The Taub Faculty of Computer Science Events and Talks

The interest in acquiring and analyzing the geometry of the world is ever increasing, fueling a wide range of computer vision algorithms in the field of geometry processing. Spectral analysis has become key component in many applications involving non-rigid shapes modeled as two-dimensional surfaces, and recently, convolutional neural networks have shown remarkable success in a variety of computer vision tasks. We designed a set of methods and tools that use these paradigms for applications such as shape correspondence, nonrigid deformations, and volumetric optical flow. In this talk we will present three different ways to infer point-to-point correspondences between deformable shapes, which is a fundamental operation in the field of geometry processing.

A well-established approach to address the non-rigid shape correspondence problem is to define a measure of dissimilarity between the shapes. One way for measuring distance between two non-rigid shapes is to embed their two-dimensional surfaces into some common Euclidean space, defining the comparison task as a problem of rigid matching in that space. In the first part of this talk we review a novel spectral embedding, named the "Spectral Gradient Fields Embedding", which exploits the local interactions between the eigenfunctions of the Laplace-Beltrami operator and the extrinsic geometry of the surface.

Next, we analyze the applicability of the spectral kernel distance, as a measure of dissimilarity between surfaces, for solving the shape matching problem. To align the spectral kernels, we developed the Iterative Closest Spectral Kernel Maps (ICSKM) algorithm. ICSKM extends the Iterative Closest Point (ICP) algorithm to the class of deformable shapes. Instead of aligning the shapes in the three dimensional Euclidean domain, this method estimatesthe transformation that best fits the embeddings of the shapes into the spectral domain.

Volumetric optical flow is a different way to address the matching problem of a three-dimensional dynamic scene. In the last part of the talk we introduce a multi-scale optical flow based deep learning architecture for predicting the next frame of a sequence of volumetric images. The fully differentiable model consists of specific crafted modules that are trained on small patches in an unsupervised manner. The approach, called "V-Flow", is useful for analyzing the temporal dynamics of three-dimensional images in applications that involve, for example, motion of viscousfluid substances or volumetric medical imaging.