Partial functional maps: dense intrinsic correspondence between deformable 3D objects with missing parts and occlusions
Finding correspondence between non-rigid 3D shapes is a challenging task underlying numerous problems in computer graphics and vision. In this talk, I will present our recent line of works on deformable partial shape correspondence in the spectral domain. I will first introduce Partial Functional Maps (PFM), showing how to robustly formulate the shape correspondence problem under missing geometry with the language of functional maps. We use perturbation analysis to show how removal of shape parts changes the Laplace-Beltrami eigenfunctions, and exploit it as a prior on the spectral representation of the correspondence. I will show further extensions to deal with the presence of clutter (deformable object-in-clutter) and multiple pieces (non-rigid puzzles). In the second part of the talk, I will show how to formulate the problem completely in the spectral domain, avoiding the cumbersome alternating optimization used in the previous approaches. This allows matching shapes with constant complexity independent of the number of points, and yields state-of-the-art results on challenging correspondence benchmarks in the presence of partiality and topological noise.
Michael Bronstein (PhD with distinction 2007, Technion, Israel) is a professor at USI Lugano, Switzerland and Imperial College, UK. He also serves as a Principal Engineer at Intel Perceptual Computing. During 2017-2018 he is a fellow at the Radcliffe Institute for Advanced Study at Harvard University. Michael's main research interest is in theoretical and computational methods for geometric data analysis. He authored over 150 papers, the book Numerical geometry of non-rigid shapes (Springer 2008), and over 20 granted patents. He was awarded three ERC grants, two Google Faculty Research awards (2015, 2017), and Rudolf Diesel fellowship (2017) at TU Munich. He was invited as a Young Scientist to the World Economic Forum, an honor bestowed on forty world’s leading scientists under the age of forty. Michael is a Senior Member of the IEEE, alumnus of the Technion Excellence Program and the Academy of Achievement, ACM Distinguished Speaker, and a member of the Young Academy of Europe. In addition to academic work, Michael is actively involved in commercial technology development and consulting to start-up companies. He was a co-founder and technology executive at Novafora (2005-2009) developing large-scale video analysis methods, and one of the chief technologists at Invision (2009-2012) developing low-cost 3D sensors. Following the multi-million acquisition of Invision by Intel in 2012, Michael has been one of the key developers of the Intel RealSense technology.