Publications

 0. The Blum Medial Linking Structure for Multi-Region Analysis, Ph.D. thesis, 2012.

 1. Skeleton-Based Recognition of Shapes in Images Via Longest Path Matching (with G. Bal, et al.), in Research in Shape Modeling, K. Leonard, S. Tari (eds.), Springer, 2015, p. 81-99.

 2. Multi-Scale Local Shape Analysis for Feature Selection in Machine Learning Applications (with P. Bendich, J. Harer, R. Izmailov, and L. Ness), Proceedings of the International Joint Conference on Neural Networks, 2015.

 3. Geometric Models for Musical Audio Data (with P. Bendich, J. Harer, and C. Tralie), Sympos. Comput. Geom. (SoCG) 2016, p. 65:1-65:5. (multimedia contribution) 

 4. Medial/Skeletal Linking Structures for Multi-Region Configurations (with J. Damon) (163 pages), Memoirs of the Amer. Math. Soc., vol. 250, 2017, p. 1-163. 

 5. Modeling Multi-Object Configurations Via Medial/Skeletal Linking Structures (with J. Damon), International Journal of Computer Vision, 124(3), 2017, p. 255-272. 

 6. Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology (with P. Bendich, J. Harer, and C. Tralie), in Research in Computational Topology, Springer, 2018, p. 93-114.

 7. A Complete Characterization of the 1-Dimensional Intrinsic Cech Persistence Diagrams for Metric Graphs (with M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier), in Research in Computational Topology, Springer, 2018, p. 33-56.

 8. Medial Fragments for Segmentation of Articulating Objects in Images (with E.W. Chambers and K. Leonard), in Research in Shape Analysis, Springer, 2018, p. 1-15.

9. Vietoris-Rips and Cech Complexes of Metric Gluings (with M. Adamaszek, H. Adams, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier), Sympos. Comput. Geom. (SoCG) 2018, p. 3:1-3:15.

10. Research in Data Science (editor, with C. Domeniconi), Springer, 2019.

11. A Structural Average of Labeled Merge Trees for Uncertainty Visualization (with L. Yan, Y. Wang, E. Munch, and B. Wang), IEEE Transactions on Visualization and Computer Graphics, 26(1), 2019, p. 832-842.

12. The Relationship Between the Intrinsic Cech and Persistence Distortion Distances for Metric Graphs (with M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier), Journal of Computational Geometry, 10(1), 2019, p. 477-499. 

13. On Homotopy Types of Vietoris-Rips Complexes of Metric Gluings (with M. Adamaszek, H. Adams, M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier), Journal of Applied and Computational Topology, 4(3), 2020, p. 425-454.

14. Local Versus Global Distances for Zigzag and Multi-Parameter Persistence Modules (with M. Gommel, E. Purvine, R. Sazdanovic, B. Wang, Y. Wang, and L. Ziegelmeier), in Research in Computational Topology 2, Springer, 2022, p. 63-76. 

15. Research in Computational Topology 2 (editor, with V. Robins and K. Turner), Springer, 2022.

16. Distances Between Immersed Graphs: Metric Properties (with M. Buchin, E. Chambers, P. Fang, B.T. Fasy, E. Munch, and C. Wenk), La Matematica, 2023, p. 1-26.

PREPRINTS

1. Shape and Positional Geometry of Multi-Object Configurations (with J. Damon), submitted.

2. Intrinsic Interleaving Distance for Merge Trees (with E. Munch, S. Oudot, K. Turner, B. Wang, and Y. Wang), submitted.

3. A medial axis-based compactness measure versus the eye test for detecting gerrymandering (with J. D'Amico, G. Malen, and M. Zhong), submitted.