IMA Thematic Year on

Imaging

September 1, 2005 - June 30, 2006

Poster:   pdf

2005-2006 Annual Report:  pdf

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Quick Links to Events

• 9/19-23/05 Tutorial: Radar and Optical Imaging
• 10/17-21/05 Workshop: Imaging from Wave Propagation
• 11/7-11/05 Workshop: Frontiers in Imaging
• 12/5-9/05 Workshop: Integration of Sensing and Processing
• 12/8/05 IMA Public Lecture: Philip Holmes, Does Math Matter to Brain Matter?
• 1/9-12/06 Workshop: New Mathematics and Algorithms for 3-D Image Analysis
• 2/6-10/06 Workshop: The Mathematics and Art of Film Editing and Restoration
• 2/8/06 IMA Public Lecture: Daniel Rockmore, Mathematics and Art
• 3/6-10/06 Workshop: Natural Images
• 3/22/06 IMA Public Lecture: Arlie O. Petters, Gravity's Cosmic Shadows: A Mathematical Unveiling
• 4/3-7/06 Workshop: Shape Spaces
• 4/19/06 IMA Public Lecture: Persi Diaconis, Mathematics and Magic Tricks
• 5/15-17/06 SIAM Conference: Imaging Science 2006, Radisson Metrodome
• 5/22-26/06 Workshop: Visual Learning and Recognition
• 6/19-30/06 New Directions Short Course: Biophysical Fluid Dynamics
• 7/17-8/4/06 Summer Workshop: Symmetries and Overdetermined Systems of Partial Differential Equations
• 8/9-18/06 Mathematical Modeling in Industry X - A Workshop for Graduate Students

Introduction

Imaging science may be naturally divided into the processes of image formation, the use of data from sensors to form images, and of image interpretation, the extraction of information from images. The IMA annual program has been organized these lines, although we fully realize the interconnectedness of the image formation and interpretation processes, and intend to encourage an interplay between them. In particular, the spring semester will begin with a period of concentration in image processing, which straddles the divisions.

Many classical and well-developed imaging techniques use wave propagation to generate data. Recently, rapid developments in sensor technology coupled with advances in mathematics for integrating the collected data, promise to provide quantitative imaging information about structures and phenomena long assumed to be inaccessible to imaging. Examples in these emerging areas include in vivo cell imaging, quantum state imaging, and network tomography. The development of imaging techniques together with the advancement of image processing methods have called for intelligent integration of these subsystems.

The process of image understanding usually begins with the storage, enhancement, and transmission of existing images. Image understanding also involves the extraction of certain features and information from the often overwhelming stream of information produced by the above imaging techniques. While this is often considered to be part of electrical engineering and computer science, it is highly mathematical and mathematics has had a major role in much of the recent progress in this field. As in all most interdisciplinary efforts, the push has occured in many ways. For example, the analysis of "shape" has driven research in differential geometry, stochastic diffusions and nonlinear partial differential equations.

Bayesian modeling and inference is based on the observation that natural images, whereas notoriously ambiguous at a local level, are perceived globally as largely unambiguous due to incorporating pre-observation and post-observation likelihoods. Special cases such as deformable templates and compositional vision lead to the construction of probability measures on complex structures, such as grammars, graphs and spaces of transformations and numerous mathematical questions arise in learning representations from data ("statistical learning"). The simple observation that the names of objects do not change under various image transformations has led to another approach to image interpretation based on "invariant" functionals--photometric, geometric and algebraic. Finally, nearly all methods encounter formidable computational challenges, inspiring new strategies for simulation, search and optimization.

Imaging science is highly interdisciplinary, naturally connecting mathematical sciences with a variety of application areas. Mathematical areas that have contributed to this field include harmonic analysis, partial differential equations, and integral geometry, calculus of variations, probability theory, statistics, and learning theory. Historically, interchange of ideas among researchers coming from different applications has been impeded by barriers of jargon and culture. By bringing together a range of researchers and emphasizing the underlying mathematical structures and algorithms in the highly interdisciplinary atmosphere of the IMA, this program is a great opportunity to significantly contribute to advances in imaging science.

Fall Semester, September-December, 2005:

Sensors to Images

Image formation refers to the process of obtaining images from sensor data. While data can now be collected on many different types of sensors, data obtained from wave propagation phenomena will receive special attention. This is an important modality with examples from radar, ultrasound, and seismic prospecting. Progress in sensor technology has meant that there are new types of data available from which images are to be reconstructed. There are several new research areas which offer exciting opportunities to mathematicians; quantum state imaging, nanoscale imaging, network tomography are a few such examples. An emerging area related imaging, Integrated Sensing and Processing, is an effort to implement intelligent integration of detection and processing in a systems approach. This area will be another focus of the Fall semester on Imaging.

Spring Semester, January-June, 2006:

Images to Understanding

Whereas much of the information carried by a digital image is generally directly accessible to a human observer (consider everyday face recognition or a radiologist studying a cat scan) the same cannot be said with automated systems. For instance, no computer program today can reliably detect a lesion in a magnetic resonance image, or convert a digital image representation of a three-dimensional scene into a symbolic description involving semantic categories. The absence of a general solution (the "semantic gap") for converting matrices of integers into useful information impedes scientific and technological advances in many areas. Broadly speaking, the workshops during the second semester are about constructing computer programs and algorithms to solve "perceptual inverse problems."

Long Term Visitors:

The following scientists are confirmed or highly likely as long-term visitors during the program. Other long-term visitors are currently being arranged.