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Abstract:
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Histology images from biopsied tissue are frequently used to diagnose breast cancer. Currently, trained pathologists examine images of tissue samples, using criteria such as cell organization for diagnosis. However, it is generally understood that a pathologist's diagnosis is just an opinion, and as such, is prone to error, resulting in a commonly accepted belief that consistent digital methods are needed to assist pathologists. Algorithm-based classification of cancer from histology images is an active area of research. One new area of statistical analysis that may prove effective in analyzing these images is the field of Topological Data Analysis. This approach uses ideas from algebraic topology to quantify the key topological shape characteristics that exist in data. Topological Data Analysis is a natural fit for this type of analysis since it naturally quantifies the cycles of cellular arrangements often exhibited in these images. We apply topological methods to study topological features present in histology images. In addition, we explore the ability of methods in Topological Data to distinguish between images of different subtypes of breast cancer.
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