Discrete & Computational Geometry
On the Local Behavior of Spaces of Natural Images
International Journal of Computer Vision
Multidimensional Size Functions for Shape Comparison
Journal of Mathematical Imaging and Vision
The Theory of Multidimensional Persistence
Discrete & Computational Geometry - 23rd Annual Symposium on Computational Geometry
A barcode shape descriptor for curve point cloud data
Computers and Graphics
On the Nonlinear Statistics of Range Image Patches
SIAM Journal on Imaging Sciences
Size functions for the morphological analysis of melanocytic lesions
Journal of Biomedical Imaging - Special issue on mathematical methods for images and surfaces
LIBSVM: A library for support vector machines
ACM Transactions on Intelligent Systems and Technology (TIST)
HISB '11 Proceedings of the 2011 IEEE First International Conference on Healthcare Informatics, Imaging and Systems Biology
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In this paper we present a methodology of classifying hepatic (liver) lesions using multidimensional persistent homology, the matching metric (also called the bottleneck distance), and a support vector machine. We present our classification results on a dataset of 132 lesions that have been outlined and annotated by radiologists. We find that topological features are useful in the classification of hepatic lesions. We also find that two-dimensional persistent homology outperforms one-dimensional persistent homology in this application.