Fast acquisition and routine use of 3D data due to the advance of modern technology and computer power makes 3D description of the real world imminent and practical in many applications such as 3D cameras, 3D printing and prototyping, etc. Although many effective techniques and efficient computational tools are well developed for 2D images from acquisition to processing, analysis and understanding, their counterparts for 3D shape space are more challenging and less developed. There are still many important technological, mathematical and computational issues that need to be addressed: for example, how to obtain, represent and reconstruct 3D models for complicated objects and scenes routinely as we do for images. Another question is how to make computers learn, analyze and understand shapes and geometries like human vision and intelligence for the purpose of registration, comparison, recognition, classification and indexing. This becomes more and more important and urgent for efficient processing and intelligent use of a large variety of 3D data.
At the same time there are many profound mathematical theories and tools for general embedded manifolds and especially for 2D surfaces, from their intrinsic geometric quantities and topologic structures to classification of all Riemannian surfaces. A lot of progress has been made recently in developing computational models and tools based on these geometric theories. In particular, these developments provide efficient computational techniques for extracting local and global intrinsic quantities and structures that are invariant under various transformations or embeddings. On the other hand, many recent advances in machine learning techniques, supervised or non-supervised, for data analysis can be very effective in learning robust and distinctive features and can be used for data or application specific tasks such as recognition and classification. For the very specific goal of 3D modeling and shape analysis, we believe that combining mathematical theory and understanding of surfaces with machine learning techniques, i.e., learning geometry from geometry, will provide more powerful and effective ways of training a computer to learn application specific features based on intrinsic geometric quantities and structures.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.
(Technion - Israel Institute of Technology, Computer Science)
Rongjie Lai (Rensselaer Polytechnic Institute)
Stanley Osher (University of California, Los Angeles (UCLA))
Olga Sorkine-Hornung (ETH Zürich)
Hong-Kai Zhao (University of California, Irvine (UCI), Mathematics)