Segmentation of carpal bones from CT images using skeletally coupled deformable models

https://doi.org/10.1016/S1361-8415(02)00065-8Get rights and content

Abstract

The in vivo investigation of joint kinematics in normal and injured wrist requires the segmentation of carpal bones from 3D (CT) images, and their registration over time. The non-uniformity of bone tissue, ranging from dense cortical bone to textured spongy bone, the irregular shape of closely packed carpal bones, small inter-bone spaces compared to the resolution of CT images, along with the presence of blood vessels, and the inherent blurring of CT imaging render the segmentation of carpal bones a challenging task. We review the performance of statistical classification, deformable models (active contours), region growing, region competition, and morphological operations for this application. We then propose a model which combines several of these approaches in a unified framework. Specifically, our approach is to use a curve evolution implementation of region growing from initialized seeds, where growth is modulated by a skeletally-mediated competition between neighboring regions. The inter-seed skeleton, which we interpret as the predicted boundary of collision between two regions, is used to couple the growth of seeds and to mediate long-range competition between them. The implementation requires subpixel representations of each growing region as well as the inter-region skeleton. This method combines the advantages of active contour models, region growing, and both local and global region competition methods. We demonstrate the effectiveness of this approach for our application where many of the difficulties presented above are overcome as illustrated by synthetic and real examples. Since this segmentation method does not rely on domain-specific knowledge, it should be applicable to a range of other medical imaging segmentation tasks.

Introduction

Degenerative joint disease is commonly attributed to alterations in joint loading and joint kinematics due to traumatic injury. In the wrist, despite widespread clinical awareness of dynamic and static wrist instability, little is known about the pathoanatomy and kinematics of these conditions. Patients may continue to be incapacitated by pain following stressful activities months after injury, even though radiographs and other static imaging studies appear normal. Characterizing the true 3D kinematics of the carpal bones following these ligament injuries would provide better insight for the development of diagnostic techniques, surgical treatment, rehabilitation, the design of prosthetic devices and more appropriate treatment strategies (Lee and Massear, 1993, Mayfield, 1984, Ruby et al., 1987, Savelberg, 1991, Savelberg et al., 1991, Savelberg et al., 1993).

Invasive methods for measuring 3D joint motion are common in orthopedic research. While instrumentation ranges from video to stereoradiogrammetry, all of the existing methods use specific landmarks (e.g. infrared reflectors or implanted tantalum balls) on each rigid body segment. Such methods have been used in vivo (Karrholm et al., 1989, Koh et al., 1992, Lafortune et al., 1992) to study the knee and hip, but the small size of the carpal bones of the wrist and the invasive nature of these methods limits the in vivo application. Our general approach to measuring 3D carpal motion in vivo requires registration of bone surfaces extracted from multiple CT volumes (Crisco et al., 1999). The extraction of these surfaces, in turn, requires robust and reliable segmentation methods. A key goal of this paper is to develop a segmentation technique suitable to this domain.

Medical image segmentation, however, has proved to be a challenging task. This is true, in particular, for the segmentation (and registration) of carpal bones in the wrist from CT images. While the segmentation of bones in X-ray and CT images is viewed to be a relatively straightforward task, carpal bone segmentation is difficult because the volumetric datasets contain irregularly shaped bones with small inter-bone distances relative to the resolution of CT imaging. A key fact is that bone tissue cannot be characterized uniformly: the outer layer of the bone tissue, or cortical bone, is denser than the spongy bone it encases. Thus, under CT imaging cortical bone appears brighter and smooth, while spongy bone appears darker and textured. In addition, due to the close spacing of some carpal bones and inherent blurring in CT imaging, the inter-bone space often appears brighter than the background (soft tissue), substantially reducing boundary contrast at these points. Finally, blood vessels resemble the background, creating gaps in the surface of bone images. In the image domain, these characteristics translate into four challenging areas for segmentation techniques (Fig. 1): (i) gaps in the cortical shell; (ii) weak or diffused bone boundaries due to the partial volume effect in CT imaging; (iii) textured areas corresponding to the spongy bone alternating between bone-like and tissue-like intensities; and (iv) the narrow inter-bone regions which tend to be diffused.

While it is possible for medical experts to segment these images by using thresholding or manual seeding, e.g., by using the ANALYZE package1 or similar tools, this process is highly labor intensive, considering the time required for accurate manual correction. Thus, the development and use of segmentation techniques that minimize user interaction is highly desirable. We have implemented and evaluated several techniques for the segmentation of carpal bones from a sequence of 2D CT images, including global thresholding (Weeks et al., 1984, James et al., 1992), statistical methods (Duda and Hart, 1973), seeded region growing (Adams and Bischof, 1994), deformable models like snakes (Kass et al., 1988), balloons (Cohen and Cohen, 1993), bubbles (Tek and Kimia, 1997), morphological watersheds (Vincent and Soille, 1991), and region competition (Zhu and Yuille, 1996). The experience with the use of these techniques in our domain has prompted us to combine three classes of these approaches in a single framework. Specifically, in one approach taken by Tek and Kimia (1997), numerous seeds are initialized, both inside and outside objects of interest, which then grow by image-dependent forces. The growing seeds merge in the absence of boundaries to form larger seeds, and finally slow down near boundaries, thus trapping the boundary between the inner and outer regions. The success of this technique is dependent on the existence of boundaries with sufficient contrast and symmetric initialization in the case of weak boundaries. This is due to the monotonic nature of growth: once a region has evolved beyond object boundaries it can no longer return to capture it. Region competition (Zhu and Yuille, 1996), on the other hand, also relies on the growth of seeds, but implements a local competition between growing seeds, once they have become adjacent. This local back and forth competitive movement of adjacent regions is based on a statistical decision depending on to which of these regions a point is more likely to belong. The central assumption underlying this scheme is that the growth of seeds leads to regions that characterize distinct areas. This assumption fails when the growing seeds in ‘waiting’ for other regions to arrive, acquire and encompass two statistically distinct domains. Seeded region growing (Adams and Bischof, 1994) avoids this difficulty by implementing a global competition among growing regions, but does not implement the local ‘back and forth’ competition between them, thus also not allowing for recovery from errors.

The approach presented in this paper combines these three ideas, namely, deformable models implemented in the curve evolution framework, local back and forth competition or region competition, and the global competition of seeded region growing, under one framework. The main idea is to rely on the inter-region skeleton as a predictor of boundaries resulting from the growth of current seeds. Assuming current growth conditions continue to hold, this predicted boundary couples two seeds and is used to affect their respective growth process by modulating their deformation speed: if a point on the pair of paths leading to the formation of a skeletal point is more likely to belong to one seed compared to another, then the former region should grow faster at that point to capture it. Region competition then becomes a special case, i.e., when the two regions become adjacent. The idea of global competition in seeded region growing is implemented by the long-distance competition among neighboring seeds, mediated by the inter-region skeleton, with the advantage that it eliminates the irrelevant interaction between the very distant seeds with other seeds in between.

This paper is organized as follows. Section 2 reviews our experience with some current segmentation techniques for carpal bone segmentation. In Section 3, we describe the skeletally coupled deformable model (SCDM). The implementation details are discussed in Section 4. The segmentation results and validation studies are reported in Section 5.

Section snippets

Segmentation of carpal bones: current approaches

We have investigated the use of several segmentation techniques for their specific use in the recovery of carpal bone surfaces from CT images. These methods include global thresholding (Weeks et al., 1984, James et al., 1992), statistical classification (Duda and Hart, 1973), seeded region growing (Adams and Bischof, 1994), region competition (Zhu and Yuille, 1996), deformable models like snakes (Kass et al., 1988), balloons (Cohen and Cohen, 1993), their curve evolution counterparts (Malladi

The skeletally coupled deformable model

Our proposed approach, the skeletally coupled deformable model (SCDM), can be viewed as a combination of three of the approaches presented above: curve evolution deformable models such as bubbles (Tek and Kimia, 1997), seeded region growing (Adams and Bischof, 1994), and region competition (Zhu and Yuille, 1996). Seeded region growing (Adams and Bischof, 1994) implements a ‘global competition’ in that every region simultaneously competes with every other. This competition is too global in the

Implementation of SCDM

We now discuss the details of implementing the framework described in Section 3. Several components are necessary to complete the implementation: (i) initialize seeds, (ii) characterize statistical properties of the seeds, (iii) compute inter-seed skeletons, (iv) couple boundary points through the inter-seed skeletons, (v) evolve seeds, and (vi) compute subpixel forces.

We first note that the evolving boundary must be represented at subpixel resolution. As the authors note in (Zhu and Yuille,

Results, evaluation and discussion

In this section we present the results of applying the SCDM method to synthetic images (Fig. 17), and to carpal bone segmentation (Fig. 16, Fig. 18, Fig. 19), especially to illustrate the performance of SCDM in the problem areas listed in Section 1, namely, gaps and weak edges, diffused edges, bone texture, and narrow inter-bone spaces. In order to segment an image using SCDM, one has to choose the user-specified parameters, namely, σd in the definition of λ (Eq. (7)), and parameters α, β in

Conclusion

In this paper, we have presented a segmentation method that combines the advantages of active contour models, region growing, and the global competition in seeded region growing as well as the local competition in region competition. The proposed method (SCDM) uses competition mediated by the inter-seed skeleton to modulate the growth of seeds. The skeletally mediated competition allows for long-range competition thus augmenting the region competition’s local competition (Zhu and Yuille, 1996).

Acknowledgements

We gratefully acknowledge the support of the Whitaker Foundation, NSF Grant IRI-9700497 and NIH grant AR44005. We are thankful to Dr. Peter-Arnold Weiss and Dr. Edward Akelman of Rhode Island Hospital for performing the validation tests.

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