Global structure constrained local shape prior estimation for medical image segmentation
Introduction
Medical image segmentation plays a crucial role in a wide range of applications, particularly in diagnosing diseases and evaluating the effects of therapy. Manual delineation is still used by radiologists, which, however, is a tedious and time consuming procedure. Thus, automatic segmentation methods are highly desired. A large number of different segmentation methods have been proposed in the past [12]. The existing methods can be roughly divided into two categories: low-level feature based methods such as region based [9] and boundary based [19], and high-level feature based methods like model based [12], [13] and atlas based [31], [16]. Nevertheless, due to various kinds of perturbing factors, such as noise, partial volume effect and missing information, medical image segmentation is still a challenging problem.
In recent years, model based segmentation approaches have been proven to be quite successful for medical image analysis [12]. Deformable model based segmentation turned out to be one of the most successful techniques for incorporating prior knowledge, which is widely used in medical image analysis [8], [34], [30]. This kind of approaches is more stable against local image artifacts and perturbation than the conventional low-level feature based algorithms. In other words, it is conducted in a top-down fashion because of containing high-level information such as shape and appearance of the structure of interest from a number of training shapes by statistical means.
A milestone in this direction is the active shape model (ASM) introduced by Cootes et al. [8]. Shape modeling is one of the most important factors affecting the accuracy of segmentation in deformable model based methods. Point distribution model (PDM) has been successfully used in modeling shape statistics [10]. PDM is a statistical approach, which is able to extract a compact representation from a set of training instances. In the framework of PDM, dimensionality reduction is an indispensable step in constructing a statistical shape model. In the existing works, most of them have employed linear learning techniques such as principal component analysis (PCA) [8].
PCA-like algorithms generally focus on a linearized shape space with small deformation modes around a single mean shape. Although successfully applied to various types of shapes (hands, faces, organs) [8], PCA may not always be able to generate shape prior suitable for the targeted structure for two reasons. Firstly, PCA is most useful in the cases, where all the shapes lie in or at least approximately in a linear subspace of the data set. Nevertheless, this assumption may be often violated by data obtained from the real-world. Secondly, PCA-like algorithms can only perform well when the learning shape set is composed of similar shapes.
To overcome the limitations imposed by the linearity requirement, a number of non-linear shape statistics learning methods were reported in the past decades. [23] proposed a hierarchical framework for shape clustering and statistics learning without using explicit models. The method was used for shape retrieval with improved efficiency. [26] presented a method for constructing a Riemannian manifold of curves for tracking deforming objects by prediction and filtering. By using a geometric metric in the space of curves, the manifold can be obtained and used for shape modeling. Those studies showed that shapes are embedded in a manifold structure, which can be efficiently used for shape modeling.
For parametric curves, the explicite manifold structure has been exploited for shape modeling. Srivastava et al. [24], Kurtek et al. [15], Younes et al. [32] presented methods for directly computing the geodesic paths over the manifolds using differential geometric techniques. Shape analysis based on those ideas was performed and improved results were demonstrated.
In stead of performing shape modeling in the original high-dimensional shape space, we look for a more compact representation of the shape model in a lower dimensional space by using the manifold learning techniques. There has also been some work on building non-linear statistical shape model in this direction. For example, Sozou et al. proposed non-linear PCA based on polynomial regression [21] and multi-layer perceptrons [22] for natural representation of variations based on bending and rotation. Twining and Taylor [29] employed Kernel PCA, which is more general than other methods. Etyngier et al. [11] tried to use diffusion maps as a framework for shape modeling. Owing to the limitation of diffusion maps, only shapes on the manifold composing a triangle around the target shape is used. In addition, the manifold assumption is not considered, which leads to the accuracy of shape prior estimation interfered by the “noise” shapes. Although the above methods consider the two limitations of PCA-like algorithms, they failed to exploit the specificity of the patient.
In this paper, our work combines the non-linear statistical shape model and the specificity of the patient to further improve the performance of segmentation. We propose a new segmentation method to estimate target-oriented shape prior. The contributions of our work are threefold:
- 1.
A new target-oriented shape prior estimation method us proposed. We model a category of shapes as a smooth finite-dimensional sub-manifold of the infinite-dimensional shape space.
- 2.
Considering the manifold assumption, shape prior is refined by the similarity of training images measured by the intensity information.
- 3.
A new shape prior term for image segmentation through a non-linear energy term is introduced to attract a shape towards its projection onto the manifold.
The rest of the paper is organized as follows. In Section 2, the motivation of target-oriented shape prior model is presented. In Section 3, a novel target-oriented shape prior estimation method is proposed to improve the accuracy of the segmentation. In Section 4, the proposed shape prior estimation method is incorporated into a deformable model based framework for image segmentation. In Section 5, a series of experiments are conducted to validate the performance of the proposed method. The paper is concluded in Section 6.
Section snippets
Target-oriented shape modeling
Accurate shape prior estimation is one of the major factors affecting the accuracy of deformable model based segmentation methods. Target-oriented shape modeling on account of the speciality of the patient is a promising strategy for enhancing the accuracy. There are two ways to implement the target-oriented shape modeling. Ideally, target-oriented shape statistics should be used. However, such target-oriented model is barely available. An alternative solution is to increase the samples in the
Structure-constrained target-oriented shape prior estimation
According to the above analysis, we elaborate on the structure-constrained target-oriented shape prior estimation algorithm in this section. The point distribution model (PDM) used in our work is a statistical approach, which has the ability to extract a compact representation from a set of training instances. In PDM, each planar shape is represented by n 2D points as the vector S = (x1, y1, … , xn, yn)T. Thus, each shape is considered as a point in the 2n dimensional space. In our work, the landmark
Model based segmentation
The complete segmentation process is presented in this section. As shown in Fig. 3, the proposed SCTO-SPM is incorporated into a deformable model based segmentation framework for medical image segmentation. This framework is illustrated by using 3D data. For 3D data, each element in the training set is a sequence of medical images of a patient and the testing data is also a sequence of slices.
Our proposed target-oriented shape prior model is an iterative approach. At the beginning of each
Materials
In our experiments, the performance of the proposed method is evaluated on the prostate images. The 2D experiment data consists of 42 MR images of the prostate. Each image contains 512 × 512 pixels, with the pixel size of 0.3;× 0.3 mm. Manual segmentation of the images obtained by a radiologist was considered as the ground truth for evaluation. The leave-one-out strategy was employed for evaluating the performance of the algorithms.
For quantitatively evaluating the performance of the automatic
Conclusion
In this paper, we proposed a structure-constrained target-oriented shape prior model to model shape priors. Our proposed method is incorporated into a model based segmentation framework for medical image segmentation, which can refine the target shape through iterations. The framework is extensively validated on 2D prostate and 3D prostate MR images. Compared with other methods, our shape prior model exhibits better performance in both studies.
In the future, we plan to apply this model to more
Acknowledgments
This work is supported by the National Basic Research Program of China (973 Program) (Grant No. 2012CB719905) and by the National Natural Science Foundation of China (Grant Nos: 61125106, 61172142, 91120302, and 61072093).
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