A Survey of Three-Dimensional Modeling Techniques for Quantitative Functional Analysis of Cardiac Images - Advance Image Processing in Magnetic Resonance Imaging - page 284

There are a variety of inputs for model recovery: (1) multiple 2-D projection images,
(2) multiple oriented 2-D slices, (3) fully 3-D gray-level images, (4) 3-D point sets,
(5) phase-contrast velocity fields, and (6) MR tagging information.
In this survey we will compare the different methods with respect to the type
of model representation and the types of input data and features that the model is

recovered from. Table 9.1 , in which the different approaches are grouped according

to the type of model representation, summarizes this section.

9.4.1 S URFACE M ODELS

Many approaches to cardiac modeling focus on the endocardial (or epicardial)
wall. Three subcategories are proposed: (a) continuous models with either global,
local, or hierarchical parameterizations, (b) discrete models, and (c) implicitly
defined deformable models.

9.4.1.1 Continuous Models

In the early studies of cardiac images by 2DE and angiocardiography, cardiolo-
gists used simplified models of the LV in order to compute functional parameters
such as ventricular volume and mass from 2-D images. Most of the time, simple

ellipsoidal models were considered (see, e.g., Vuille and Weyman [ 14 ] and Dulce
et al. [ 46 ] for a comprehensive review of such models and a comparison of their

accuracy). In the last decades, however, approaches have appeared that make use
of 3-D acquisitions to reconstruct models varying from global parameterizations
of the LV surface [5,29,112,119-121,123,194], to hierarchically parameterized
models [9,114,116,136,150,160].

9.4.1.1.1 Global Approaches
In this category, we will discuss surface representations that are based on simple
geometric models. In general they can provide, with a limited number of global
parameters, a rough shape approximation. We also include in this category surface
representations obtained as series of basis functions with global support.
Cauvin et al. [112] model the LV as a truncated bullet, a combination of an
ellipsoid and a cylinder, that is fitted to the morphological skeleton of the LV.
Metaxas and Terzopoulos [195] have proposed superquadrics [196] to model
simple objects with a small number of parameters. Since the introduction of
superquadrics, several extensions have appeared in the literature. Chen et al. [118]
apply superquadrics with tapering and bending deformations to model the LV in
an integrated approach for image segmentation and shape analysis. The method
iterates between a region-based clusterization step [197], using statistics of image
intensity and gradient, and a shape-based step that checks the consistency between
the current segmentation and a superquadric model. Park, Metaxas, Young, and
Axel [6] have extended the flexibility of superquadrics by introducing parameter
functions: radial and longitudinal contraction, twisting, and long-axis deforma-
tion. These allow for a more detailed representation of the LV while retaining
the intrinsic geometrical meaning of the superquadric parameters. LV midwall