Segmentation of interest region in medical volume images using geometric deformable model

doi:10.1016/j.compbiomed.2012.01.005

Computers in Biology and Medicine

Volume 42, Issue 5, May 2012, Pages 523-537

https://doi.org/10.1016/j.compbiomed.2012.01.005 Get rights and content

Abstract

In this paper, we present a new segmentation method using the level set framework for medical volume images. The method was implemented using the surface evolution principle based on the geometric deformable model and the level set theory. And, the speed function in the level set approach consists of a hybrid combination of three integral measures derived from the calculus of variation principle. The terms are defined as robust alignment, active region, and smoothing. These terms can help to obtain the precise surface of the target object and prevent the boundary leakage problem. The proposed method has been tested on synthetic and various medical volume images with normal tissue and tumor regions in order to evaluate its performance on visual and quantitative data. The quantitative validation of the proposed segmentation is shown with higher Jaccard's measure score (72.52%–94.17%) and lower Hausdorff distance (1.2654 mm–3.1527 mm) than the other methods such as mean speed (67.67%–93.36% and 1.3361 mm–3.4463 mm), mean-variance speed (63.44%–94.72% and 1.3361 mm–3.4616 mm), and edge-based speed (0.76%–42.44% and 3.8010 mm–6.5389 mm). The experimental results confirm that the effectiveness and performance of our method is excellent compared with traditional approaches.

Introduction

Segmentation is the process of separating objects in an image. For volume medical images, its field of application is wide. For example, 3D visualizations of anatomic structures could benefit enormously from exact segmentation. Thus, volume segmentation is becoming an increasingly important part of computer-based medical applications for diagnosis and analysis of anatomical data. However, segmentation in medical imaging is considered to be a very difficult problem, even though methods specialized for a particular volume usually provides better results [1]. Recently, the use of a geometric deformable model approach to extract the deformable surface from a volume image has become very common [2]. In particular, many researchers have explored the use of deformable models for volume segmentation. Active deformable models are the most popular methods for the volume segmentation of Region-Of-Interest (ROI) in medical images, implicitly in the form of a level set function or explicitly as a snake function. Moreover, the popularly of the level set method has increased because it can handle complex geometries and topological changes. The level set is a shape-driven tool based on a defined speed function that can grow and shrink and take the shape of any complex object of interest. The level set method does not generally depend on the parameters settings of the model [3]. This makes it a very attractive and flexible method for shape modeling and object detection. Another advantage of the level set approach is that the entire segmentation procedure is fully automatic and is based on the initial model. Unlike other methods, the extension of the algorithm to a volume dataset is straightforward and does not require additional mechanisms. These properties make the level set method a state-of-the-art method for segmentation, especially volume segmentation. Therefore, the focus of our paper is on a geometric deformable model for ROI segmentation in medical images.

However, it is difficult to detect object volumes based on an active contour model that is sensitive to certain circumstances. One problem is that the active contour formulation entails the tuning of several parameters. In order to overcome the difficulty of adjusting parameters, a partial differential equation is used for immediate user feedback on the parameter settings of the active contour model. The user can tune the parameters and control the shape of the active contour model by solving the partial differential equation [4], [5]. In particular, Leventon et al. performed more generic and automated detection of tumor regions through level set evolution with statistical shape information [6]. But, the disadvantage of their method is that it may be difficult to obtain statistical prior knowledge in various cases, especially for tumor segmentation. T. Chan et al. proposed active contours to detect object regions in a given image based on the theory of curve evolution and level sets without boundary information [7]. Also, level set approaches based on K-mean clustering and fuzzy classification are proposed in [8], [9], [10]. In these methods a clustering step is performed and the deformable model then grows on top of the clustered pixels. For the speed function of the level set, Ho et al. implemented the histogram of a difference image fitted by parametric distributions for both the enhanced parts and the noisy background [11]. Many level set algorithms may be distinguished on the basis of their speed functions. Some approaches, for example, require user interaction while others rely on prior estimation of the tumor density function [12].

In this paper, we are interested in segmentation of tumor and normal tissue in medical volume images using geometric deformable models based on evolution theory and the level set method. Our approach handles topological changes of deformable surfaces using several geometric integral measures. These measures are derived by the hybrid method, which considers a region and boundary information for tumor tissue. They contain three terms called robust alignment, active region, and smoothing. First, the alignment term should move the model towards the boundaries of objects given in the input images dataset. This is decided by the inner product of the surface normal and the gradient of an input image for which the normal best aligns with the image gradient. Second, the active region term efficiently splits the interior and exterior of the surface of the object. This model can not only overcome some of the weaknesses in the boundary-based model such as dependency of local information and initialization, but it can also optimally partition a given image into some homogenous regions. Third, the smoothing term helps to ensure a smooth surface by eliminating noise. This is determined by the mean curvature computed at a given point. The new method is iteratively applied with the weighted average of three terms until we obtain the optimal segmentation result. Finally, we have proposed an algorithm that can update the parameter values iteratively. This also provides the basis for a numerical scheme that is used by geometric deformable models.

The remainder of our paper consists of five sections. In Section 2, we introduce the active deformable model and the level set theory. Section 3 proposes the hybrid speed function in the level set method. Section 4 provides a detailed analysis of the accuracy and robustness of the proposed algorithm. In Section 5, we show the various segmentation results for medical volume images, and we conclude our paper in Section 6.

Section snippets

Geometric integral measures for active surfaces

Let S(r,s):ℝ²→ℝ³ be a parameterized two-dimensional surface in 3D space defined as follows: S(r,s)={(x(r,s),y(r,s),z(r,s)): 0≤r≤L₁,0≤s≤L₂}. Then, the energy functional E(S) for a surface S can be defined as two types of integral measures that are related via the Green theorem [13]. The first functional integrates the function g(S(r,s)) defined on the surface, and is considered as a surface based measure in the general form of: $E_{1} (S) = \int_{0}^{L_{1}} \int_{0}^{L_{2}} g (S (r, s)) d r d s .$

The second functional integrates the

Robust alignment term

First, we are aiming to propagate an initial surface S that approximates as closely as possible an object's surface given medical volume images. To this end, we use a geometric functional that is expressed by the inner product between the volume image gradient and the surface normal. It is reasonable to assume that in many cases the gradient direction is a good estimator of the orientation of the evolving surface. The inner product will be a high value if the surface normal aligns with the

Level set initialization

First, in order to show that the proposed method does not depend on the initial values, we have implemented image segmentation using various initial values for up to 300 iterations of the level set function. Fig. 2 shows examples of initial contours obtained from the reference slices.

In Fig. 3, we show box-and-whisker plots of the pixel value means in the segmented region obtained using various iteration numbers for each initialization. This is a demonstration of the robustness of our algorithm

Experimental results

We compare the performance of our hybrid speed function with traditional speeds, such as mean speed (Chan & Vese [7]), mean-variance speed (Rousson & Deriche [26]), and edge based speed (Caselles et al. [16]), and validate the segmentation results. Five datasets of various patients acquired from the UNC CASILab [28] are used to evaluate the segmentation performance for each method. These include four brain MR volume datasets with a tumor and one lung CT volume dataset. Each MR and CT volume

Conclusions

We have presented a detection method for anatomic structures in volume medical images using the level set method with a new hybrid speed function. The level set procedure can segment the volume images much more accurately, and it has less sensitively to noise. It works by exploiting three speed terms, which are robust alignment, active region, and smoothing. We analyzed the characteristics of these terms using the original, texture, blurring, and noisy images. The experimental results show that

Myungeun Lee received the B.S., M.S. and Ph.D. degrees in Electronics Engineering from Mokpo National University, Korea, in 1998, 2001 and 2007, respectively. From 2007 to 2011, she was a postdoctoral research fellow and a research professor in the Department of Computer Science, Chonnam National University, Korea. Since 2011, she has been a senior member of research staff in Medical Research Center, Seoul National University, Korea. Her research interests are medical image processing, pattern

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Wanhyun Cho received both B.S. degree and M.S. degree from the Department of Mathematics, Chonnam National University, Korea, in 1977, 1981, respectively and Ph.D. degree from the Department of Statistics, Korea University, Korea in 1988. He is now teaching in Chonnam National University. His research interests are statistical modeling, pattern recognition, image processing, and medical image processing.

Sunworl Kim received the B.S. degree in Information Statistics from Korea National Open University, Korea, in 2004, and the M.S. degrees in Statistics from Chonnam National University in 2006. She is currently studying the Ph.D. course in the Department of Statistics, Chonnam National University, Korea. Her research interests include medical image segmentation, registration, pattern recognition and statistical modeling.

Soonyoung Park received B.S. degree in Electronics Engineering from Yonsei University, Seoul, Korea in 1982 and M.S. and Ph.D. degrees in Electrical and Computer Engineering from State University of New York at Buffalo, in 1986 and 1989, respectively. From 1989 to 1990, he was a Postdoctoral Research Fellow in the department of Electrical and Computer Engineering at the State University of New York at Buffalo. Since 1990, he has been a Professor with Department of Electronics Engineering, Mokpo National University, Korea. His research interests include biomedical image processing, image protection and authentication, and image retrieval techniques.

Jong Hyo Kim received the B.Sc., M.Sc, and Ph.D. degrees in Electronics Engineering from Seoul National University, Seoul, Korea in 1982, 1986, and 1994, respectively. He is currently an Associate Professor at Department of Intelligent Convergence Systems, Graduate School of Convergence Science, and Department of Radiology, College of Medicine, Seoul National University. His research interests include computer aided diagnosis, and computational modeling in medical imaging.

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Grants:

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0004970).

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education, Science and Technology (2011-0014828).

The research was supported by the Converging Research Center Program through the Ministry of Education, Science and Technology (2011K000718).

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Segmentation of interest region in medical volume images using geometric deformable model☆

Abstract

Introduction

Section snippets

Geometric integral measures for active surfaces

Robust alignment term

Level set initialization

Experimental results

Conclusions

Image and Vision Computing

Pattern Recognition

3D segmentation techniques for medical volumes

Res. Rep.

A topology preserving level set method for geometric deformable models

IEEE Trans. PAMI

Level Set Methods and Fast Marching Methods: Evolving Interfaces in Geometry, Fluid Mechanics, Computer Vision, and Materials Science

Active contours without edges

IEEE Trans. Image Process.

Cardiac MR image segmentation and left ventricle surface reconstruction based on level set method

Studies Health Technol. Inf.

3D brain tumor segmentation using fuzzy classification and deformable models

Workshop on Fuzzy Logic and Appl.

Fast edge integration, Geometric Level Set Methods in Imaging, Vision, and Graphics