Associate Professor, University of Utah
This paper introduces and extension to our previous papers to handle anomalies in the point based object slicing method. The anomalies handled are point, line and plane touch cases as well as overlaps.
Continue readingIn 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.
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In this paper, we propose a novel method using persistent homology to quantify structural changes in time-varying graphs. Specifically, we transform each instance of the time-varying graph into a metric space, extract topological features using persistent homology, and compare those features over time. We provide a visualization that assists in time-varying graph exploration and helps to identify patterns of behavior within the data.
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We study the topological construction called Mapper in the context of simply connected domains, in particular on images.
Continue readingAssessing 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.
Continue readingWe 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.
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This paper revisits a more than half-a century-old problem: slice a free-form object into layers for manufacturing. A point-based approach is taken that would have been prohibitive even a decade ago.
Continue readingIn this paper, we perform a
feasibility study for applying topological data analysis and visualization techniques never before tested by the ALMA (Atacama Large Millimeter Array) community. Through techniques based on contour trees, we seek to improve upon existing analysis and visualization workflows of ALMA data cubes, in terms of accuracy and speed in feature extraction.
Distributed mapper Mustafa Hajij, Basem Assiri, and Paul Rosen arXiv preprint arXiv:1712.03660, 2017
Continue readingIn this paper, ten key challenges and their implications for CAD cyber education are discussed. The purpose of this paper is not to provide a dismal outlook for cyberlearning, but to incite discussion, research, and development into these areas with the anticipation of a viable and attractive alternative to traditional classroom education.
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