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Spatiotemporal Shape Space Modeling for Cardiac MR Sequence Analysis

• Principal Investigator: Prof. Kim L. Boyer

Overview

This project addresses the problem of automated analysis and space-time generalized shape characterization of the cardiac cycle from magnetic resonance image sequences of the heart. We propose to represent the tissue boundaries, by type, in an abstract shape space, to be developed as an extension of the active shape models (ASMs) pioneered by Cootes, et al. and subsequently adopted and extended in work by Sonka and colleagues. These are examples of point distribution models, which describe a given shape as an average plus a linear combination of eigenvectors of the covariance matrix of feature point locations, as estimated from training data. N landmark points on the tissue boundaries are encoded by 3D spatial position and concatenated into an observation vector:

The shape space is an abstract vector space spanned by the eigenvectors of the covariance matrix: The expectation is estimated from training data, and a point in this space describes a given shape. We will extend

this formalism to characterize a given subject's cardiac cycle in a spatiotemporal shape space constructed from the four-dimensional space-time data hypervolume; that is, our landmark points are encoded by position and time (relative position in the cardiac cycle). In this manner we can capture, for instance, the behavior of a given chamber in terms of its shape evolution over the cycle. By representing each chamber (and/or other features, such as valves) in its own spatiotemporal shape space, we can characterize the action of the subject heart.

Training data can be used to discover "canonical" behavior classes to study the effectiveness of, and ultimately to indicate, various treatment options. By clustering data in the spatiotemporal shape space, we hypothesize that we can identify a reasonable number of canonical shape representatives. A hierarchically organized database, constructed along information-theoretical lines in an extension of our prior work with structural modelbases offers an effective means of addressing within-class variability, and an elegant method for accommodating subclass definitions within the database.

The eigenvalues that form the basis for shape description (the shape space), automatically provide the framework for organizing the database. Because we are not given an a priori set of classes, we will first build an intermediate shape space using the well-known principal components analysis (PCA). Unsupervised clustering in this space can be done using any of several well-known methods (K-means, mixture models, etc.). Clusters will correspond to the natural, canonical shape classes, or modes of tissue-type spatial distributions.

Work to Date

Prof. Boyer and his student, Paulo Gotardo, began work on this problem in mid-March 2004. Dr. Raman has provided some cardiac MR data to get us started. MR images display significant spatial variations in gain (baseline intensity). By developing our representation in terms of tissue boundaries, we circumvent this problem. Boyer's prior work with Raman and Sarkar in finding and organizing tissue boundaries in MR data forms a basis for identifying and focusing these interfaces across multiple scales. This allows us to extract the boundaries of major anatomical features of importance and focus them to a high-resolution representation while avoiding the clutter that arises in a direct fine-scale edge analysis. The optimal zero-crossing operator (OZCO), developed by Sarkar and Boyer, is a fast, recursive filter that extends readily to three dimensions, even for anisotropic sampling, as we have here. We propose to extend our earlier work in contour-based edge-focusing to (hyper) surfaces in 3D (4D) as part of this effort.

Below we present some selected frames from a cardiac cycle, and the preliminary (unfiltered, unfocused) edge maps produced by the OZCO.

Tentative Research Plan

1. Begin with fixed scale, hand-selected contours from OZCO
   1. Slice by slice, t by t
   2. Group edge contour segments across slices (fixed t )
   3. Group edge contour segments across time (fixed slice position)
2. Variable scale, focusing across scales
   1. Individual slices (t, position)
   2. Operate directly on grouped contours
3. Active Shape Models, contour (group) selection, class discovery of pathology
   1. 2D
   2. 3D
   3. 4D
4. Multiscale Active Shape Models?