Biomedical Engineering Reference
In-Depth Information
a method based on level sets and statistical models to improve the accuracy of
the vascular segmentation.
9.2 Stochastic Image Models
The objective of modeling in image analysis is to capture the intrinsic character
of images in a few parameters so as to understand the nature of the phenomenon
generating the images. Image models are also useful in quantitatively specifying
natural constraints and general assumptions about the physical world and the
imaging process. The introduction of stochastic models in image analysis has
led to the development of many practical algorithms that would not have been
realized with ad hoc processing. Approaching problems in image analysis from
the modeling viewpoint, we focus on the key issues of model selection, sampling,
parameter estimation, and goodness-of-fit.
Formal mathematical image models have long been used in the design of
image algorithms for applications such as compression, restoration, and en-
hancement [1]. Such models are traditionally low stochastic models of limited
complexity. In recent years, however, important theoretical advances and in-
creasingly powerful computers have led to more complex and sophisticated
image models. Depending on the application, researchers have proposed both
low-level and high-level models.
Low-level image models describe the behavior of individual image pixels rel-
ative to one another. Markov random fields and other spatial interaction models
have proven useful for a variety of applications, including image segmentation
and restoration [2, 3]. Bouman et al. [4], along with Willsky and Benvensite [5, 6],
have developed multiscale stochastic models for image data.
High-level models are generally used to describe a more restrictive class of
images. These models explicitly describe larger structures in the image, rather
than describing individual pixel interactions. Grenander et al., for example, pro-
pose a model based on deformable templates to describe images of nonrigid ob-
jects [7], while Kopec and his colleagues model document images using a Markov
source model for symbol generation in conjunction with a noisy channel [8, 9].
The following part of this chapter is organized as follows: First, a short
introduction about Gibbs random field (GRF) and Markov random field (MRF)
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