Date of Award

8-2014

Level of Access

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Andre Khalil

Second Committee Member

William Halteman

Third Committee Member

Robert Franzosa

Abstract

In this thesis, we use the mathematical formalism called the metric space technique to quantitatively compare the complexity of mammogram data. The technique uses one-dimensional output functions to find differences in the morphological data inherent to the mammogram images. The tool is used to analyze 1044 mammograms with a resolution between 43.5-50 μm per pixel. Every mammogram sub-image is compared to a standard image generating standardized metric spaces. Also, the subimages are compared to the same locality in the mammogram of the opposite breast to form a ‘relative’ metric space. The distribution of the complexity values are generated. and analyzed. As an additional approach, this study stresses the importance of studying the output functions themselves on a threshold by threshold basis. From the distributions generated, we develop a probabilistic model, with the capability of classifying arbitrary mammogram sub-images. The probabilistic model is applied to whole mammograms as a means to identify regions previously identified as mass tissue by a trained radiologist.

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