A Morphological Multiphase Active Contour for Vascular Segmentation
Victoria Lynn Fox, Mariofana Milanova, Salim Ganim Saeed Al-Ali · International Journal on Bioinformatics & Biosciences · 2013
International Journal on Bioinformatics & Biosciences (IJBB) Vol.3, No.3, September 2013 DOI: 10.5121/ijbb.2013.3301 1 A MORPHOLOGICAL MULTIPHASE ACTIVE CONTOUR FOR VASCULAR SEGMENTATION Victoria L. Fox1 , Mariofana Milanova2 , and Salim Al-Ali3 1Department of Applied Science, University of Arkansas at Little Rock, USA 2Department of Computer Science, University of Arkansas at Little Rock, USA 2Department of Computer Science, University of Arkansas at Little Rock, USA ABSTRACT This paper presents a morphological active contour ideal for vascular segmentation in biomedical images. The unenhanced images of vessels and background are successfully segmented using a two-step morphological active contour based upon Chan and Vese’s Active Contour without Edges. Using dilation and erosion as an approximation of curve evolution, the contour provides an efficient, simple, and robust alternative to solving partial differential equations used by traditional level-set Active Contour models. The proposed method is demonstrated with segmented data set images and compared to results garnered from multiphase Active Contour without Edges, morphological watershed, and Fuzzy C-means segmentations. KEYWORDS Active Contour, Morphology, Segmentation, Curve Evolution 1. INTRODUCTION Image segmentation is responsible for partitioning an image into sub-regions based on a desired feature and is an essential first task in many disciplines. Biomedical segmentation separates a medical image into different regions based upon pathology, anatomical structure, tissue classes, or many other inherent criteria. Often, these partitions are challenging to construct due to noise, low contrast, and image artefacts embedded in the figure. Methods for biomedical segmentation range from basic thresholding techniques [1],fuzzy logic approaches[2], to intricate partial differential equation models[3]. 1.1. Segmentation Techniques Using the assumption that regions of interest in an image are identifiable by separating intensity values, thresholding sets a value in which pixels above the threshold are grouped as the region of interest and pixels below are segmented as background pixels. For images with sharp edges, the method proves effective; once influenced by speckle or varying intensity levels, this approach loses its effectiveness. Region growing techniques build on the idea of thresholding by starting with a seed pixel known to be inside the region of interest. Using a threshold, the neighbourhood of the seed pixel is categorized as foreground or background. This process then performs a search through the pixels of the image classifying each. However, it is difficult to set a threshold which completely confines the region of interest and image leakage is a common shortcoming of the method [4]. International Journal on Bioinformatics & Biosciences (IJBB) Vol.3, No.3, September 2013 2 Fuzzy logic approaches have the advantage of allowing a pixel to belong to multiple clusters in the segmentation. To determine the clusters in which to assign a pixel, the algorithm sets a degree of belonging to each cluster for the pixel. Using this reasoning, a pixel on the edge of the region of interest will have a lower degree of belonging to the cluster than a pixel located near the center of the region of interest. The flexibility inherent in the method involves a trade-off in increased computational complexity. Additionally, noisy images cause a decrease in accuracy of the method [5] due to the nature of its clustering methodology. However, because of its flexibility, a popular fuzzy model – the Fuzzy C-means method – is widely used in segmentation of medical images. Segmentation methods based on minimization of energy functionals are commonly referred to as active contour methods and are popular due to their ability to always produce sub regions with continuous boundaries. The original active contour method, the snake, and its variations [6 -11] are disposed to large error results when dealing with “false” edges and noisy images. Several implementations, such as the minimal path technique by Cohen et al. [12-13] or dual snakes [14], and other similar methods [15-19], have been suggested to correct the error associated with challenging images. Unfortunately, all of these classical snakes and active contour models can only detect objects with edges defined by the gradient, and, as expected, the performance of the totally edge based methods is often inadequate. In the past two decades, the creation of a region-based functional that is less likely to give unwanted local minima when compared to the simpler, edge-based energy functions has been an area of active research. The region-based models [20], use information not only near the active contour, but image statistics both inside and outside the contour. In 2001, Chan and Vese [21], based a region-based functional on the Mumford-Shah functional to propose an active contour without edges. For the Active Contours without Edges, the functional of a curve ࣝ is (1) ܨܿ)ଵ , ܿଶ + ((ࣝ)inside(area ∙ ݒ + (ࣝ)length ∙ ߤ = (ࣝ , ߣଵ∫௦ௗ ࣝ ࣝ ௗ௨௧௦∫ଶߣ + ࢞݀‖ଵ) − ܿ࢞)ܫ‖ ,ݔ݀‖ଶ) − ܿݔ)ܫ‖ where the non-negative parameters ߤ ,ݒ ,ߣଵ , ߣଶ control the strength of each term and ܿଵ , ܿଶ provide the statistics of the interior and exterior regions of the contour, respectively.The energy in the Chan-Vese model can be seen as a particular case of the minimal partition problem, and the active contour is evolved in the level set formulation. With the introduction of the Chan-Vese model, region-based models could now handle objects with boundaries not necessarily gradientdefined. However, the computations for the pixel intensities within each region had a high computational cost. Many variations, such as [22] in which the simplicity of the k-means algorithm is utilized or [23] in which the algorithm directly calculates the energy alterations rather than solving the underlying PDE equations, have been proposed to improve the efficiency and accuracy of the Chan-Vese model. 1.2. Morphological Active Contours Morphological approaches for image processing include operators for denoising, enhancing, and simplification [24]. In the setting of segmentation, morphology has played a direct role in the evolution of a discrete scheme for the mean curvature motion of level sets [25]. In edge based active contour methods, the contour is composed of three components: a balloon force, a smoothing force, and an edge attraction force. Region based models also contain a balloon force and a smoothing force. Since such models take into account the statistics of the interior and exterior regions of the contour, there is a need to replace the edge attraction force with an image attachment term which provides the statistics needed for the formulation. International Journal on Bioinformatics & Biosciences (IJBB) Vol.3, No.3, September 2013 3 Recent studies in the effectiveness of using morphological operators to drive curve evolution focus primarily on the development of a sequence of erosions and dilations with specific structuring elements. In Jalba and Roerdink’s research [26], the authors detail a discrete approach to curve evolution. By iteratively eroding an input set embedding the initial curve by a morphological structuring element, the authors partially segmented a 2D vascular image and successfully segmented the bones of the human feet in a CT scan.The partial segmentation of the 2D image is explained as a result of sacrificing accuracy for efficiency. For Alarez et al., the study [27] is concerned with a full morphological scheme which approximates the action of the Geodesic Active Contour model curve evolution. The scheme is further extended in [25] to an approximation of Active Contours without Edges and turbo pixels. The morphological aspects of the scheme occur in the approximation of the balloon force and smoothing force for the Geodesic Active Contour model and primarily in the smoothing force in the Active Contour without Edges Model. As the morphological equivalent of the mean curvature motion, the smoothing force is comprised of a series linear structuring elements iteratively applied to the contour. In our approach, we also use a structuring element iteratively applied to the contour to approximate the mean curvature motion of a level-set active contour. Our structuring element is more straightforward in implementation than the series of linear structuring elements applied in [25] or [27] and we achieve more accurate results than Jalba and Roerdink’s 2D segmentation. The implementation of the scheme is efficient and robust to noise, blurred edges, and image artefacts in the medical images and easily be extended into three-dimensional applications. Finally, it relies upon region based statistics and can be fully automated in segmentation applications. 2. A MORPHOLOGICAL ACTIVE CONTOUR FORMULATION The underlying principle of mean curvature motion is the evolution of a simple closed curve whose points move in the direction of the normal with specified velocity [28]. Figure 1: Motion of a curve by curvature. The arrows represent the velocity at some points. Here, the velocity is a nondecreasing function of the curvature. In the level set framework, ࣝ is implicitly represented by a higher dimensional Lipschtiz function ߶ where ࣝ)} = ݔ ,ݕ)߶|(ݔ ,ݕ = (0}. The deforming curve is given by the zero level set at time ݐ of function ߶(ݔ ,ݕ,ݐ .(Evolving the curve in its normal direction with speed ܨ can be achieved by solving (2) డథ ,‖߶∇‖ܨ = డ௧ with the initial condition of ߶(ݔ ,ݕ ,0) = ߶(ݔ ,ݕ ,(where ߶(ݔ ,ݕ (is the initial signed distance function of ࣝ .For the Active Contour without Edges functional (1), the steepest descent method gives us this variation of (2): International Journal on Bioinformatics & Biosciences (IJBB) Vol.3, No.3, September 2013 4 (3) డథ ଶ − ܿܫ)]ߣ + ݒ − κ ∙ ߤ} = డ௧ ) ଶ − (ܫܿ − ଵ ) ଶ ]}‖∇߶‖. In solving for ߶, it is important to