Reconstructing a geometric shape from a finite, noisy sample around it is a challenging problem, with a myriad of practical applications. To aid the inference, I focus on a topological construction known as the Vietoris–Rips complex to thicken the sample at different scales to extract the shape of the data at various resolutions.
Collaborators
- Rafal Komendarczyk, Tulane University
- Atish Mishra, Montana Technological University
- Brittany Fasy, Montana State University (past)
- Carola Wenk, Tulane University (past)
Publications
[1]
B. T. Fasy, R. Komendarczyk, S. Majhi, and C. Wenk, “On the reconstruction of geodesic subspaces of \mathbb{R}^N,” International Journal of Computational Geometry & Applications, vol. 32, no. 01n02, pp. 91–117, 2022, doi: 10.1142/S0218195922500066. Available: https://doi.org/10.1142/S0218195922500066
[2]
S. Majhi, “Vietoris–Rips complexes of metric spaces near a metric graph,” J. Appl. Comput. Topol., vol. 7, no. 4, pp. 741–770, Dec. 2023.
[3]
S. Majhi, “Demystifying latschev’s theorem: Manifold reconstruction from noisy data,” Discrete Comput. Geom., May 2024.
[4]
S. Majhi, “Demystifying Latschev’s Theorem: Manifold Reconstruction from Noisy Data,” in 40th international symposium on computational geometry (SoCG 2024), W. Mulzer and J. M. Phillips, Eds., in Leibniz international proceedings in informatics (LIPIcs), vol. 293. Dagstuhl, Germany: Schloss Dagstuhl – Leibniz-Zentrum für Informatik, 2024, pp. 73:1–73:16. doi: 10.4230/LIPIcs.SoCG.2024.73. Available: https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2024.73
[5]
R. Komendarczyk, S. Majhi, and W. Tran, “Topological stability and latschev-type reconstruction theorems for \boldsymbol{\mathrm{CAT}(\kappa)} spaces,” 2024.