Spectral analysis of three-dimensional media

Alex Bronstein
Tel Aviv University

During roughly a century of its turbulent life, electronic
media has faced several leaps, most of which are related to an increase in the number of dimensions, such as the transition from voice to television, and from black-and white to color. Today, with the advent of affordable three-dimensional acquisition and display technologies, we are facing yet another increase in the dimensionality
of media. Accurate and reliable 3D acquisition also offers a
formidable tool for quantifying and understanding the geometry of the world surrounding us, which is one of the fundamental challenges in machine vision with potential applications impacting virtually every aspect of our life. The gradual penetration of 3D technologies into
the consumer markets makes many analysts foresee a rapid growth in 3D content, similar to the explosive growth in the amounts of visual content that followed the introduction of digital media storage, acquisition, and transmission technologies in the early ’90s. In many
aspects, geometric data are more challenging to analyze than the regular two-dimensional images. The majority of objects around us can undergo a wealth of non-rigid deformations such as articulations and bending. Dealing with such a vast number of degrees of freedom is one
of the main challenges of shape analysis, to which no satisfactory answer has yet been offered. Recent development of theoretical and computational methods for spectral analysis of non-Euclidean geometries bring forth powerful instruments for the study of deformable shapes. In this talk, I will highlight the challenges arising in large-scale deformable shape analysis. Using the umbrella
of spectral methods, I will show how to extend several classical computer vision approaches, very popular in the study of images, to deformable 3D shapes.

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