My research interests are Algorithms, Computational Geometry, Shape Matching, Graph Drawing, Biomedical Applications, and Topological Data Analysis. I enjoy investigating both theoretical issues and applied problems.

I am grateful to the National Science Foundation to have funded my research with the following grants:

6/1/21 - 5/31/25	"Collaborative Research: AF: Medium: A Unified Framework for Geometric and Topological Signature-Based Shape Comparison", National Science Foundation and National Institutes of Health, NSF-CCF 2107434, $473,760. Role: PI. Collaboration with Erin Chambers at Saint Louis University and Liz Munch at Michigan State University; $1,247,301 total grant amount.
8/1/17 - 7/31/20	"QuBBD: Collaborative Research: Quantifying Morphologic Phenotypes in Prostate Cancer - Developing Topological Descriptors for Machine Learning Algorithms", National Science Foundation and National Institutes of Health, NSF-DMS 1664848, $479,293. Role: PI. Collaboration with Co-PIs Quincy Brown (Biomedical Engineering), Andrew Sholl (Pathology), and Brian Summa (Computer Science) at Tulane and with Brittany Fasy at Montana State University; $899,999 total grant amount.
9/1/16 - 8/31/20	"AitF: Collaborative Research: Modeling movement on transportation networks using uncertain data", National Science Foundation, NSF-CCF 1637576, $317,681. Role: PI. Collaboration with Dieter Pfoser and Andreas Züfle at George Mason University; $825,533 total grant amount.
7/1/16 - 6/30/18	"AF: Small: Collaborative Research: Geometric and Topological Algorithms for Analyzing Road Network Data", National Science Foundation, $158,052. Role: PI. Collaboration with Brittany Fasy at Montana State University and with Yusu Wang at Ohio State University; $499,975 total grant amount.
9/15/15 - 8/31/17	"QuBBD: Collaborative Research: Towards Automated Quantitative Prostate Cancer Diagnosis", National Science Foundation, NSF-DMS 1557750, $52,931. Role: PI. Collaboration with Co-PI Quincy Brown (Biomedical Engineering) at Tulane and with Brittany Fasy at Montana State University; $99,570 total grant amount.
9/1/12 - 8/31/16	"AF: Small: Geometric Algorithms for Constructing Road Networks from Trajectories", National Science Foundation, NSF CCF-1301911, $303,624. Role: PI.
3/1/07 - 2/28/13	"CAREER: Application and Theory of Geometric Shape Handling", National Science Foundation, NSF CCF-1331009 (previously 0643597), $400,468. Role: PI.

Code from my research projects is available on my code page.

Geospatial Data Analysis

	Modeling Movement on Transportation Networks Using Uncertain Data Develop probabilistic network movement models that use as many available data sources as possible to extract meaningful traffic and movement information automatically from the data.
	Geometric and Topological Algorithms for Analyzing Road Network Data Develop algorithms to align realistic trajectories to a network, to reconstruct road networks from trajectory and density data, and to compare data-endowed networks.
	Constructing Road Networks from Trajectories Develop geometric algorithms with quality and performance guarantees for constructing road networks from geo-referenced trajectory data.
	Map-Matching and Routing Algorithms for matching GPS curves to a given roadmap and reactive routing algorithms that adapt to dynamically changing travel-times are essential technical components for Traffic Estimation and Prediction Systems.

Shape Matching

	Shape Matching of Curves Compare geometric shapes described by polygonal curves using adequate distance measures such as the "man-dog" Fréchet distance.
	Geodesic Distances for Shapes Compare shapes on surfaces using shortest distances between points along the surface. This has high applicability in military and GIS applications in which objects traveling on various terrains are involved.
	2D Fréchet Distance The Frechet distance is a well-suited distance measure for the comparison of surfaces.
	Fitting Prehistoric Stone Knives Archaeologists need to find out which prehistoric stone knives have been chopped from the same core stone.

Biomedical Applications

	Quantifying Morphologic Phenotypes in Prostate Cancer - Developing Topological Descriptors for Machine Learning Algorithms Develop mathematical and computational tools based on topological descriptors and machine learning in order to distinguish between different morphological types of prostate cancer.
	Towards Automated Quantitative Prostate Cancer Diagnosis Develop quantitative topological descriptors that capture architectural features of prostate glands in pathology images.
	Analysis of 2D Electrophoresis Gels Correctly modeling the shapes of protein spots in 2D electrophoresis gels as well as comparing two and more of such gels is highly important in Computational Proteomics.
	Neuron Morphometrics Semi-automated processing of cultured neuron images.

Graph Drawing

Drawing Graphs with Fat Edges Drawing graphs with edges of variable thickness. The thickness of an edge is often used as a visualization cue, to indicate importance, or to convey some additional information.