This thesis is a study of the probabilistic relationship between objects in an image and image appearance. We give a hierarchical, probabilistic criterion for the Bayesian segmentation of photographic images. We validate the segmentation against the Berkeley Segmentation Data Set, where human subjects were asked to partition digital images into segments each representing a 'distinguished thing'. We show that there exists a strong dependency between the hierarchical segmentation criterion, based

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... on our assumptions about the visual appearance of objects, and the distribution of ground truth data. That is, if two pixels have similar visual properties then they will often have the same ground truth state. Segmentation accuracy is quantified by measuring the information cross-entropy between the ground truth probability distribution and an estimate obtained from the segmentation. We consider the proposed method for estimating joint ground truth probability to be an important tool for future image analysis and visualization work.