification of a quality metric for algorithms comparison. The metric is used to assess the accuracy of the outcomes of a number of correspondence algorithms, which are used to match a wide variety of input surface pairs. The metric is used to demonstrate that each algorithm is application specific, and highlight the types of surfaces that can be matched by each algorithm. Thus, it is shown that algorithms that are implemented within the framework can be selected for particular surface correspondence tasks. The final contribution made is this dissertation is the expansion of the correspondence framework beyond the surface matching domain. The correspondence framework is maintained in its original form, and is used for image matching algorithms. Existing algorithms from three image matching applications are implemented and modified using the framework. It is shown how the framework provides a consistent means and uniform terminology for developing both surface and image matching algorithms. In summary, this thesis presents a correspondence framework for surface matching algorithms. The framework is general, encompassing a comprehensive set of algorithms, and flexible, expanding beyond surface matching to major image matching applications.