Date: Thursday April 8, 2010
Place: Room E305
Time: 12:00 PM
Speaker: Prof. James Hobert
Topic: Improving the Data Augmentation Algorithm
Abstract:
After a brief review of the data augmentation (DA) algorithm, I will
introduce a simple modification that results in a new Markov chain
that remains reversible with respect to the target distribution. The
DA and modified algorithms are compared in the context of a toy
Bayesian mixture model where exact eigen-analysis is possible.
General results showing that the modified algorithm is always better
are presented. I will end by describing a second comparison of the
two algorithms in a specific example, this time using a more realistic
Bayesian mixture model with normal components.
Date: Thursday March 25, 2010
Place: Room 520A
Time: 12:00 PM
Speaker: Angelos Barmpoutis
Topic: A unified framework for estimating diffusion tensors of any order with symmetric positive-definite constraints
Paper Link:
[PDF]
Abstract:
Cartesian tensors of various orders have been employed for either modeling the diffusivity or the
orientation distribution function in Diffusion-Weighted MRI datasets. In both cases, the estimated
tensors have to be positive-definite since they model positive-valued functions. In this paper we
present a novel unified framework for estimating positive-definite tensors of any order, in contrast
to the existing methods in literature, which are either order-specific or fail to handle the
positive-definite property. The proposed framework employs a homogeneous polynomial parametrization
that covers the full space of any order positive-definite tensors and explicitly imposes the
positive-definite constraint on the estimated tensors. We show that this parametrization leads to
a linear system that is solved using the non-negative least squares technique. The framework is
demonstrated using synthetic and real data from an excised rat hippocampus.
Date: Friday March 5, 2010
Place: Room E404
Time: 3:30 PM
Speaker: Prof. Fernando De la Torre
Topic: Learning Components for Human Sensing
Abstract:
Providing computers with the ability to understand human behavior from
sensory data (e.g. video, audio, or wearable sensors) is an essential part
of many applications that can benefit society such as clinical diagnosis,
human computer interaction, and social robotics. A critical element in the
design of any behavioral sensing system is to find a good representation of
the data for encoding, segmenting, classifying and predicting subtle human
behavior. In this talk I will propose several extensions of Component
Analysis (CA) techniques (e.g. kernel principal component analysis, support
vector machines, and spectral clustering) that are able to learn
spatio-temporal representations or components useful in many human sensing
tasks.
In the first part of the talk I will give an overview of several ongoing
projects in the CMU Human Sensing Laboratory, including our current work on
depression assessment from video, as well as hot-flash detection from
wearable sensors. In the second part of the talk I will show how several
extensions of the CA methods outperform state-of-the-art algorithms in
problems such as temporal alignment of human behavior, temporal
segmentation/clustering of human activities, joint segmentation and
classification of human behavior, and facial feature detection in images.
The talk will be adaptive, and I will discuss the topics of major interest
to the audience.
Biography:
Fernando De la Torre received his B.Sc. degree in Telecommunications (1994),
M.Sc. (1996), and Ph. D. (2002) degrees in Electronic Engineering from La
Salle School of Engineering in Ramon Llull University, Barcelona, Spain. In
1997 and 2000 he was an Assistant and Associate Professor in the Department
of Communications and Signal Theory in Enginyeria La Salle. Since 2005 he
has been a Research Assistant Professor in the Robotics Institute at
Carnegie Mellon University. Dr. De la Torre's research interests include
computer vision and machine learning, in particular face analysis,
optimization and component analysis methods, and its applications to human
sensing. Dr. De la Torre co-organized the first workshop on component
analysis methods for modeling, classification and clustering problems in
computer vision in conjunction with CVPR'07, and the workshop on human
sensing from video jointly with CVPR'06. He has also given several tutorials
at international conferences (ECCV'06, CVPR'06, ICME'07, ICPR'08) on the use
and extensions of component analysis methods. Currently he leads the
Component Analysis Laboratory (http://ca.cs.cmu.edu) and the Human Sensing
Laboratory (http://humansensing.cs.cmu.edu).
Date: Thursday Oct 22, 2009
Place: Room E305
Time: 11:00 AM
Speaker: Karthik
Topic: A Schrodinger Equation for the Fast Computation of Approximate Euclidean Distance Functions
Paper Link:
[PDF]
Abstract:
Computational techniques adapted from classical mechanics and used
in image analysis run the gamut from Lagrangian action principles to Hamilton-
Jacobi field equations: witness the popularity of the fast marching and fast sweeping
methods which are essentially fast Hamilton-Jacobi solvers. In sharp contrast,
there are very few applications of quantum mechanics inspired computational
methods. Given the fact that most of classical mechanics can be obtained as a
limiting case of quantum mechanics (as Planck’s constant h tends to zero), this
paucity of quantum mechanics inspired methods is surprising. In this work, we
derive relationships between nonlinear Hamilton-Jacobi and linear Schrödinger
equations for the Euclidean distance function problem (in 1D, 2D and 3D). We
then solve the Schrödinger wave equation instead of the corresponding Hamilton-
Jacobi equation. We show that the Schrödinger equation has a closed form solution
and that this solution can be efficiently computed in O(N logN), N being
the number of grid points. The Euclidean distance can then be recovered from
the wave function. Since the wave function is computed for a small but non-zero
h, the obtained Euclidean distance function is an approximation. We derive analytic
bounds for the error of the approximation and experimentally compare the
results of our approach with the exact Euclidean distance function on real and
synthetic data.
Date: Thursday Oct 15, 2009
Place: Room E305
Time: 11:00 AM
Speaker: Ting Chen
Topic: Group-wise Point-set registration using a novel CDF-based
Havrda-Charvát Divergence
Paper Link:
[PDF]
Abstract:
This paper presents a novel and robust technique for group-wise registration of point sets
with unknown correspondence. We begin by defining a Havrda-Charvát (HC) entropy valid
for cumulative distribution functions (CDFs) which we dub the HC Cumulative Residual Entropy
(HC-CRE). Based on this definition, we propose a new measure called the CDF-HC divergence
which is used to quantify the dis-similarity between CDFs estimated from each point-set
in the given population of point sets. This CDF-HC divergence generalizes the CDF based
Jensen-Shannon (CDF-JS) divergence introduced earlier in the literature, but is much simpler
in implementation and computationally more efficient.
A closed-form formula for the analytic gradient of the cost function with respect to the nonrigid
registration parameters has been derived, which is conducive for efficient quasi-Newton
optimization. Our CDF-HC algorithm is especially useful for unbiased point-set atlas construction
and can do so without the need to establish correspondences. Mathematical analysis and
experimental results indicate that this CDF-HC registration algorithm outperforms the previous
group-wise point-set registration algorithms in terms of efficiency, accuracy and robustness.
Date: Thursday Sep 17, 2009
Place: Room E305
Time: 11:00 AM
Speaker: Guang Cheng
Topic: Non-rigid Registration of High Angular Resolution Diffusion Images Represented by Gaussian Mixture Fields
Paper Link:
[PDF]
Abstract:
In this paper, we present a novel algorithm for non-rigidly
registering two high angular resolution diffusion weighted MRIs (HARDI),
each represented by a Gaussian mixture field (GMF). We model the non-
rigid warp by a thin-plate spline and formulate the registration problem
as the minimization of the L2 distance between the two given GMFs. The
key mathematical contributions of this work are, (i) a closed form ex-
pression for the derivatives of this objective function with respect to the
parameters of the registration and (ii) a novel and simpler re-orientation
scheme based on an extension to the ”Preservation of Principle Direc-
tions” technique. We present results of our algorithm’s performance on
several synthetic and real HARDI data sets.