Category: Publications

Pairing critical points enables forming topological fingerprints, known as persistence diagrams, that provides insights into the structure and noise in data. In this paper, we discuss two algorithmic approaches for pairing critical points in Reeb graphs, first a multipass approach, followed by a new single-pass algorithm, called Propagate and Pair.

In this paper, we leverage the contour tree to extract a hierarchical representation of the topology of an image. We propose 4 topology-aware transfer functions for editing features of the image using local topological properties, instead of global image properties.

This research paper employs a data-driven, explainable, and scalable approach to the development and application of an online peer review form in computer science and engineering courses.

In this paper, we explore a dimensionality reduction technique that achieves the criterion of homology preservation, a generalized version of topology preservation. Specifically, we use topology-inspired manifold landmarking and manifold tearing to aid such a process and evaluate their effectiveness.

Assessing the quality of 3D printed models before they are printed remains a challenging problem, particularly when considering point cloud based models. This paper introduces an approach to quality assessment, which uses techniques from the field of Topological Data Analysis to compute a topological abstraction of the eventual printed model. This abstraction enables investigating certain qualities of the model, with respect to print quality, and identify potential anomalies that may appear in the final product.

We introduce an approach to calculating join tree that combines three strategies, pruning, spatial-domain parallelization, and value-domain parallelization, to parallelize join tree construction using OpenCL.