Abstract
This thesis investigates approaches to object recognition in computer vision. The starting point of the investigation is depth, or range, images of visible object surfaces. At the representation level, we use attributed relational graphs (ARGs), for object-centered descriptions of surfaces in images as well as models. An ARG encodes invariant properties such as curvature of surfaces, and relations such as distances and normal angles between them. At the computational level, the main problems studied concern firstly the extraction of ARG representation from range images, which involves the issues of continuity-controlled smoothing and reliable computation of surface curvature, and secondly inexact matching between the image ARG and object model ARGs. First we propose a unified computational framework for solving low, intermediate and high level computer vision problems in 3D object recognition from range images. All three levels of computation are cast in an optimisation framework and are suited for implementation on parallel distributed, or neuron-like, architectures. In the low level computation, the tasks are to estimate the curvature images from the input range data, in which depth discontinuities are taken into account to avoid oversmoothing. Subsequent processing at the intermediate level is concerned with segmenting these curvature images into coherent curvature sign maps. At the high level, image features are matched against model features based on the object-centered ARG representation. It is shown that the above computational tasks at each of the three different levels can all be formulated as optimising an energy function. The optimisation is performed using parallel and distributed relaxation-based algorithms which are well suited for neural network implementation. We then further develop the low level work by proposing a class of adaptive regularizer (AR) for continuity-controlled smoothing. We analyze mechanisms by which the AR works. The analysis shows that the fundamental difference between different regularizes lies in properties of interaction between neighboring points, which relates to the smoothing strength, determined by these regularizes. Based on this, we derive conditions under which regularizes are adaptive to discontinuities to avoid oversmoothing. The analysis also shows that adaptive regularization solutions have a closer affinity to solving Euler equations than to minimising some close-formed energy functionals. We further develop the high level work by proposing a parallel distributed approach for matching and recognizing overlapping partially occluded objects. Simultaneous separation and inexact matching of superimposed sub-ARGs is performed by optimising a global gain functional using relaxation labelling methods. We suggest that the approach could potentially perform simultaneous recognition of overlapping free-formed 3D objects directly from range data without segmentation: Segmentation, matching and recognition are all done once the direct mapping from pixels to models is found. The algorithm is inherently parallel and distributive and could be efficiently implemented on commercially available SIMD architectures such as the Connectionist Machine.