Two-Parameter Persistence for Images via Distance Transform

Chuan-Shen Hu, Austin Lawson, Yu-Min Chung, Kaitlin Keegan; Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops, 2021, pp. 4176-4184

Abstract

The distance transform of a binary image is a classic tool in computer vision and it has been widely used in the field of Topological Data Analysis (TDA) to study porous media. A common practice is to convert grayscale images to binary ones to apply the distance transform. In this work, by considering the threshold decomposition of a grayscale image, we prove that threshold decomposition and distance transform together to formulate a two-parameter filtration. This would offer the TDA community a concrete example to apply multi-parameter persistence on digital image analysis. We demonstrate our method on the firn dataset.

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[bibtex]
@InProceedings{Hu_2021_ICCV, author = {Hu, Chuan-Shen and Lawson, Austin and Chung, Yu-Min and Keegan, Kaitlin}, title = {Two-Parameter Persistence for Images via Distance Transform}, booktitle = {Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) Workshops}, month = {October}, year = {2021}, pages = {4176-4184} }