CAREER: Signal Processing for Surfaces

New York University, New York NY

Investigators

Abstract

Complex geometry becomes increasingly common in applications arising in diverse areas. Plastic surgeons use computer models to plan and perform operations. Mechanical engineers virtually assemble and test cars and planes. Animators create complex characters and effects indistinguishable from reality. Geometric modeling has found its way into art conservation: it is now feasible to create computer models of sculptures capturing the most subtle of details. Increasing complexity of geometric data calls for new efficient representations and algorithms. The goal of our long-term research plan is to study representations of complex geometric data, surfaces in particular. We plan to launch a broad and fundamental program to explore three types of representations: piecewise-smooth surfaces, multiscale surfaces and combined volume-surface representations. Our approach to designing complex surface representations is based on the concept of subdivision, a powerful technique for modeling smooth surfaces. Subdivision algorithms, while being more flexible and general, retain a number of useful properties of splines. Most importantly, the surfaces generated by these algorithms have a natural hierarchical structure and are computed using efficient local rules; subdivision algorithms can be easily extended to represent multiscale data. The general goal of our research is to design representations supporting efficient algorithms for construction, rendering, manipulation, processing, transmission and storage of surface data. We will explore in close coordination both theoretical properties of these representations (regularity, convergence rates, fairness, stability) and their practical applications. The specific goal of the proposed project is to generalize to surfaces the signal processing tools that were designed and are extensively used for images. The research program is integrated with the education plan, which has three main goals: (1) prepare graduate students for research in computer graphics and related areas, (2) incorporate the latest advances in research into curriculum at all levels, including undergraduate, and engage motivated undergraduate students in research (3) transfer knowledge about latest research advances to professionals in the industry.