Abstract
Taking images is an efficient way to collect data about the physical world. It can be done fast and in exquisite detail. By definition, image processing is the field that concerns itself with the computation aimed at harnessing the information contained in images [10]. This talk is concerned with topological information. Our main thesis is that persistent homology [5] is a useful method to quantify and summarize topological information, building a bridge that connects algebraic topology with applications. We provide supporting evidence for this thesis by touching upon four technical developments in the overlap between persistent homology and image processing.
This research is partially supported by the European Science Foundation (ESF) under the Research Network Programme, the European Union under the Toposys Project FP7-ICT-318493-STREP, the Russian Government under the Mega Project 11.G34.31.0053.
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Edelsbrunner, H. (2013). Persistent Homology in Image Processing. In: Kropatsch, W.G., Artner, N.M., Haxhimusa, Y., Jiang, X. (eds) Graph-Based Representations in Pattern Recognition. GbRPR 2013. Lecture Notes in Computer Science, vol 7877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38221-5_19
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DOI: https://doi.org/10.1007/978-3-642-38221-5_19
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