The panel on the left shows three photographs of a woman who developed a condition known as acromegaly. The first picture is shown when she is young and symptom-free. The second and third photos show the progress of the disease over time. This condition results from an excess of growth hormone, and causes disfiguring growth of the bones of the skull and swelling of the face, hands, and feet. Our goal in this project is to detect acromegaly automatically from generic photographs so that it can be diagnosed earlier, leading to better clinical outcomes. In collaboration with Volker Blanz and others, we have developed a classification system which prescreens patients for acromegaly. This project was originally conceived by my father, Dr. Ralph E. Miller, who practices endocrinology in Lexington, Kentucky. Qifeng (Luke) Lu at UMass has been a major contributor as well. The goal of magnetic resonance (MR) imaging is to form images of patient anatomy for diagnosis and other analyses. Often these images exhibit brightness distortions due to imperfections in the measurement apparatus. The goal of this work is to eliminate these imperfections from MR images. Previous approaches have been model-based (Wells) or have operated on a single image to reduce brightness entropies (Viola). Our method reduces entropies ACROSS images, using information about the distribution of brightness values at a particular location. Near uniform partitions are a technique for dividing a probability space, using only a set of random samples from that space, into chunks of approximately equal probability measure, or into chunks whose probability measure is approximately linear in the number of constituent subregions. The figure at left shows how samples from a two-dimensional Gaussian distribution can be used to split the Gaussian up into chunks whose probability masses are approximately linear in the number of subregions. Notice that regions in area of high density are smaller, and regions in area of low density are larger, resulting in a near uniform mass for each region. Near uniform partitions can be used in estimation of information theoretic quantities such as entropy, mutual information, and Kullback-Leibler divergence. They can also be used in hypothesis testing. For a discussion of their use in entropy estimation, see this short ICASSP paper. Christophe Chefd'hotel and I developed kernels for these curved spaces, allowing us to obtain better probability density estimates for these 'shape' spaces. This work is described in a CVPR paper here. The figure at right shows conceptually that a direct 'Euclidean distance' between points is not always appropriate in a curved space. Most non-parametric probability density estimators, which estimate a probability density from a set of sample points, are used in Euclidean spaces with standard Euclidean probability densities like the multidimensional Gaussian distribution. Certain spaces, however, like the set of linear image deformations (represented by 2x2 matrices) are more naturally described by a curved space. Hence, modeling densities on such spaces using mixtures of Gaussian distributions is not appropriate. Check out my Master's Thesis if you're a fan of stochastic geometry. It addresses the advantages and disadvantages of using various voxel shapes (other than the standard rectangular prisms) to tessellate 3-D space. Source.

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