The VI AMMCS International Conference

Waterloo, Ontario, Canada | August 14-18, 2023

AMMCS 2023 Plenary Talk

Skeletal models for two- and three-dimensional shape understanding

Kathryn Leonard (Occidental College, Los Angeles)

Shape understanding - looking at a shape and intuitively understanding which parts are, e.g., body, arms, legs, toes, and ears - is almost effortless for humans. Training a computer to understand shapes in a similar way, however, presents substantial challenges. This talk will describe a useful mathematical shape model, the Blum medial axis (BMA), and methodologies based on the BMA for automatically decomposing a shape into a hierarchy of parts and determining the similarity between those parts. In 2D, we compare our automated results to human perception data gathered from a massive user study, and also provide some useful applications. Unfortunately, the BMA is notoriously sensitive to noise, which is unavoidable in applications. To address this, we propose geometrically coherent approaches to denoising that provide approximation guarantees for the shape boundary. Finally, because the BMA also provides an interesting example of a Whitney stratified set, we will explore some of the resulting elegant mathematical constructions.
Kathryn Leonard is Associate Dean for Curricular Affairs, and Professor and Founding Chair of Computer Science, at Occidental College. She completed a postdoctoral fellowship in Applied and Computational Mathematics at Caltech after finishing her PhD in Mathematics at Brown University. She is the director of the National Science Foundation-funded Center for Undergraduate Research in Mathematics, and is Past President of the Association for Women in Mathematics (AWM). She has received a Henry L. Alder Award for Excellence in Teaching from the Mathematical Association of America and a service award from AWM. Her research interests are in geometric modeling for data science, computer vision, and computer graphics applications, with an emphasis on explainable AI. Her research has been recognized with an NSF CAREER award and other research grants, and she is founding co-Editor-in-Chief of the mathematics research journal, La Matematica.