CAM colloquium - Friday, April 21
3:30 p.m.
253 Rhodes Hall - Note Room Change
Speaker: M. Alex O. Vasilescu, Massachusetts Institute of Technology
Title: A Tensor Algebraic Framework for Computer Vision and Graphics
Abstract: Principal components analysis (PCA) is one of the
most valuable results from applied linear algebra. It is used ubiquitously
in all forms of data analysis -- in data mining, biometrics, psychometrics,
chemometrics, bioinformatics, computer vision, computer graphics,
etc. This is because it is a simple, non-parametric method for extracting
relevant information through the demensionality reduction of high-dimensional
datasets in order to reveal hidden underlying variables. PCA is a
linear method, however, and as such it has severe limitations when
applied to real world data. We are addressing this shortcoming via
multilinear algebra, the algebra of higher order tensors.
In the context of computer vision and graphics, we deal with natural
images which are the consequence of multiple factors related to scene
structure, illumination, and imaging. Multilinear algebra offers a
potent mathematical framework for explicitly dealing with multifactor
image datasets. I will present two multilinear models that learn (nonlinear)
manifold representations of image ensembles in which the multiple
constituent factors (or modes) are disentangled and analyzed explicitly.
Our nonlinear models are computed via a tensor decomposition, known
as the M-mode SVD, which is an extension to tensors of the conventional
matrix singular value decomposition (SVD), or through a generalization
of conventional (linear) ICA called Multilinear Independent Components
Analysis (MICA).
I will demonstrate the potency of our novel statistical learning
approach in the context of facial image biometrics, where the relevant
factors include different facial geometries, expressions, lighting
conditions, and viewpoints. When applied to the difficult problem
of automated face recognition, our multilinear representations, called
TensorFaces (M-mode PCA) and Independent TensorFaces (MICA), yields
significantly improved recognition rates relative to the standard
PCA and ICA approaches. Recognition is achieved with a novel Multilinear
Projection Operator.
In computer graphics, our image-based rendering technique, called
TensorTextures, is a multilinear generative model that, from a sparse
set of example images of a surface, learns the interaction between
viewpoint, illumination and geometry, which determines surface appearance,
including complex details such as self-occlusion and self shadowing.
Our tensor algebraic framework is also applicable to human motion
data in order to extract "human motion signatures" that
are useful in graphical animation synthesis and motion recognition.
BIO:
M. Alex O. Vasilescu (www.media.mit.edu/~maov) was educated at MIT
and the University of Toronto. Currently, she is a research scientist
at the MIT Media Lab. She has done research at IBM, Intel, Compaq,
and Schlumberger corporations and at the MIT Artificial Intelligence
Lab. She has published papers in computer vision and computer graphics,
particularly in the areas of face recognition, human motion analysis/synthesis,
image-based rendering, and physics-based modeling (deformable models).
She has given several invited talks about her work and has three patents
pending. Her face recognition research, known as TensorFaces, has
been funded by the TSWG, the Department of Defense's Combating Terrorism
Support Program. She was named by MIT's Technology Review Magazine
to their 2003 TR100 List of Top Young Innovators.
Refreshments at 4:30 in 657 Rhodes Hall.