A hybrid active contour model with structured feature for image segmentation
Introduction
Active contour models have been widely used in image processing and computer vision applications, especially in image segmentations. Depending on how object boundary is detected, active contour models can be categorized into parameterized [1], [2], [3], [4], [5] and non-parameterized models [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17]. The typical parameterized models assume that the prior information of the object boundary is available, which is not always realistic. Hence, the shortcomings of these parameterized models usually include initialization sensitivity and failure to converge to concavities. To avoid this drawback, the external forces, e.g., the balloon force proposed as in [2] are introduced. The gradient vector flow (GVF) method [4], [5] is one of the most effective parameterized active contours models. It extends the gradient force near the edges to the whole image so that the deformation of the active contour is more flexible and the deformation scope of the active contour is extended to the whole image. Nevertheless, it also has some disadvantages, such as expensive computational load, the ambiguous relationship between the capture and parameters. Non-parameterized models have some advantages over parameterized models. Firstly, by using non-parameterized models, the object boundary detection based on the image gradient is not affected by noise and weak edges. Secondly, they are also significantly less sensitive to initialization. By using the Mumford–Shah functional [18] for segmentation, the Chan–Vese (CV) model [6] extracts object boundary with intensity information in a global region but not with the gradient information. This model assumes that each image region is statistically homogeneous. It has been successfully used in the binary phase segmentation, which is implemented through the level set method [19]. The CV model has motivated many other non-parameterized active contour models [7], [8], [9], [10], [11], [12], [15], [16], [17], [21], [22], [29] as well.
Medical images including magnetic resonance images (MRI) contain several anatomical structures. Accurate segmentation of one object is quite important for diagnosis and therapeutic interventional planning. Generally, some common features in medical images, such as low-contrast object boundaries, elongated structures, and the intensity un-uniformity, make it more challenging to segment the target objects than other applications. Hence, it is widely investigated in the research field. In literatures [7], [8], [9], [10], [11], [12] local statistical information is embedded into a non-parameterized active contour model in order to overcome intensity un-uniformity (the intensities in the same sub-region vary spatially) and noise. However, the intensities in an image vary spatially and so does intensity un-uniformity. The fixed-scale estimation method for calculating the local statistical information in [7], [8], [9], [10], [11], [12] may lead to imprecise results. Additionally, the active contours based on region statistical information, including global and local ones, are both lack of structure information to extract elongated structures.
In this paper, we propose an anisotropic data fitting term that differentiates the sub-regions according to local intensity information along the active contour and the global intensity information adaptively. When a contour is close to object boundaries, the anisotropic fitting term mainly detects the local intensity information near the contour; whereas when there is no obvious intensity variation near the contour, it mainly detects the global intensity information. This new data fitting term focuses on calculating the intensities near the active contours along the local directions where the intensity changes notably. On the other hand, it calculates the global intensity information when a region is flat, i.e., there is no obvious intensity variation. Hence, the anisotropic data fitting term extracts the local information only when there is intensity non-uniformity, while it accelerates the contour evolution with the global intensity information. Particularly, we introduce a new regularization term coupling with a structured gradient vector flow model. With this new regularization term, structured information is extracted by minimizing the energy functional of structured gradient vector flow with respect to the dual variable of the level set function. Experiments on synthetic and medical images show that the active contour captures more elongated structures effectively. The proposed model is solved through a split dual formulation of the global minimization problem [15] to avoid the instability and the un-differentiability issues induced by traditional gradient descent method.
This paper is organized as follows. The previous work is reviewed in Section 2. Then the proposed model and algorithm are described in Section 3. Section 4 shows the experiment and results of the proposed method. Finally a brief conclusion comes in Section 5.
Section snippets
The global convex segmentation model
In order to overcome the local optimizer of the evolution process and the topology problem caused by the parameterized active contour model [4], Caselles et al. [3] proposed Geodesic Active Contour model (GAC). In a continuous formulation, the GAC model is equivalent to the weighted total variation (TV) as shown by Bresson et al. [15]. Combined this weighted TV with the global convex energy functional of the CV model (GCV) [13], the global convex segmentation model (GCS) [14], [15] is defined
Improved regularization term with structured gradient vector flow
A two-dimensional image is considered as on a two-dimensional domain of size Nx×Ny. Giusti [20] proposed that the standard total variation of the level set function ϕ can be defined in the continuous setting for ϕ∈L1(Ω) (Ω is the image domain) as follows:where p=(p1,p2) is the dual variable of the level set function ϕ (see for instance [20]), . For more details, readers may refer to [20].
Experiments
In this section, we present the experimental results from our model on some medical images and other images. All the experiments are run in Matlab code on a laptop with CPU 2.67 GHz and RAM 4.00G. In Fig. 3, Fig. 4, we show the experimental results of medical image segmentation by using following five models: the region-scale fitting model (RSF) [11], the GCS model [14], [15], the GCV model [13], the non-local active contour model (NLAC) [16], the model of unified tensor level set for image
Conclusion
This paper presented a new non-parameterized active contour model for image segmentation. The proposed model is different from other non-parameterized models in two ways. Firstly, the new regularization term introduced in the proposed method embeds the structure information of images via its dual formulation. Secondly, we propose an anisotropic region fitting term including a local region fitting term and a global region fitting term adaptively utilizes the intensity information in global and
Acknowledgment
The authors would like to thank the anonymous reviewers for their many valuable comments and suggestions that helped to improve both the technical content and the presentation quality of this paper. This work was supported in part by the Jiangsu Province Natural Science Foundation of China (BK20130868), Natural Science Research Project in Jiangsu Province Colleges and Universities (13KJB510022), NJUPT Talent Introduction Foundation (BY213007).
References (30)
On active contour models and balloons,
Comput. Graph. Image Process.
(1991)- et al.
Generalized gradient vector flow external forces for active contours
Signal Process.
(1998) - et al.
Active contours driven by local gaussian distribution fitting energy
Signal Process.
(2009) - et al.
Active contours driven by local image fitting energy
Pattern Recognit.
(2010) - et al.
Global structure constrained local shape prior estimation for medical image segmentation
Comput. Vis. Image Understand.
(2013) - et al.
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton–Jacobi formulation
J. Comput. Phys.
(1988) - et al.
Magnetic resonance image tissue classification using a partial volume model
Neuroimage
(2001) - et al.
Snake: active contours model
Int. J. Comput. Vis.
(1991) - et al.
Geodesic active contours
Int. J. Comput. Vis.
(1997) - et al.
Snakes, shapes, and gradient vector flow
IEEE Trans. Image Process.
(1998)