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Skin cancer is one of the most common cancers in the United States. Astechnological advancements are made, algorithmic diagnosis of skin lesions isbecoming more important. In this paper, we develop algorithms for segmentingthe actual diseased area of skin in a given image of a skin lesion, and forclassifying different types of skin lesions pictured in a given image. Thecores of the algorithms used were based in persistent homology, an algebraictopology technique that is part of the rising field of Topological DataAnalysis (TDA). The segmentation algorithm utilizes a similar concept topersistent homology that captures the robustness of segmented regions. Forclassification, we design two families of topological features from persistencediagrams---which we refer to as {\em persistence statistics} (PS) and {\empersistence curves} (PC), and use linear support vector machine as classifiers.We also combined those topological features, PS and PC, into ResNet-101 model,which we call {\em TopoResNet-101}, the results show that PS and PC areeffective in two folds---improving classification performances and stabilizingthe training process. Although convolutional features are the most importantlearning targets in CNN models, global information of images may be lost in thetraining process. Because topological features were extracted globally, ourresults show that the global property of topological features provideadditional information to machine learning models.

TopoResNet: A hybrid deep learning architecture and its application to skin lesion classification