Biomedical Engineering Reference
In-Depth Information
less noise, and simple shape. However, the recovery of shapes of the human
body is more difficult compared to other imaging fields, and the original level set-
based method was not capable of solving the more complicated medical imaging
tasks. Thus, the segmentation methods in the level set framework were embed-
ded with many different powerful regularizers or propagating forces to improve
robustness. These methods can be classified in four categories: clustering-based
[31], Bayesian bidirectional classifier-based [35], shape-based [36], and coupled
constrained-based [32]. All these features did improve the robustness and accu-
racy in specific applications. However, these methods did not make full use of the
regional information combined with statistic shape information.
Motivated by combining regional and statistic shape information, many at-
tempts have been made in order to make good use of the global shape and regional
information, including work by Tsai et al. [37] and Rousson et al. [38]. In this
chapter, we will introduce this family of state-of-the-art medical image segmenta-
tion methods within a level set framework. The reader will gain an understanding
of what is the regional-based active contour in the level set framework, how it solves
the segmentation problem without using image gradient information, which is a
major control factor for other approaches, and how it could be implemented via
the level set method. In addition, the reader will be shown how statistical shape in-
formation can be extracted from a training procedure and combined with regional
information for segmentation.
The layout of the remainder of this chapter is as follows In the Section 2, a
short introduction to the level set method and the theoretical background appears.
Section 3 describes a typical application using the level set method. Section 4
deals with the relationship between active methods and level set methods. Addi-
tionally, active contours using the level set framework will be discussed in more
detail, including the mathematical background and applications in image process-
ing. Section 5 discusses a segmentation method in the level set framework using
regional information and prior shape knowledge in greater detail. Relative appli-
cations are also introduced. Finally, Section 6 offers a brief conclusion of to the
chapter and discusses the pros and cons of this method.
2.
BRIEF MATHEMATICAL FORMULATION OF LEVEL SETS
2.1. Front Evolution
Front evolution is a useful technique in image analysis for object extraction,
object tracking, etc. The basic idea behind the method is to evolve a curve to-
ward the lowest potential of a cost function, where its definition reflects the task
to be addressed and imposes certain smoothness constraints. Propagating inter-
faces occur in a wide variety of settings, and include ocean waves, flames, and
material boundaries. Less obvious boundaries are equally important and include
shapes against backgrounds, handwritten characters, and iso-intensity contours in
