Speaker: Dr. Aaron Lanterman

Title: Texture Analysis via an Asymptotic Assault on the Pernicious Partition Function

Date: November 01, 2002

Time: 3:00 pm

Location: GCATT Room 325

Abstract:
Many researchers have characterized textures as realizations of Gauss-Markov random fields. Exploiting these fields in image analysis, where some kind of flexible shape must be fit to the data, is computationally challenging since the normalizer (partition function) of the Gaussian form must be constantly recomputed as the inference proceeds. In the mid-90's, Ulf Grenander, Michael Miller, and myself attacked these dastardly partition functions with an arsenal of asymptotic arguments. We consider fields induced by stochastic difference equations driven by white noise. Our secret weapon is the realization that the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator-induced random field model.

We will show examples of texture parameters estimated from training data via asymptotic maximum-likelihood. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures have been explored, with parameters estimated for mitochondria and actin-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models have been used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds.

Rapid, convenient real-time Gaussian texture analysis, alas, remains an undefeated, yet worthy adversary. We will discuss some unsolved problems, and focus greatly on potential areas for future work to encourage other mathematical soldiers to enlist in this endeavor.

Biography:
Aaron Lanterman attended Washington University in St. Louis, where he finished a triple major consisting of a B.A. in music, B.S. in computer science, and B.S. in electrical engineering in 1993. He stayed on for graduate school, receiving an M.S. (1995) and D.Sc. (1998) in electrical engineering. His graduate work focused on target recognition for infrared imagery as part of the multi-university U.S. Army Center for Imaging Science. After graduation, he joined the Coordinated Science Laboratory at the Univ. of Illinois at Urbana-Champaign as a postdoctoral research associate and then visiting assistant professor, where he managed a large project on covert radar systems which exploit "illuminators of opportunity" such as commercial television and FM radio signals. Other research interests include texture analysis and image reconstruction, particularly medical and astronomical imaging. He joined the Georgia Tech faculty as Assistant Professor of Electrical and Computer Engineering in the fall of 2001. In August 2001, he received the NIC Certificate of Excellence "for outstanding contributions to the National Intelligence Council and exceptional service to the Intelligence Community."

Slides:

Speaker:	Dr. Aaron Lanterman
Title:	Texture Analysis via an Asymptotic Assault on the Pernicious Partition Function
Date:	November 01, 2002
Time:	3:00 pm
Location:	GCATT Room 325
Abstract:	Many researchers have characterized textures as realizations of Gauss-Markov random fields. Exploiting these fields in image analysis, where some kind of flexible shape must be fit to the data, is computationally challenging since the normalizer (partition function) of the Gaussian form must be constantly recomputed as the inference proceeds. In the mid-90's, Ulf Grenander, Michael Miller, and myself attacked these dastardly partition functions with an arsenal of asymptotic arguments. We consider fields induced by stochastic difference equations driven by white noise. Our secret weapon is the realization that the scale of the underlying shape increases, the log-normalizer converges to the integral of the log-spectrum of the operator inducing the random field. Fitting the covariance of the fields amounts to fitting the parameters of the spectrum of the differential operator-induced random field model. We will show examples of texture parameters estimated from training data via asymptotic maximum-likelihood. Isotropic models involving powers of the Laplacian and directional models involving partial derivative mixtures have been explored, with parameters estimated for mitochondria and actin-myocin complexes in electron micrographs and clutter in forward-looking infrared images. Deformable template models have been used to infer the shape of mitochondria in electron micrographs, with the asymptotic approximation allowing easy recomputation of the partition function as inference proceeds. Rapid, convenient real-time Gaussian texture analysis, alas, remains an undefeated, yet worthy adversary. We will discuss some unsolved problems, and focus greatly on potential areas for future work to encourage other mathematical soldiers to enlist in this endeavor.
Biography:	Aaron Lanterman attended Washington University in St. Louis, where he finished a triple major consisting of a B.A. in music, B.S. in computer science, and B.S. in electrical engineering in 1993. He stayed on for graduate school, receiving an M.S. (1995) and D.Sc. (1998) in electrical engineering. His graduate work focused on target recognition for infrared imagery as part of the multi-university U.S. Army Center for Imaging Science. After graduation, he joined the Coordinated Science Laboratory at the Univ. of Illinois at Urbana-Champaign as a postdoctoral research associate and then visiting assistant professor, where he managed a large project on covert radar systems which exploit "illuminators of opportunity" such as commercial television and FM radio signals. Other research interests include texture analysis and image reconstruction, particularly medical and astronomical imaging. He joined the Georgia Tech faculty as Assistant Professor of Electrical and Computer Engineering in the fall of 2001. In August 2001, he received the NIC Certificate of Excellence "for outstanding contributions to the National Intelligence Council and exceptional service to the Intelligence Community."
Slides: