Sparse Decomposition and Modeling of Anatomical Shape Variation

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Sparse Decomposition and Modeling of Anatomical Shape Variation

via Medical Imaging, IEEE Transactions on - new TOC on 12/3/07

Recent advances in statistics have spawned powerful methods for regression and data decomposition that promote sparsity, a property that facilitates interpretation of the results. Sparse models use a small subset of the available variables and may perform as well or better than their full counterparts if constructed carefully. In most medical applications, models are required to have both good statistical performance and a relevant clinical interpretation to be of value. Morphometry of the corpus callosum is one illustrative example. This paper presents a method for relating spatial features to clinical outcome data. A set of parsimonious variables is extracted using sparse principal component analysis, producing simple yet characteristic features. The relation of these variables with clinical data is then established using a regression model. The result may be visualized as patterns of anatomical variation related to clinical outcome. In the present application, landmark-based shape data of the corpus callosum is analyzed in relation to age, gender, and clinical tests of walking speed and verbal fluency. To put the data-driven sparse principal component method into perspective, we consider two alternative techniques, one where features are derived using a model-based wavelet approach, and one where the original variables are regressed directly on the outcome.

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Possible topics for Winter 888

Gaussian Processes for Machine Learning

"Roughly speaking a stochastic process is a generalization of a probability distribution (which describes a finite-dimensional random variable) to functions. By focussing on processes which are Gaussian, it turns out that the computations required for inference and learning become relatively easy. Thus, the supervised learning problems in machine learning which can be thought of as learning a function from examples can be cast directly into the Gaussian
process framework."

The book is online.

Graphical Models

"Graphical models are a marriage between probability theory and graph theory. They provide a natural tool for dealing with two problems that occur throughout applied mathematics and engineering -- uncertainty and complexity -- and in particular they are playing an increasingly important role in the design and analysis of machine learning algorithms. Fundamental to the idea of a graphical model is the notion of modularity -- a complex system is built by combining simpler parts. Probability theory provides the glue whereby the parts are combined, ensuring that the system as a whole is consistent, and providing ways to interface models to data. The graph theoretic side of graphical models provides both an intuitively appealing interface by which humans can model highly-interacting sets of variables as well as a data structure that lends itself naturally to the design of efficient general-purpose algorithms.

Many of the classical multivariate probabalistic systems studied in fields such as statistics, systems engineering, information theory, pattern recognition and statistical mechanics are special cases of the general graphical model formalism -- examples include mixture models, factor analysis, hidden Markov models, Kalman filters and Ising models. The graphical model framework provides a way to view all of these systems as instances of a common underlying formalism. This view has many advantages -- in particular, specialized techniques that have been developed in one field can be transferred between research communities and exploited more widely. Moreover, the graphical model formalism provides a natural framework for the design of new systems." --- Michael Jordan, 1998.

Point Matching

Shape Contexts¹ by Belongie, Malik, and Puzicha at Berkeley looks like a promising approach for finding point correspondences (along the lines of ICP, TPS-RPM, etc).

 

Give it a looksie whenever you get the time.

 

¹ http://www.eecs.berkeley.edu/Research/Projects/CS/vision/shape/sc_digits.html

IEEE International Symposium on Biomedical Imaging - ISBI 2008 Call for Papers

From: IEEE SPS Lists
Sent: Monday, November 19, 2007 17:56
Subject: IEEE International Symposium on Biomedical Imaging - ISBI 2008 Call for Papers

CALL FOR PAPERS
2008 IEEE International Symposium
on Biomedical Imaging: From Nano to Macro

May 14-17, 2008
Paris Marriott Rive Gauche Hotel & Conference Center, Paris, France

** Paper Submission Deadline: December 7, 2007 **

The Fifth IEEE International Symposium on Biomedical Imaging (ISBI'08) will be held May 14-17, 2008, in Paris, France. The previous meetings have played a leading role in facilitating interaction between researchers in medical and biological imaging. The 2008 meeting will continue the tradition of fostering cross-fertilization between different imaging communities and contributing to an integrative imaging approach across all scales of observation.

ISBI 2008 is a joint initiative of the IEEE Signal Processing Society (SPS) and the IEEE Engineering in Medicine and Biology Society (EMBS), with the support of Optics Valley. The meeting will feature an opening afternoon of tutorials and short courses, followed by a strong scientific program of plenary talks and special sessions as well as oral and poster presentations of peer-reviewed contributed papers. An industrial exhibition is planned.

High-quality papers are solicited containing original contributions to the algorithmic, mathematical and computational aspects of biomedical imaging, from nano- to macroscale. Topics of interest include image formation and reconstruction, computational and statistical image processing and analysis, dynamic imaging, visualization, image quality assessment, and physical, biological and statistical modeling. Papers on all molecular, cellular, anatomical and functional imaging modalities and applications are welcomed. All accepted papers will be published in the proceedings of the symposium and will afterwards also be made available online through the IEEExplore database.

Important Dates:
Deadline for submission of 4-page paper:
7 December 2007 (Midnight at International Date Line)

Notification of acceptance/rejection:
15 February 2008

Submission of final accepted 4-page paper:
14 March 2008

Deadline for early registration:
14 March 2008

Organizing Committee

General Chair
Jean-Christophe Olivo-Marin, Institut Pasteur, Paris, France

Program Chairs
Isabelle Bloch, ENST, Paris, France
Andrew Laine, Columbia University, NYC, USA

Special Sessions
Josiane Zerubia, INRIA, Sophia-Antipolis, France
Wiro Niessen, Erasmus Medical Ctr, Rotterdam, The Netherlands

Plenaries
Christian Roux ,ENST Bretagne, Brest, France

Tutorials
Michael Unser, EPFL, Lausanne, Switzerland

Finances
Elsa Angelini, ENST, Paris, France

Publications
Habib Benali, Inserm, Paris, France

Local Arrangements
Severine Dubuisson, Univ. Pierre et Marie Curie, Paris, France
Vannary Meas-Yedid, Institut Pasteur, Paris, France

Industrial Liaison
Spencer Shorte, Institut Pasteur, Paris, France
Nicholas Ayache, INRIA, Sophia-Antipolis, France

Institutional Liaison
Claude Boccara, ESPCI, Paris, France

Technical Liaison
Sebastian Ourselin, CSIRO, Brisbane, Australia

American Liaison
Jeff Fessler, University of Michigan, Ann Arbor, USA

Diffeomorphic deformation fields

Gary E. Christensen, Sarang C. Joshi, Michael I. Miller, "Volumetric Transformation of Brain Anatomy" IEEE Trans. Med. Imag. (1997) 

 

http://citeseer.ist.psu.edu/cache/papers/cs/25121/http:zSzzSzwww.icaen.uiowa.eduzSz~geczSzpaperszSzchristensen_tmi97.pdf/christensen97volumetric.pdf

 

 

Abstract

This paper presents diffeomorphic transformations of three-dimensional (3-D) anatomical image data of the macaque occipital lobe and whole brain cryosection imagery and of deep brain structures in human brains as imaged via magnetic resonance imagery. These transformations are generated in a hierarchical manner, accommodating both global and local anatomical detail. The initial low-dimensional registration is accomplished by constraining the transformation to be in a low-dimensional basis. The basis is defined by the Green’s function of the elasticity operator placed at predefined locations in the anatomy and the eigenfunctions of the elasticity operator. The high-dimensional large deformations are vector fields generated via the mismatch between the template and target-image volumes constrained to be the solution of a Navier–Stokes fluid model. As part of this procedure, the Jacobian of the transformation is tracked, insuring the generation of diffeomorphisms. It is shown that transformations constrained by quadratic regularization methods such as the Laplacian, biharmonic, and linear elasticity models, do not ensure that the transformation maintains topology and, therefore, must only be used for coarse global registration.

A history of quaternions

A very delightful account of the story, the logic and the personalities behind
Hamilton's development of quaternions and versors at
http://www.jstor.org/view/00255572/ap060385/06a00280/0

Tutorial on computational methods

A good resource for the computational aspects of stochastic theory, ode’s, pde’s and statistical mechanics (from a computational physics point of view) at:

http://homepage.univie.ac.at/franz.vesely/cp_tut/nol2h/new/index.html

by Franz J. Vesely at the University of Vienna.

IEEE Visualization 2007

We're at Vis 2007. Here's the program

Some interesting papers -

Visualizing Whole-Brain DTI Tractography with GPU-based Tuboids and LoD Management. Vid Petrovic, James Fallon, Falko Kuester.

Stellar presentation by Mosaliganti

I presented the use of N-point correlation functions in geometry-driven visualization process at KAV 08. The presentation was well-received and couple of the panel members did walk upto me and express their appreciation. During the panel meeting, one of the committee members brought up my paper as a special mention.

Here's a link to the presentation.