Generalized pixel profiling and comparative segmentation with application to arteriovenous malformation segmentation
Graphical abstract
Highlights
► New method for segmenting the inner structure of arteriovenous malformation (AVM). ► Pixel profile function values compared to the current pixel value. ► Linear combination of basic functions generates optimal profile function. ► AVM blood vessels (feeding arteries, draining vein and nidus) delineated in detail. ► Accurate AVM volume calculation.
Introduction
Segmentation and visualization of brain blood vessels is of great importance in clinical practice for diagnostic and surgical purpose. A special interest is taken in visualization and segmentation of aneurysms and cerebral arteriovenous malformation (AVM), which is a collection of malformed blood vessels, representing a threat of intra cranial hemorrhage (i.e. internal head bleeding). For surgical planning, the position, geometry and volume of the AVM, as well as the position of feeding arteries and draining veins is of utmost importance. There exist a number of methods and applications for finding and visualizing the position of ingoing arteries and outgoing veins (Coenen et al., 2005, Säring et al., 2007), but without giving a deeper insight into inner structure of the AVM. Examining the inner structure of the malformation is of great interest in embolization (a surgery to insert coils or glue for making occlusion in the AVM).
Most of the vessel extraction techniques used in clinical practice today are semi-automatic (Kirbas and Quek, 2004, Lesage et al., 2009, Yaniv and Cleary, 2006), relying on user interaction to incorporate expert prior knowledge. A large number of studies treat visualization of cerebral aneurysms and malformations, as well as blood vessels of brain in general (Antiga and Steinman, 2006, Bullitt et al., 2001, Forkert et al., 2009, Piccinelli et al., 2009), however, these visualizations are usually not capable of fine delineation between the feeding arteries, draining vein and nidus, which is exactly the focus of this work. Digital subtraction angiography (DSA) methods (Coste et al., 2001, Söderman et al., 2000) have proven to be crucial in surgery of AVMs (Zhang et al., 2003), and validation methods for this imaging modality have also been developed (Berger et al., 2008). However, DSA methods (Coste et al., 2001, Söderman et al., 2000), while efficient in determining volume of the AVM, are not able to delineate the inner structure of the malformation. Diffusion tensor (DT) fiber tractography has also been applied in AVM examination and is more suitable for therapeutic stages (Okada et al., 2007). The resolution typically used in computed tomography angiogram (CTA) brain vessel imaging is often not sufficient for visualization of the AVM structure, which consists of large number of intertwined vessels in a very small volume. Segmentation of blood vessels is a difficult task in general, because of varying structure, size and direction of blood vessels in a 3-D image and these problems escalate in the case of the AVM segmentation, because of its highly unpredictable structure. Therefore, prior knowledge concerning the position of blood vessels and even their number in the malformation is limited. Shape and flow driven methods optimized for segmenting tubular structures (Cebral et al., 2005, Castro and Cebral, 2007, Hoi et al., 2004, Nain et al., 2004) are able to segment vessels going in or out of the malformation, but are not applicable for segmenting complex structure (such as the nidus of the malformation) at lower resolutions. Active contours (Shang et al., 2008) give good results when segmenting blood vessels in images of sufficient resolution, which is not the case in AVM segmentation. Adaptive thresholding and connected components methods (De Bock and Philips, 2010) have difficulties in dealing with high variety of pixel intensities. In this paper we propose a new segmentation method based on multiscale operators, taking into account both local spatial context of the pixel and pixel intensities. The advantage of our approach is that we develop methods for automatic parameter setting, which results in little manual intervention from the user.
The classical morphological operators (Serra, 1982, Soille, 1986) make use of a structuring element (SE) of a given shape (like square or circle) and size. The most common SE shapes are square and circle-like neighborhoods (these can be defined as equidistant neighborhoods by using different metrics). The SE shape and size can also be adaptive, varying from pixel to pixel, like in (Cheng and Venetsanopoulos, 2000). In remote sensing applications morphological profile methods (Bellens et al., 2008, Pesaresi and Benediktsson, 2001, Plaza et al., 2004) were shown effective. These methods estimate object boundaries by examining the values of morphological operators at different size. The (Qian et al., 2009) approach is similar to ours in sense of examining the polar neighbor intensity profile of a voxel in order to determine the vesselness measure for characterizing vascular structures. A vesselness measure is usually obtained on the basis of eigenvalues of the Hessian as in (Frangi et al., 1998), where an assumption is used that a single cylinder exists around each voxel. However, the vesselness measure is hard to determine in case of complex AVM structures. In this work, we develop a generalized profiling approach (based on our previous segmentation approach in Babin et al. (2009)) and demonstrate its effectiveness in AVM segmentation.
The main novelties of our work in comparison to existing morphological profiles (MP) are the following. Firstly, we define more general SE shaped by variation of two parameters (instead of only one “size” parameter in classical MPs). Secondly, we define more general operators as opposed to only minimum and maximum operators in MPs. Finally, another important novelty of our work is the introduction of comparative segmentation principle, which is used to measure calculated profiles and obtain final segmentation. The experimental results show a clear benefit from both of these extensions to classical morphological profiles. Moreover, morphological profiling was previously reported in remote sensing applications only and to our knowledge this is the first application of this type of methods for blood vessel segmentation.
The main idea of our generalized profiling method is to measure the extent to which properties of interest in a neighborhood with certain shape and size relate to the central pixel. For example, if a pixel belonging to a bright object in the image is considered, we want to determine to what size of its neighborhood is the pixel brighter than its considered neighborhood, where the “brightness” of a neighborhood can be defined using variety of functions. The new pixel value will be the size of the neighborhood to which the described condition is fulfilled for all smaller neighborhood sizes. The final segmentation is done by thresholding the transformed image by a predefined threshold value. We propose a method for automatic selection of the optimal function as a combination of elementary filters (basic functions), which we calculate for each slice separately. The principle is similar to AdaBoost classifiers (Freund and Schapire, 1995), where a number of weak classifiers is combined into a stronger classifier.
The paper is organized as follows. Section 2 gives an insight in related work on morphology and morphological profiles. In Section 3 we explain the idea of generalized profiling and proposed comparative segmentation method. Section 4 presents the results of the proposed algorithm applied to the CTA images of cerebral AVM and Section 5 concludes this work.
Section snippets
Notation and related work
Throughout the work we use the following notation. Lowercase letters denote scalars and functions. Morphological functions are marked by lowercase Greek letters ε, δ, γ and φ for erosion, dilation, opening and closing, respectively. Uppercase Latin letters indicate a set of values (e.g. D and S), and bold uppercase letters indicate vectors or matrices (e.g. Π, and ). The pixel coordinates will be denoted by a single index p, like in raster scanning.
Mathematical morphology (Serra, 1982,
Material and methods
The proposed approach is a generalization of the morphological profiles (Bellens et al., 2008, Pesaresi and Benediktsson, 2001, Plaza et al., 2004). Although we construct our method on the discrete 2-D space, the proposed idea is applicable to a discrete space of any dimension.
Results and discussion
In our experiments we use phantom data and real CTA data sets, where we compare our method with 8 different segmentation approaches.
Conclusion
We have introduced in this work a novel method of generalized pixel profiling and comparative segmentation with an application to segmentation of 3-D CTA images of arteriovenous malformation. Our method generalizes morphological profiles, that were previously shown effective in remote sensing applications. The results demonstrate the effectiveness of the proposed method, especially on low resolution images with high intensity variations. Using the presented profiling method we have designed an
Acknowledgment
This research is supported by IBBT and IUAP Project NIMI P6/38 financed by the Belgian Science Policy institute (BELSPO). B. Goossens is a postdoctoral research fellow of the Fund for Scientific research in Flanders (FWO). We thank the reviewers for thoroughly reviewing our paper and providing a clear and helpful advice for its improvement.
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These authors are postdoctoral research fellows of the Fund for Scientific research in Flanders (FWO).