(Radiographics. 2002;22:437-448.)
© RSNA, 2002
Medical Image Segmentation with Knowledge-guided Robust Active Contours1
Riccardo Boscolo, MS,
Matthew S. Brown, PhD and
Michael F. McNitt-Gray, PhD
1 From the Department of Electrical Engineering, University of California at Los Angeles (R.B.), and the Department of Radiological Sciences, UCLA School of Medicine, Box 951721, Los Angeles, CA 90095-1721 (M.S.B., M.F.M.-G.). Received April 4, 2001; revision requested May 31 and received November 27; accepted January 4, 2002. Address correspondence to M.S.B. (e-mail: mbrown@mednet.ucla.edu).
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Abstract
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Medical image segmentation techniques typically require some form of expert human supervision to provide accurate and consistent identification of anatomic structures of interest. A novel segmentation technique was developed that combines a knowledge-based segmentation system with a sophisticated active contour model. This approach exploits the guidance of a higher-level process to robustly perform the segmentation of various anatomic structures. The user need not provide initial contour placement, and the high-level process carries out the required parameter optimization automatically. Knowledge about the anatomic structures to be segmented is defined statistically in terms of probability density functions of parameters such as location, size, and image intensity (eg, computed tomographic [CT] attenuation value). Preliminary results suggest that the performance of the algorithm at chest and abdominal CT is comparable to that of more traditional segmentation techniques like region growing and morphologic operators. In some cases, the active contour–based technique may outperform standard segmentation methods due to its capacity to fully enforce the available a priori knowledge concerning the anatomic structure of interest. The active contour algorithm is particularly suitable for integration with high-level image understanding frameworks, providing a robust and easily controlled low-level segmentation tool. Further study is required to determine whether the proposed algorithm is indeed capable of providing consistently superior segmentation.
© RSNA, 2002
Index Terms: Computers • Images, digitization • Images, display • Images, processing
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Introduction
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The robust segmentation and labeling of anatomic structures on medical images is an important area of research. The increased number and availability of medical imaging modalities (eg, computed tomography [CT], magnetic resonance imaging, positron emission tomography) has yielded a concomitant increase in the demand for automatic or semiautomatic image interpretation tools designed to manage the large amount of information made available by these imaging techniques.
Segmenting anatomic structures on medical images and reconstructing their shape represents a particularly challenging problem due to the complexity and variability of human anatomy. Several classical image processing techniques (eg, multiple thresholding, region growing, morphologic filtering) have been applied to try to solve this problem, with variable outcomes (1,2). Such techniques tend to be unreliable when segmenting a structure that is surrounded by other structures with similar image intensity (eg, low-contrast structures). Moreover, these techniques typically make very limited use of the available knowledge of the underlying anatomy. User intervention is usually required to separate adjacent structures of similar image intensity. Kostis et al (3) and Zhao et al (4) applied image processing techniques specifically to the problem of lung nodule segmentation. Both studies clearly demonstrate the importance of selecting the correct segmentation algorithm parameters and the need for user intervention, at least in the initialization phase. More recently, several model-based image segmentation methods have been investigated and successfully implemented (2,5,6). The common goal of all these methods is to integrate available a priori knowledge with sophisticated image processing techniques. In general, these types of frameworks are somewhat successful as automatic or semiautomatic segmentation tools and have countless applications in medical image analysis.
In this context, deformable active contours have been the subject of much research because of their potential to overcome some of the limitations of classical image processing algorithms. The capability of combining image features with simple shape constraints, as well as robustness to image noise, make the use of active contours a very powerful technique for segmentation. As originally defined by Kass et al (7), a deformable contour or "snake" is an "energy-minimizing spline influenced by image forces that pull it towards features of interest, such as lines and edges." The main idea behind the active contour model is that the presence of an image feature depends not only on the value of the image at a given point in space or on its derivatives, but also on the spatial distribution of such features. Snakes incorporate this a priori knowledge by controlling parameters like the continuity and curvature of the contour, combined with local strength of features of interest.
Williams and Shah (8) and Amini et al (9) have tackled some of the problems that characterized the original model developed by Kass et al (eg, numeric instability and the tendency for points to group together around strong image features). Williams and Shah introduced a simplified and discretized version of the active contour model that exploits local optimization techniques to arrive at optimal solutions. In contrast, Amini et al developed a dynamic programming architecture that allows inclusion of a more general class of hard constraints in the energy minimization algorithm. Cohen and Cohen (10) developed an approach that uses internal pressure to "inflate" the contour and counterbalance the "shrinking" action of the internal forces. However, if the model parameters are not suitably adjusted, the model will not converge to the desired contour. Other investigators, such as Lobregt and Viergever (11), aimed at simplifying the model to improve its stability and controllability, whereas Gunn and Nixon (12) addressed the problem of the robustness of the snake implementation, proposing a dual active contour technique. Each of these approaches improved the active contour method and made it more stable but still has certain limitations and requires manual placement of the initial contour.
In this article, we present a framework for integrating the active contour model with available a priori knowledge in an attempt to show that combining a higher-level image understanding system with a lower-level contouring method may contribute to the success of a fully automated, robust image segmentation system.
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Knowledge-based Segmentation Framework
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Several types of knowledge-based segmentation frameworks have been designed and successfully implemented (2). In particular, the framework described in a number of studies by Brown et al (13–16) represents a suitable candidate to serve as the high-level image understanding system. In this framework, an anatomic model (knowledge base) of a specific volume of the human body is stored as a semantic network. Each node of the network represents an anatomic region that is described in terms of parametric features (eg, size, volume, image intensity) and spatial relationships to other nodes in the network (eg, inside of, outside of, part of, not part of, and so forth). To segment a given anatomic region, low-level segmentation routines, including region growing and morphologic operators, are used to extract three-dimensional (3D) candidate regions from the image. The best candidate is then selected based on how well its features agree with the expected values as defined in the model. Fuzzy logic is used to generate a confidence score for each candidate based on the numeric feature values, and the candidate with the highest confidence score is selected.
This architecture proved effective in several studies conducted with chest radiographs and chest CT scans: Basic anatomic regions such as the lungs, tracheobronchial tree, chest wall, and mediastinal area were successfully recognized across different data sets (13–16). More complex tasks such as the identification of lung lesions were accomplished by introducing relatively simple extensions into the anatomic model. The low-level image segmentation is performed with a combination of gray-level thresholding, 3D region growing, and morphologic operators. These conventional algorithms are spatially constrained with information from the knowledge base. The performance of the system may be limited in cases in which the information available from the model cannot be fully transferred to the segmentation algorithms. For example, information regarding shape and texture is not used to guide the simple image segmentation operators. This is not a limitation of the knowledge-based architecture but rather of the tools currently embedded in it.
Active contours represent a natural extension of the set of tools currently available for the system described by Brown et al (13). Their attractiveness derives not only from the intrinsic robustness to image noise and low contrast but also from the capability to enforce constraints from a specific model. The main objective of this study was to develop a framework for efficiently transferring the information made available by the knowledge base to the deformable model.
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Active Contour Model
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An active contour is essentially a set of points describing a curve in two dimensions (2D) whose characteristics are controlled by an energy functional. The energy-minimizing instance of this curve results in the final segmentation. The purpose of this functional is twofold. On one hand, the energy term should be smaller when the contour lies in proximity to features of interest on the image. For example, in the segmentation of an anatomic structure, the functional should be minimized when the active contour coincides with the edges of the structure. However, the boundaries of a structure are not always well defined. In particular, image noise or poor image contrast can result in inaccurate edge definition. This type of problem is overcome in the active contour model with the inclusion of additional terms in the energy functional. These terms are responsible for controlling, for example, the continuity and smoothness of the contour. Further details of the mathematic formulation of the active contour method are provided in the Appendix.
The novelty of this study consists in the introduction of additional constraints into the energy functional that enforce consistency of the active contour with the a priori knowledge regarding the structure to be segmented. There are several properties we would like to be able to transfer from the a priori model to the contour. The following paragraphs describe a set of energy functionals that enforce different types of constraints on contour evolution: center, size, average image intensity, and aspect ratio.
Center
With an appropriate energy functional, the contour location, defined in terms of its centroid (cx, cy), can be forced to be close to the expected location (according to the knowledge base) of the structure to be segmented.
Size
The optimal size of a contour that is expected to be approximately circular can be defined in terms of the equivalent radius. Aspect ratio (described later) is used in an energy term that weights deviation from this expected circularity.
Average Image Intensity
The expected pixel values of a structure to be segmented can also be determined by introducing an applicable term into the energy functional. For example, the average pixel value inside the contour can be evaluated and compared with expectations defined in the knowledge base.
Aspect Ratio
The aspect ratio (AR) of the model can be controlled by adding a term such that AR = ly/lx, where lx and ly are the lengths of the principal axes of the contour. This term takes into account the deviation from circularity, which shape is assumed when estimating contour size.
The set of possible features that can be transferred to the model from the a priori information is not limited to those just described, and more sophisticated constraints on contour shape and texture can be enforced.
Within the energy functional, different weightings are applied to each term. Typically, these weightings are assigned on the basis of some heuristic criteria. In the framework described in this study, the high-level process controls the selection of these parameters. For example, if the structure to be segmented is known to have sharp contour irregularities (eg, spiculations, corners), the automated system decreases the weight of the curvature term that enforces smoothness, thereby allowing abrupt variation in the local direction of the contour.
The energy minimization algorithm implemented in this framework is based on the "greedy" algorithm developed by Williams and Shah (8). If the optimization procedure is to converge correctly to the global minimum energy (ie, optimal contour position), the algorithm must avoid local minima during its iterations. The knowledge-based system controls the contour initialization process so that the contour is automatically placed in the neighborhood of the global optimum, reducing the likelihood of incorrect convergence to local minima of the energy function.
Once the high-level process has completed contour initialization, energy minimization is carried on locally, updating the location of the contour points one at a time. The changes in total energy associated with moving a given contour point to locations within a 5 x 5 neighborhood are calculated, and the update resulting in the lowest energy value is selected. A single iteration of the algorithm is complete once all the points in the contour have been updated. Convergence of the algorithm is attained once the total energy value falls below a designated threshold.
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Results
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The performance of the knowledge-guided active contour method was tested on several CT data sets. In particular, we investigated the segmentation of lung nodules on chest CT scans and of the kidneys on abdominal CT scans. Chest CT scans were acquired with 1–10-mm collimation and reconstructed contiguously. Abdominal CT scans were acquired with 3–5-mm collimation and reconstructed with 50% overlap. The anisotropy of these data sets did not allow use of a fully 3D active contour model. Instead, a 2D model was developed in which consistency across sections is enforced, adding an extra term to the energy functional. This extra term ensures that excessive deviations from the average of the contour centroids are penalized.
Figure 1 demonstrates the results of applying the knowledge-based segmentation technique to a chest CT scan (for convenience, only one section of an 18-section set of 3D images is shown). The fully automated system correctly identifies different anatomic regions of interest such as the chest walls, airspace, mediastinal region, and areas of increased attenuation within the airspace. The anatomic regions are segmented approximately, thereby serving as crude landmarks to guide the segmentation of structures of interest. In particular, the mediastinal region is generically defined as the area "between" the lungs because, in this specific example, the goal is accurate identification of the airspace and of candidate nodules within it. Therefore, the region growing is constrained to include all voxels between the endpoints of the lungs on each horizontal line; thus, the mediastinal region appears with flat horizontal borders and includes part of the spine.
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Figure 1a. Segmentation results produced by applying the knowledge-based method to a chest CT scan. Different regions of interest are automatically identified without user supervision: the chest wall (a), airspace (b), and approximate mediastinal region (c) and areas of increased attenuation within the airspace (d).
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Figure 1b. Segmentation results produced by applying the knowledge-based method to a chest CT scan. Different regions of interest are automatically identified without user supervision: the chest wall (a), airspace (b), and approximate mediastinal region (c) and areas of increased attenuation within the airspace (d).
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Figure 1c. Segmentation results produced by applying the knowledge-based method to a chest CT scan. Different regions of interest are automatically identified without user supervision: the chest wall (a), airspace (b), and approximate mediastinal region (c) and areas of increased attenuation within the airspace (d).
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Figure 1d. Segmentation results produced by applying the knowledge-based method to a chest CT scan. Different regions of interest are automatically identified without user supervision: the chest wall (a), airspace (b), and approximate mediastinal region (c) and areas of increased attenuation within the airspace (d).
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Figure 2 shows the main steps of the knowledge-guided active contour algorithm. The knowledge-based system automatically identifies areas of increased attenuation within the airspace (Fig 2a) and looks for possible nodule candidates. Once a candidate is identified (Fig 2b), information about its size and location is used to initialize the active contour (Fig 2c). The additional a priori knowledge about the shape and aspect ratio of the nodule is also transferred to the deformable model by means of the energy function terms described previously. Figure 2d shows the final segmentation result.
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Figure 2a. Main steps of the knowledge-guided active contour algorithm. Images show how the system automatically identifies areas of increased attenuation within the airspace (a) and a nodule candidate (b), automatically initializes the active contour according to the size and location of the possible nodule (c), and generates the final segmentation result (d).
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Figure 2b. Main steps of the knowledge-guided active contour algorithm. Images show how the system automatically identifies areas of increased attenuation within the airspace (a) and a nodule candidate (b), automatically initializes the active contour according to the size and location of the possible nodule (c), and generates the final segmentation result (d).
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Figure 2c. Main steps of the knowledge-guided active contour algorithm. Images show how the system automatically identifies areas of increased attenuation within the airspace (a) and a nodule candidate (b), automatically initializes the active contour according to the size and location of the possible nodule (c), and generates the final segmentation result (d).
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Figure 2d. Main steps of the knowledge-guided active contour algorithm. Images show how the system automatically identifies areas of increased attenuation within the airspace (a) and a nodule candidate (b), automatically initializes the active contour according to the size and location of the possible nodule (c), and generates the final segmentation result (d).
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Figure 3 shows the nodule candidate on four adjacent sections as recognized by the original knowledge-based system with use of region-growing segmentation. The same nodule is displayed in Figure 4, this time segmented with the active contour system. The latter results do not appear significantly different from the former, with the active contour including some airspace.
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Figure 3. Segmentation of an isolated lung nodule with the original knowledge-based system by means of a combination of region growing and morphologic operators. Images represent four adjacent 1-mm-thick sections.
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Figure 4. Segmentation of the same isolated lung nodule as in Figure 3 produced with the knowledge-guided active contour algorithm. The active contour model appears to be slightly more sensitive to the jaggedness of the nodule boundaries, resulting in the inclusion of some airspace.
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Figure 5 shows segmentation of a nodule in contact with the lung walls performed with the original knowledge-based system. Figure 6 demonstrates that the active contour algorithm seems to be capable of improving the segmentation result.
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Figure 5. Segmentation of a nodule in contact with the lung walls produced by means of a combination of region growing and morphologic operators. Although the segmentation is fairly accurate, part of the nodule tissue is not included on the first two images. This case is particularly challenging because the nodule is in contact with the chest wall.
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Figure 6. Segmentation of the same nodule as in Figure 5 produced with the knowledge-guided active contour algorithm. The results appear slightly more accurate than those shown in Figure 5: The active contours completely enclose the nodule tissue on all four images.
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The significance of the method becomes more clear when one considers the results of an attempt to segment a nodule in contact with the mediastinum via a large vessel (Figs 7, 8). The original knowledge-based system yields satisfactory results on only two of the four sections; it is incapable of segmenting the lesion without "flooding" into the mediastinum (Fig 7). Morphologic operators cannot be applied automatically to reliably segment lesions that are in contact with the mediastinum because, unlike the smooth chest wall, the mediastinum has irregular boundaries. On the other hand, the active contour algorithm correctly identifies and segments the lesion on all four sections (Fig 8).
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Figure 7. Segmentation of a nodule in contact with the mediastinum via a large vessel produced by means of a combination of region growing and morphologic operators. Segmentation is particularly challenging in this case because of the large connecting vessel. The region-growing algorithm is unsuccessful on two of the four images because of the absence of a true boundary between the nodule and the mediastinum.
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Figure 8. Segmentation of the same nodule as in Figure 7 produced with the knowledge-guided active contour algorithm. The algorithm identifies and segments the nodule on all four images. The curvature constraints prevent the contour from assuming the tubular shape of the connecting vessel, which is therefore not included in the segmentation. A dark area that appears to be part of an airway is included within the final contour on the first three images; this finding is due to the fact that our active contour model is sensitive to the image edges rather than to the absolute intensity values.
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To demonstrate the effectiveness of the framework in segmenting different types of anatomic structures, we also tested the system on some CT scans of the abdomen. The goal was to accurately segment the kidneys. This task is made particularly challenging by the small gradient in attenuation level between the kidney and the neighboring organs (liver and spleen). Figure 9 demonstrates segmentation of the kidney obtained with the original knowledge-based technique by means of a combination of region growing and morphologic operators (17). The results obtained with the knowledge-guided active contour method are comparable (Fig 10) but somewhat less conservative in that more of the renal structure is correctly segmented.
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Figure 9. Segmentation of a kidney produced with the original knowledge-based method by means of a combination of region growing and morphologic operators. The knowledge-based system provides accurate segmentation of the kidneys when these standard image processing techniques are used. A small section of the parenchyma is not included in the final segmentation result.
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Figure 10. Segmentation of the same kidney as in Figure 9 produced with the knowledge-guided active contour algorithm. The algorithm is capable of contouring the kidneys completely and accurately and generates results that appear somewhat less conservative than those shown in Figure 9.
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Demonstration of the System
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The knowledge-based active contour method was demonstrated as part of an infoRAD exhibit at the 86th Scientific Assembly and Annual Meeting of the Radiological Society of North America in 2000 (18). The software was "ported" to the Windows environment (Microsoft, Redmond, Wash) running on a Pentium III (Intel, Santa Clara, Calif)–based personal computer, and a simple graphical user interface was built to allow the user to experiment with the knowledge-based segmentation framework on some given CT data sets.
The graphical user interface was built with standard Microsoft Foundation Class libraries, and the C++ source code was compiled with Microsoft Visual C++. Figure 11 shows the main screen, on which the knowledge-based segmentation results can be displayed using different colors for different anatomic structures.
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Figure 11. Segmentation of the region of the mediastinum produced with the original knowledge-based segmentation system. The small pop-up window on the right is used to select the anatomic region of interest to be visualized. The approximate segmentation of the region of the mediastinum is shown in bright white.
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Once identification of the various anatomic structures is complete, the user has the option of examining the different segmented structures or proceeding with the automatic segmentation of a structure using the active contour technique. The system shows the initial placement of the contour for a particular structure and then runs the energy minimization procedure either automatically until convergence or step-by-step following the user prompt. Figure 12 shows four steps in contour evolution on a single section during segmentation of a lung nodule.
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Figure 12. Four steps in contour evolution in the segmentation of a lung nodule in contact with the mediastinum with the knowledge-based active contour method. The algorithm can be run automatically until convergence or step-by-step, depending on user preference. Contour initialization is performed automatically.
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Conclusions
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We have developed a novel segmentation approach that combines a knowledge-based system with a sophisticated active contour model. Visual inspection of the preliminary results suggests that the performance of the algorithm is comparable to that of more traditional segmentation techniques like region growing and morphologic operators. In some cases, the active contour–based technique may outperform standard segmentation methods due to its capacity to fully enforce the available a priori knowledge concerning the anatomic structure of interest. Further study is required to determine whether the proposed algorithm is indeed capable of providing consistently superior segmentation.
The type of a priori knowledge that was applied in connection with the active contour method represents only a small fraction of the available domain knowledge. More detailed information about the shape and texture of the anatomic structure of interest could be transferred to the model by applying methods similar to those described in this article.
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Appendix
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Typically, the contour v(s) and the energy functional E in the active contour algorithm are defined (in 2D) as follows:
and
where the subdivision of E into internal energy (Eint) and external energy (Eext) is merely a convention and reflects the fact that the functional depends on both the actual image features (through Eext) and the location of the points in the contour (through Eint). The optimal contour is the one that minimizes the energy functional for a specific image and a specific parameter selection. A typical choice for Eint in Equation (A2) is
where the first term in the integral is used to enforce the continuity of the contour and the second term constrains the curvature between adjacent points. The parameters 
(s) and ß(s) are the coefficients that weigh the two components at each specific spatial location. The external energy is usually obtained from some transformation of the image data and is designed to be small in proximity to features of interest. An example is the negative of the absolute value of the image gradient (
I) as defined in Equation (A4), which tends to attract the contour toward the image edges:
In the active contour model that we developed, the internal energy functionals are closely related to those defined by Williams and Shah (8). The functional terms defined so far are standard in the literature concerning the active contour method.
This article focuses on the introduction of additional constraints into the energy functional that enforce consistency of the active contour with the a priori knowledge regarding the structure to be segmented. Following a convention also found in a study by Storvik (19), we express these constraints in terms of the expected value of a function of the contour points and model the uncertainty about this expected value as a probability density function. Typically, the deviation from the desired value can be represented with a Gaussian probability density function, with variance selected to quantify the uncertainty. The most general formulation is given in Equation (A5), in which the functional f(v) (generally nonlinear) expresses some property of the model as a function of the contour coordinates, and f0 = Ef(v) is the expected value derived from the knowledge base for this particular realization of the contour. The probability density function f can be written as follows:
Because we are working with energy functionals rather than probability density functions, a reasonable choice for an energy term derived from the probability density function in Equation (A5) is
This functional is minimized for f(v) = f0, where it is equal to 1, and increases monotonically to infinity for values either smaller or larger than f0. This functional is used to enforce the constraints described earlier in the section entitled "Active Contour Model."
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Footnotes
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Abbreviations: 3D = three-dimensional,
2D = two-dimensional
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References
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Abstract
Introduction
