Shape and Deformable Models in Biomedical Imaging

Sanjo Hall, University of Tokyo, Japan

September 25, 2002, 9:30AM-1:00PM

Goals. This half-day intensive workshop will focus on techniques to measure, map and model biological shape in medical images. It will concentrate on current mathematical methods, including deformable models, for extracting, representing and analyzing the shapes of biological structures. These methods show enormous promise in understanding how diseases such as Alzheimer's, schizophrenia, tumor growth and abnormal development emerge in the brain, and help in investigating their effects. Deformable models also help understand how biological structures such as the heart, or the brain during surgery, change dynamically over time. They can also capture statistics on how anatomy and physiology vary in healthy and diseased populations.

Experts who are pioneers in medical image analysis will describe the basic mathematics of the approaches, highlighting current applications and challenges in radiology and neuroscience. Talks will be of interest to newcomers and experts in the field.

SCHEDULE:

SEPTEMBER 25, 2002, 9:30AM-1:00PM

Session Co-Chairs: Paul Thompson and Steve Haker

9:30-9:35 Paul Thompson (UCLA School of Medicine): Introduction and Welcome

9:35-10:05 Guido Gerig (UNC Chapel Hill, Computer Science and Psychiatry):
Statistical Shape Models for Segmentation and Characterization of Group Differences
10:05-10:35 Steve Haker (Surgical Planning Lab, Brigham Women's Hospital/Harvard Univ.)
10:35-11:05 Polina Golland (MIT Artificial Intelligence Laboratory):
Deformation Analysis for Shape Based Classification

11:05-11:20 Questions and Short Break

11:20-11:50 James Gee (Univ. of Pennsylvania):
Non-Rigid Tensor Registration
11:50-12:20 Gary Christensen (Department of Electrical and Computer Engineering, University of Iowa):
Inverse Consistent Medical Image Registration
[Tutorial Notes, 1.4 MB, .pdf]
12:20-12:50 Colin Studholme (University of California, San Francisco):
Detecting and Analyzing Brain Shape Change from Serial MRI

12:50-1:00 Questions and Closing Remarks (Paul Thompson)

1:00 LUNCH

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Abstracts:

Guido Gerig (UNC Chapel Hill, Computer Science and Psychiatry)

Title: Statistical Shape Models for Segmentation and Characterization of Group Differences

Abstract: In various clinical disciplines, imaging and extraction of anatomical organ geometry becomes a routine procedure for noninvasive patient population studies and for therapy planning and monitoring, and similar procedures are vital for surgical planning and image-guided therapy. Increased robustness and efficiency has been demonstrated for techniques that use prior knowledge about the geometry of the anatomic objects and its variability.

We will present work in progress towards building and using statistical shape models based on point distribution models and medial representations. These representations will be compared based on their ability to support segmentation by deformable models and to provide statistical characterization of shape differences between groups. The discussion includes most recent research towards a combined representation of groups of objects and their interrelationship, a new multi-scale object intensity boundary representation, and a statistical test method for shape population differences that includes various patient parameters. The talk will be illustrated by presenting most recent results in neuroimaging research of mental illness which aims at finding markers for disease status and progress.

Polina Golland (MIT Artificial Intelligence Laboratory)

Title: Deformation Analysis for Shape Based Classification

Abstract: We present a computational framework for image-based statistical analysis of anatomical shape in different populations. Applications of such analysis include understanding developmental and anatomical aspects of disorders when comparing patients vs. normal controls, studying morphological changes caused by aging, or even differences in normal anatomy, for example, differences between genders.

Once a quantitative description of organ shape is extracted from input images, the problem of identifying differences between the two groups can be reduced to one of the classical questions in machine learning, namely constructing a classifier function for assigning new examples to one of the two groups while making as few mistakes as possible. In the traditional classification setting, the resulting classifier is rarely analyzed in terms of the properties of the input data that are captured by the discriminative model. In contrast, interpretation of the statistical model in the original image domain is an important component of morphological analysis. We propose a novel approach to such interpretation that allows medical researchers to argue about the identified shape differences in anatomically meaningful terms of organ development and deformation. For each example in the input space, we derive a discriminative direction that corresponds to the differences between the classes implicitly represented by the classifier function. For morphological studies, the discriminative direction can be conveniently represented by a deformation of the original shape, yielding an intuitive description of shape differences for visualization and further analysis.

Based on this approach, we present a system for statistical shape analysis using distance transforms for shape representation and the Support Vector Machines learning algorithm for the optimal classifier estimation. We demonstrate it on artificially generated data sets, as well as real medical studies.

Figure: Deformation of the right hippocampus example from the schizophrenia group "towards" normal control group. The color coding is used to indicate the direction and the magnitude of the deformation, changing from blue (inwards) to green (no deformation) to red (outwards). [Image courtesy of Polina Golland].

James Gee (University of Pennsylvania)

Title: Non-Rigid Tensor Registration

Abstract: In this talk we motivate and discuss the problem of registering diffusion tensor magnetic resonance images. These images contain orientational information that must be handled appropriately when the image is transformed spatially. We present solutions for global transformations of 3-D images up to 12-parameter affine complexity and indicate how our methods can be extended to higher order transformations. We also discuss relevant comparative measures of similarity between diffusion tensors and a new formulation for their implementation.

Gary Christensen (Department of Electrical and Computer Engineering, University of Iowa)

Title: Inverse Consistent Medical Image Registration

[Tutorial Notes, 1.4 MB, .pdf]

Abstract: Landmark-based, thin-plate-spline image registration is one of the most commonly used methods for non-rigid medical image registration and anatomical shape analysis. It is well known that this method does not produce a unique correspondence between two images away from the landmark locations because interchanging the role of source and target landmarks does not produce forward and reverse transformations that are inverses of each other.

In this talk, we present two new image registration algorithms that minimize the thin-plate spline bending energy and the inverse consistency error---the error between the forward and the inverse of the reverse transformation. The landmark-based consistent thin-plate spline algorithm registers images given a set of corresponding landmarks while the intensity-based consistent thin-plate spline algorithm uses both corresponding landmarks and image intensities.

Results are presented that demonstrate that using landmark and intensity information to jointly estimate the forward and reverse transformations provides better correspondence than using landmarks or intensity alone.