Title: Computing representative shapes for compatible, situated shapes

Mukul Sati,

Computer Science Ph.D. Student,

School of Interactive Computing,

College of Computing,

Georgia Institute of Technology

Date: Wednesday, November 28th, 2018

Time: 2:00pm to 4:00pm (EDT)

Location: TSRB, 222

Committee:

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Dr. Jarek Rossignac, (Advisor), School of Interactive Computing, Georgia Institute of Technology

Dr. Greg Turk, School of Interactive Computing, Georgia Institute of Technology

Dr. Concettina Guerra, School of Interactive Computing, Georgia Institute of Technology

Dr. Thomas Kurfess, School of Mechanical Engineering, Georgia Institute of Technology

Abstract:

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The proposed thesis focuses on providing definitions, closed-form expressions and algorithmic solutions for computing averages of sets of shapes and associated standard deviation fields. By shapes, we mean lines, planes, curves, and surfaces. Note that these shapes are situated, a term by which we mean that their scales, orientations, and positions are fixed and important.

We establish sufficient conditions on sets of shapes for which our proposed solutions

yield topologically valid results, and call such sets compatible. We propose, study and apply suitable generalizations of the statistical formulations of the average and standard deviation of sets of numbers to sets of compatible shapes. In particular, the solutions proposed extend naturally the popular concept of the medial axis to two and more curves in the plane or in three-dimensions and to two or more surfaces.