# The Persistent Homology of Dual Digital Image Constructions

@inproceedings{Bleile2021ThePH, title={The Persistent Homology of Dual Digital Image Constructions}, author={Beatrice Bleile and Ad'elie Garin and Teresa Heiss and K. A. R. Maggs and Vanessa Robins}, year={2021} }

To compute the persistent homology of a grayscale digital image one needs to build a simplicial or cubical complex from it. For cubical complexes, the two commonly used constructions (corresponding to direct and indirect digital adjacencies) can give different results for the same image. The two constructions are almost dual to each other, and we use this relationship to extend and modify the cubical complexes to become dual filtered cell complexes. We derive a general relationship between the…

## 5 Citations

### A Convolutional Persistence Transform

- MathematicsArXiv
- 2022

—We consider a new topological feauturization of d - dimensional images, obtained by convolving images with various ﬁlters before computing persistence. Viewing a convolution ﬁlter as a motif within…

### The Impact of Changes in Resolution on the Persistent Homology of Images

- Mathematics2021 IEEE International Conference on Big Data (Big Data)
- 2021

The impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales, is studied.

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- Computer Science
- 2021

It is experimentally demonstrate that deep networks trained with the Persistent-Homology-based loss yield reconstructions of road networks and neuronal processes that preserve the connectivity of the originals better than existing topological and non-topological loss functions.

### Extending conventional surface roughness ISO parameters using topological data analysis for shot peened surfaces

- Materials ScienceScientific reports
- 2022

The roughness of material surfaces is of greatest relevance for applications. These include wear, friction, fatigue, cytocompatibility, or corrosion resistance. Today’s descriptors of the…

### Euler Characteristic Curves and Profiles: a stable shape invariant for big data problems

- Computer Science, Mathematics
- 2022

It is shown that the Euler Curves and Profiles enjoys certain type of stability which makes them robust tool in data analysis, and practical applicability for big data problems.

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