Effective Image Segmentation using Composite Energy Metric in Levelset Based Curve Evolution

Accurate segmentation of anatomical organs in medical images is a complex task due to wide inter-patient variability and several acquisition dependent artefacts. Moreover, image noise, low contrast and intensity inhomogeneity in medical data further amplifies the challeng. In this work, we propose an effective yet simple algorithm based on composite energy metric for precise detection of object boundaries. A number of methods have been proposed in literature for image segmentation; however, these methods employ individual characteristics of image including gradient, regional intensity or texture map. Segmentation based on individual featres often fail for complex images, especially for medical imagery. Accordingly, we propose that the segmentation quality can be improved by integrating local and global image features in the curve evolution. This work employs the classic snake model aka active contour model; however, the curve evolution force has been updated. In contast to the conventional image-based regional intensity statistics, the proposed snake model evolves using composite image energy. Hence, the proposed method offers a greater resistance to the local optima problem as well as initialization perturbations. Experimental results for both synthetic and 2D (Two Dimensional) real clinal images are presented in this work to validate the performance of the proposed method. The performance of the proposed model is evaluated with respect to expert-based manual ground truth. Accordingly, the proposed model achieves higher accuracy in comparison to the state-of-the-art region based segmentation methods of Lankton and Yin as reported in results section.


INTRODUCTION
of anatomical structures often makes task challenging. A simple benchmark for object differentiation in an image is edge or discontinuity measure as defined in Equation (1). Edge -based segmentation works fine for images having strong boundaries but ambiguous object boundaries are often over segmented as weak edges are surpassed during evolution.
where R 1 , … R n represent distinct regions in the image. It is important to mention that depending upon the nature and complexity of the imaging modality, a number of image features can be combined i.e. intensity and geometric for effective segmentation of object. In addition to the conventional edge and region based methods, some other techniques for object segmentation include threshold, clustering and watershed interpretation. Moreover, the idea of deformable contours is also used frequently which evolves based of partial differential equations to detect object boundaries.  Chan and Vese [4], Yezzi et. al. [5] and Roussan [6] reported successful implementation of region based segmentation.

RELATED WORK
However, intensity in homogeneity in medical images often leads to over segmentation in these methods as they rely on assumption of piecewise constant intensity which is often violated in medical data. To address the intensity variations in medical images, an efficient framework was proposed by Lankton and Tannenbaum [7]. Proposed framework named LRBAC (Localized Region Based Active Contours) demonstrates successful segmentation for heterogeneous images however the computational cost increases in relation to localization scope. Consequently, computational burden can be addressed by intelligent initialization and selection of localization radius but in practice it is difficult to place smart initializations for complex medical vasculature in presence of anomalies. A computationally robust model for heterogeneous imagery was proposed by Li et. al. [8,11] where the localized information was used at adjustable scales but the associated limitation of extreme dependency on initial mask demands certain prior information. Yin and Liatsis [9] proposed an efficient technique for hybrid energy based

PROPOSED METHOD
In Consequently, the integrated use of two terms in curve evolution leads to precise detection of object boundaries as total curve force can be computed as: Here F local and F global represent image-based local and global energy terms and  is constant, regulating the influence of the global energy component in overall curve evolution. A high value of  leads to capture sharp edges, whereas a low value minimizes the global influence. In this work,  has been set equal to 0.5 based on empirical evidence.

Modelling Local Energy
As an extension of Mumford and Shah [10] piecewise smoothness assumption, Chan and Vese proposed region based active contour model for image segmentation as defined in Equation (4): where C is the curve to be evolved, I(x) is input image, c 1 and c 2 represent interior and exterior mean intensities and  is regularization weight controlling the smoothness of contour. Level set formulation [12][13] expressed in Equation (5) is obtained by replacing unknown curve C with level set function  (often signed distance function is used for quick differentiation). The interior and exterior points of curve are obtained using Heaviside approximation (H) whereas curve itself is identified by using derivative of Heaviside function termed as Dirac delta ().
Energy optimization problem of Equation (5) is solved by a series of differential operations on Euler-Lagrange formulation as proposed in original work of Chan-Vese.
Using gradient descent method optimal change in level set function (can be calculated using Equation (6). For complete mathematical formulation, readers are referred to [4].
Due to the inherent problem of intensity inhomogeneity in medical images, we employed the localization model of Lankton and Tannenbaum [7] by using ball kernel of radius 5 pixels. This mask ensures to use constrained neighborhood in energy computation for moving curve as shown in Fig. 1(a-b). Mathematical presentation for kernel selection is defined in Equation (7).
Mean intensity inside and outside the contour in localized neighborhood is computed by applying ball mask and Heaviside function as follows: Final curve evolution equation using localized Chan-Vese energy model can be expressed by Equation (9) where I(y) represents localized image selected by mask.
By discarding the regularization term in Equation (9), localized curve driving force regulating the evolution can be written as Equation (10):

Modeling Global Energy
In contrast to Wang and Liatsis [9], where the global Consequently, the label image representing global behavior is used to compute global force component in bass based constraint region as follows: Finally, two components are combined to compute composite force metric responsible for curve evolution in our method as follows: Substituting the local curve driving force by composite force metric, Equation (13) can be rewritten as Equation (14) which defines the curve deformation force used in this work.

RESULTS
In this section we present segmentation results for   Fig. 4(c). Yin's hybrid method mistakenly labels some of the background pixels as part of object due to severe intensity shift, resulting in inaccurate segmentation as evident in Fig. 4(b). Similarly,

CONCLUSION
An effective yet simple image segmentation method has been proposed in this work that employs composite image force for optimal segmentation. In recent years, hybrid energy based curve evolution has been proposed, the curve evolution can be regulated by combining intensity whereas a very small value leads to local energy based segmentation results. The future work aims to compute the optimal value for  using regression, and to extend this work for 3D segmentation of coronary arteries in CTA volume which is part of an ongoing project in our centre.