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This thesis primarily addresses the problem of automatic measurement of ore textures by image analysis in a way that is relevant to mineral processing. Specifically, it addresses the following major hypotheses: • Automatic logging of drill core by image analysis provides a feasible alternative to manual logging by geologists. • Image analysis can quantify process mineralogy by physically meaningful parameters. • Multi-scale image analysis, over a wide range of size scales, provides potential benefits to process mineralogy that are additional to those available from small-scale analysis alone, and also better retains the information content of manual logging. • Image analysis can provide physically meaningful, ore-texture-related, additive regionalised variables that can be input to geostatistical models and the definition of domains. The central focus of the thesis is the development of an automatic, multi-scale method to identify and measure objects in an image, using a specially-developed skeleton termed the morphological CWT skeleton. This skeleton is a multi-scale extension of the morphological skeleton commonly used in image analysis, and is derived from the continuous wavelet transform (CWT). Objects take the form of hierarchical segments from image segmentation based on the CWT. Only the Mexican hat, also known as the Laplacian-of-Gaussian, wavelet is used, although other wavelet shapes are possible. The natural scale of each object is defined to be the size scale at which its CWT signal (the contrast between the interior and exterior of the object) is strongest. In addition to the natural scale, the analysis automatically records the mineral composition of both the interior and exterior of each object, and shape descriptors of the object. The measurements of natural scale, mineral composition and shape are designed to relate to: • The size to which ore must be broken in order to liberate objects. • Minerals that need to be separated by physical or chemical means once objects have been liberated. • Capability to distinguish qualitatively different ore-texture types that may have different geological origins and for which different processing regimes may provide an economic benefit. Measurements are taken over size scales from three pixels to hundreds of pixels. For the major case study the pixel size is about 50 µm, but the methodology is equally applicable to photomicrographs in which the pixel size is about 4 µm. The methodology for identifying objects in images contributes to the field of scale-space image segmentation, and has advantages in performing the following actions automatically: • Finding optimal size scales in hierarchical image segmentation (natural scale). • Merging segments that are similar and spatially close together (although not necessarily touching), using the structure of the morphological CWT skeleton, thus aiding recognition of complex structures in an image. • Defining the contrast between each segment and its surrounding segments appropriately for the size scale of the segment, in a way that extends well beyond the segment boundary. For process mineralogy this contrast quantifies mineral associations at different size scales. The notion of natural scale defined in this thesis may have applications to other fields of image processing, such as mammography and cell measurements in biological microscopy. The objects identified in images are input to cluster analysis, using a finite mixture model to group the objects into object populations according to their size, composition and shape descriptors. Each image is then characterised by the abundances of different object populations that occur in it. These abundances form additive, regionalised variables that can be input into geostatistical block models. The images are themselves input to higher-level cluster analysis based on a hidden Markov model. A collection of images is divided into different ore texture types, based on differences in the abundances of the textural object populations. The ore texture types help to define geostatistical domains in an ore body. Input images for the methodology take the form of mineral maps, in which a particular mineral has been assigned to each pixel in the image prior to analysis. A method of analysing unmapped, raw colour images of ore is also outlined, as is a new model for fracture of ore. The major case study in the thesis is an analysis of approximately 1000 metres of continuously-imaged drill core from four drill holes in the Ernest Henry iron-oxide-copper-gold ore deposit (Queensland, Australia). Thirty-one texture-related variables are used to summarise the individual half-metres of drill core, and ten major ore texture types are identified. Good agreement is obtained between locations of major changes in ore type found by automatic image analysis, and those identified from manual core logging carried out by geologists. The texture-related variables are found to explain a significant amount of the variation in comminution hardness of ore within the deposit, over and above that explained by changes in abundances of the component minerals. The thesis also contributes new algorithms with wide applicability in image processing: • A fast algorithm for computing the continuous wavelet transform of a signal or image: The new algorithm is simpler in form and several times faster than the best previously-published algorithms. It consists of a single finite impulse response (FIR) filter. • A fast algorithm for computing Euclidean geodesic distance. This algorithm runs in O(1) arithmetic operations per pixel processed, which has not been achieved by any previously published algorithm. Geodesic distance is widely used in image processing, for segmentation and shape characterisation.