“Spectral Mesh Processing” by Levy and Zhang

  • ©Bruno Levy and Hao (Richard) Zhang


Entry Number: 05


    Spectral Mesh Processing

Course Organizer(s):



    Knowledge about mesh processing, programming, mesh data structures, basic notions of linear algebra and signal processing.  

    Who Should Attend
    Researcher in the areas of geometry processing, shape analysis, and computer graphics, as well as practitioners who want to learn more about how to implement these new techniques and what are the applications. 

    In this course, you will learn the basics of Fourier  analysis on meshes, how to implement it, and how to use it for filtering, remeshing, matching, compressing, and segmenting meshes. 

    Abstract: Spectral mesh processing is an idea that was proposed at the be- ginning of the 90’s, to port the “signal processing toolbox” to the setting of  3D mesh models. Recent advances in both computer horsepower and numerical  software make it possible to fully implement this vision. In the more classical context of sound and image processing, Fourier analysis was a corner stone  in the development of a wide spectrum of techniques, such as filtering, compression, and recognition. In this course, attendees will learn how to transfer  the underlying concepts to the setting of a mesh model, how to implement the “spectral mesh processing” toolbox and use it for real applications, including filtering, shape matching, remeshing, segmentation, and parameterization.  

    Background: Some elements of this course appeared in the “Geometric Modeling based on Polygon Meshes” course (SIGGRAPH 07, Eurographics 08), the  “Mesh Parameterization, Theory and Practice” course (SIGGRAPH 07), and  the “Mesh Processing” course (invited course, ECCV 08). Based on some feedback from the attendees, it seems that there is a need for a course focused on the  spectral aspects. Whereas these previous courses just mentioned some applications of spectral methods, this course details the notions relevant to spectral  mesh processing, from theory to implementation. Spectral methods for mesh processing had been presented as a Eurographics State-of-the-art report in 2007 and a subsequent survey was completed in 2009. Some coverages in the current notes, in particular those on applications, have been selected from the survey. This course, given at ACM SIGGRAPH ASIA 2009 and ACM SIGGRAPH 2010, starts with a more basic setup and include updates from some of the most recent developments in spectral mesh processing.