Research and Projects: Geometric Deformable Model
Автор: Chris Wyatt
Источник: http://wfubmc.edu
Introduction
Medical image analysis has become an important topic within image processing and computer vision, developing into a distinct field with its own problems and solutions. The increasing reliance on imaging in the clinical setting, coupled with the vast amounts of data produced by modern medical imaging modalities, heightens the importance of developing analysis techniques to assist with clinical tasks. Such techniques are useful for diagnosis, treatment planning, surgical guidance as well as monitoring of disease. One of the main focus points of medical image analysis research has been segmentation of images into their meaningful anatomical and/or functional parts. This allows relevant information to be presented in a manner which facilitates accurate and timely interpretation.
A review of the segmentation literature reveals some desirable characteristics of a successful approach. First, model based approaches seem to be the most robust method for solving medical image analysis problems. Second, a widely applicable approach will have few parameters or be insensitive to their selection over a wide range of values. These two considerations are necessary, in part, due to the large variability in the type and quality of medical images.
One such method for segmenting a variety of two and three dimensional structures from medical images is a variational technique referred to as the geometric deformable model (GDM). A recent development in the image analysis field, the GDM has been shown by previous research to be a promising technique for segmentation in medical images. The GDM is based on an area minimizing gradient flow using a conformal (non-Euclidean) metric. This metric is defined using the image and derived features.
The GDM has the following advantages over other segmentation methods. It has the ability handle topological changes in a natural way, an important improvement over the physically based deformable models. The GDM uses local information with global constraints to locate a finite number of boundaries. Thus, it does not attempt to segment the entire image. The GDM also combines edge detection and edge linking into a single low-level process. In addition, the formulation of the model does not include many parameters and is derived in a principled manner using variational calculus.
The GDM, as it is currently implemented, performs best in high contrast, low noise situations where topological flexibility is necessary and a close estimate of the desired object boundary is available. However, the application of the GDM to date has revealed some limitations of the method. These limitations include theoretical concerns such as sensitivity to initialization, imaging parameters, and noise, as well as practical concerns such as computational complexity. In general, the GDM has difficulty extracting boundaries in low contrast regions with significant noise levels and blurring of edges. Such complications are typical in medical images and have, so far, prevented the GDM from widespread application as a segmentation tool for medical image analysis.
Three Dimensional Medical Imaging Modalities and the Clinical Task
The introduction of three dimensional imaging has led to many possibilities for abnormality detection and surgical planning in the clinical arena. With the advent of tomographic and magnetic resonance imaging it is possible to generate measurements on a 3D lattice. This allows the visualization of three dimensional structures and relationships in vivo and has already had a large impact on the way patients are diagnosed and treated. Each of the imaging modalities described below have a multitude of issues associated with their application, the most important of which is reconstruction. However, only a brief introduction to the four primary 3D modalities is given below with descriptions of some clinical uses. Also, note that these modalities, as described, are used for tissue level imaging, but that CT and MRI have also found uses in microscopy and spectroscopy.
The Geometric Deformable Model
The original deformable contour approach, used a physical model and a spline approximation to derive an algorithm for attracting a contour to edges in a regular way using a variational approach. This model required initialization of the original contour very close to the final desired contour. The later introduction of a constant expansion force reduced the dependence on initialization at the cost of accuracy. These physically based deformable models have been applied in many areas of computer vision and medical image analysis. Through these efforts, the model parameters such as the bending energy have been determined by experimentation for a number of applications, but no principled selection mechanism has been found. Another problem with the physically based deformable models is the implementation, which uses marker methods, an approach known by the numerical PDE community to have problems with topologically complicated situations.
The introduction of level set methods for tracking surfaces allowed the formation of a topologically adaptive deformable model. In this method, the concept of optimizing an energy functional is replaced by a curvature dependent gradient flow in which the contour propagates. The energy optimization concept was reintroduced and implemented using the level set numerical schemes in what is called the geometric deformable model (GDM) and has been applied to medical images.
The GDM is based on an area minimizing gradient flow using a conformal (non-Euclidean) metric. A family of surfaces is produced that iteratively move, in the steepest descent direction, toward a minimum of an area functional.