GIST: an interactive, GPU-based level set segmentation tool for 3D medical images
Introduction
Image segmentation is arguably the most widely studied problem in image processing, and the literature shows a plethora of image segmentation algorithms that rely on a diverse range of strategies such as statistics, differential geometry, heuristics, graph theory, and algebra. No one segmentation technique has emerged as being superior to all others in all circumstances, and thus it seems that the field of medical image processing will evolve to a state where researchers and clinicians have access to a set of segmentation tools, i.e. a toolbox, from which they can choose the particular tool that is best suited for their particular application.
A complete segmentation toolbox will include a set of general purpose tools as well as various specialized segmentation tools. General purpose tools are those that can be quickly launched and used as the need arises in a wide range of applications. Specialized tools rely on stronger assumptions about a specific modality, anatomy, or application. When properly trained, tuned, and applied we would expect specialized tools to perform better than general purpose tools – when all other factors, such as operator time and compute time, are equal. Among general tools, the most popular example, and the goal standard for many applications, is hand contouring, which entails a knowledgeable user (e.g. a medical doctor) creating a 2D curve, drawn by manipulating a mouse, on a sequence of slices to delineate the object of interest.
This paper describes a new, general-purpose segmentation tool that relies on interactive deformable models implemented as level sets. While level sets have demonstrated a great potential for 3D medical image segmentation, their usefulness has been limited by two problems. First, 3D level sets are relatively slow to compute. Second, their formulation usually entails several free parameters, which can be very difficult to correctly tune for specific applications. The second problem is compounded by the first. That is, users find it impractical to explore the space of possible parameter settings when an example result from a point in that space requires minutes or hours to generate. The tool presented in this paper alleviates these two problems by marrying a very fast solver with an intuitive speed function, a combination that allows a user to interactively guide a level-set based segmentation.
The software application described in this paper is called GPU-based interactive segmentation tool (GIST). GIST updates a level-set surface model at interactive rates on commodity graphics cards (GPUs), such as those that are commonly found on consumer-level personal computers. It can be applied to a general set of medical and biological applications by tuning several free parameters. Despite its general nature, we demonstrate the effectiveness of GIST by a quantitative comparison to a specialized tool and the associated gold standard for a specific problem: brain tumor segmentation (Kaus et al., 2001, Warfield et al., 2000). This paper makes the following contributions:
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A 3D segmentation tool that uses a new level-set deformation solver to achieve interactive rates (approximately 10–15× faster than previous solutions).
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An interactive mechanism for defining a level-set speed function that works on both scalar and multivalued (i.e. spectral) data.
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Quantitative and qualitative evidence that this interactive level-set approach is effective for brain tumor segmentation.
The remainder of the paper, which is an extended version of (Lefohn et al., 2003), is organized as follows. The next section gives some technical background and related work on level sets, GPUs, and segmentation evaluation methods. Section 3 describes the formulation of the level-set equations and the solution on the GPU. Section 5.2 presents qualitative results on various datasets and a quantitative analysis of the performance of the method for brain tumor segmentation. Section 6 summarizes this work.
Section snippets
Level sets
This paper relies on an implicit representation of deformable surface models called the method of level sets, proposed by Osher and Sethian (1988). The level-set method (see also Section 3) computes the motion of a moving interface by solving a partial differential equation (PDE) on a volume. The use of level sets has been widely documented in the medical imaging literature, and several works give more comprehensive reviews of the method and the associated numerical techniques (Sethian, 1999,
Level-set formulation and algorithms
We begin this section with a brief review of the notation and mathematics of level-set methods and describe the particular formulation that is relevant to this paper. Comprehensive reviews of level-set methods are given in the literature (Sethian, 1999, Fedkiw and Osher, 2002).
An implicit model is a surface representation in which the surface consists of all points , where . Level-set methods relate the motion of that surface to a PDE on the volume, i.e. ,
Software application design
This section describes GIST, an interactive level-set segmentation tool, and the GPU implementation that makes it possible. It begins with a brief overview of the GPU-based level-set solver, describes the visualization of the volume data and surface models, and then describes the user interface to GIST. The complete description of the GPU level-set algorithm, including technical details of its implementation, is given in (Lefohn et al., 2004).
Results
This section presents results from the application of our GPU-based level-set segmentation tool to a range of scalar and spectral data. The evaluations in this section include qualitative and quantitative comparisons with hand contouring as well as two other user-assisted methods. We choose hand contouring as the main focus of the comparison for several reasons. First, it is, like the proposed method, a general purpose segmentation method. Second, the field at large considers hand contouring by
Summary and conclusions
A careful implementation of real-time visualization and a sparse level-set solver on a GPU provides a new tool, called GIST, for interactive 3D segmentation. Users can manipulate several parameters simultaneously in order to find a set of values that are appropriate for a particular segmentation task. The quantitative results of using this tool for brain tumor segmentation suggest that it is compares well with hand contouring and state-of-the-art automated methods. However, the tool as built
References (59)
- et al.
Deformable meshes with automated topology changes for coarse-to-fine 3D surface extraction
Medical Image Analysis
(1999) - et al.
Fronts propogating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulations
Journal of Computational Physics
(1988) - et al.
A PDE based fast local level set method
Journal of Computational Physics
(1999) - et al.
Watershed-based segmentation of 3D MR data for volume quantization
Magnetic Resonance Imaging
(1997) - et al.
A direct approach to estimating surfaces in tomographic data
Medical Image Analysis
(2002) - Ackerman, M., Yoo, T., Jenkins, D., 2000. The visible human project: from data to knowledge. In: Proceedings of...
- et al.
A fast level set method for propogating interfaces
Journal of Computational Physics
(1995) - Beers, A.C., Agrawala, M., Chaddha, N., 1996. Rendering from compressed textures. In: Proceedings of the 23rd Annual...
- Bolz, J., Farmer, I., Grinspun, E., Schröder, P., 2003. Sparse matrix solvers on the GPU: conjugate gradients and...
- Buck, I., Foley, T., Horn, D., Sugerman, J., Fatahalian, K., Houston, M., Hanrahan, P., 2004. Brook for GPUs: stream...