Designing a Topological Algorithm for 3D Activity Recognition

Jiménez, Manuel García; Medrano, Belén; Monaghan, David; O’Connor, Noel E.

doi:10.1007/978-3-319-39441-1_18

Cited by 2 publications

(1 citation statement)

References 20 publications

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“…PH can be regarded as a framework to compute representations of raw data that can be used for further processing or as inputs to learning algorithms. There are numerous successful applications of PH in the last decade, from face, gait and activity recognition [47,51,55,97] or digital forensics [6], to discriminating breast cancer subtypes [79], quantifying the porosity of nanoporous materials [54], classifying fingerprints [42], or studying the morphology of leaves [56] 1 . At the same time, the reasons behind these successes are not well understood.…”

Section: Introductionmentioning

confidence: 99%

On the effectiveness of persistent homology

Turkeš¹,

Montúfar²,

Otter³

2022

Preprint

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Persistent homology (PH) is one of the most popular methods in Topological Data Analysis. While PH has been used in many different types of applications, the reasons behind its success remain elusive. In particular, it is not known for which classes of problems it is most effective, or to what extent it can detect geometric or topological features. The goal of this work is to identify some types of problems on which PH performs well or even better than other methods in data analysis. We consider three fundamental shape-analysis tasks: the detection of the number of holes, curvature and convexity from 2D and 3D point clouds sampled from shapes. Experiments demonstrate that PH is successful in these tasks, outperforming several baselines, including PointNet, an architecture inspired precisely by the properties of point clouds. In addition, we observe that PH remains effective for limited computational resources and limited training data, as well as out-of-distribution test data, including various data transformations and noise.

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