Surface- and Volume-Based Techniques for Shape Modeling and Analysis

    Thursday, 21 November

    14:15 - 18:00

    Room S222

    Extending a shape-driven map to the interior of the input shape and to the surrounding volume is a difficult problem since it typically relies on the integration of shape-based and volumetric information, together with smoothness conditions, interpolating constraints, preservation of feature values at both a local and global level.

    In this context, this course revises the main out-of-sample approximation schemes for both 3D shapes and d-dimensional data, and provides a unified discussion on the integration of surface- and volume-based shape information. Then, it describes the application of shape-based and volumetric techniques to shape modeling and analysis through the definition of volumetric shape descriptors; shape processing through volumetric parameterization and polycube splines; feature-driven approximation through kernels and radial basis functions.

    We also discuss the Hamilton's Ricci flow, which is a powerful tool to compute the conformal structure of the shapes and to design Riemannian metrics of manifolds by prescribed curvatures and shape descriptors using conformal welding. We conclude the presentation by discussing applications to shape analysis and medicine, open problems, and future perspectives.



    Intended Audience

    The target audience includes graduate students and researchers interested in Riemannian geometry, spectral geometry processing, implicit modeling. Our goals are threefold: (i) to show the integration of shape- and volume-based information; (ii) to discuss fundamental results and applications that are relevant to computer graphics; (iii) to identify open problems.


    Knowledge about differential geometry, mesh processing, function approximation, basic notions of linear algebra and signal processing.


    Giuseppe Patane, CNR-IMATI
    Xin Shane Li, Louisiana State University
    David Xianfeng Gu, Stony Brook University

    Giuseppe Patane` is a researcher at CNR-IMATI, Italy. He received a Ph.D. in ”Mathematics and Applications” from the University of Genova (2005). From 2001, his research activities have been focused on the definition of paradigms and algorithms for modeling and analyzing digital shapes and multidimensional data.

    Xin Li is an assistant professor in Department of Electrical and Computer Engineering, Louisiana State University. He received his Ph.D. in Computer Science from Stony Brook University (SUNY) (2008). His research activities are related to geometric modeling and processing, and their applications in graphics, vision, computational medicine, forensics, and robotics.

    David Gu is an associate professor in Computer Science department, Stony Brook University. He received a Ph.D. from Harvard university (2003), supervised by a Fields medalist, Prof. Shing-Tung Yau. His research focuses on computational conformal geometry, and its applications in graphics, vision, geometric modeling networks and medical imaging.