Fast and robust brain tumor segmentation using level set method with multiple image information

Abstract

BACKGROUND: Brain tumor segmentation is a challenging task for its variation in intensity. The phenomenon is caused by the inhomogeneous content of tumor tissue and the choice of imaging modality. In 2010 Zhang developed the Selective Binary Gaussian Filtering Regularizing Level Set (SBGFRLS) model that combined the merits of edge-based and region-based segmentation.

OBJECTIVE: To improve the SBGFRLS method by modifying the singed pressure force (SPF) term with multiple image information and demonstrate effectiveness of proposed method on clinical images.

METHODS: In original SBGFRLS model, the contour evolution direction mainly depends on the SPF. By introducing a directional term in SPF, the metric could control the evolution direction. The SPF is altered by statistic values enclosed by the contour. This concept can be extended to jointly incorporate multiple image information. The new SPF term is expected to bring a solution for blur edge problem in brain tumor segmentation. The proposed method is validated with clinical images including pre- and post-contrast magnetic resonance images. The accuracy and robustness is compared with sensitivity, specificity, DICE similarity coefficient and Jaccard similarity index.

RESULTS: Experimental results show improvement, in particular the increase of sensitivity at the same specificity, in segmenting all types of tumors except for the diffused tumor.

CONCLUSION: The novel brain tumor segmentation method is clinical-oriented with fast, robust and accurate implementation and a minimal user interaction. The method effectively segmented homogeneously enhanced, non-enhanced, heterogeneously-enhanced, and ring-enhanced tumor under MR imaging. Though the method is limited by identifying edema and diffuse tumor, several possible solutions are suggested to turn the curve evolution into a fully functional clinical diagnosis tool.

Keywords

Brain tumor segmentation evaluation of tumor segmentation accuracy Selective Binary Gaussian Filtering Regularizing Level Set (SBGFRLS)Singed Pressure Force (SPF)

1 Introduction

Brain tumor segmentation remains challenging in this decade. It is difficult to segregate brain tumor from the medical images because the malignant tumors have various size, shape, and location [1, 2]. While brain tumor quantification is an important procedure in surgical and treatment planning, the segmentation is achieved manually by experts in clinical routine. The conventional approach is time costly and subjective to individual operators [3].

Brain tumor could be observed via multiple medical imaging modalities [4]. Recently magnetic resonance imaging (MRI) has contributed fruitfully in the diagnostic stage. By using multi-parametric imaging sequence, such like T1-weighted (T1W), T2-weighted (T2W) and proton density weighted (PDW) imaging [5], clinicians could predominate the composition and nature of the brain tumor. Depends on the acquisition sequence and tissue content, tumor information is presented by hyper-intensity and hypo-intensity image contrasts mapping. The tumor could also be subdivided into different regions, including necrosis, active site, inactive site, edema, and synovium [6]. Calcification and cyst formation are observed in certain cases [7]. The heterogeneous tumor contents and sequence application cause a wide range of variation in cerebral MRI intensities, making the artificial intelligent segmentation a difficult task.

In 1987, Kass et al. [8] first introduced the active contour model (ACM) in image segmentation. The algorithm has become one of the most popular techniques in automated computer vision. In this method, a curve evolves towards to the object boundary by minimizing the energy. The iteration terminates when the curve evolution reaches the desired boundary. The existing ACM can be categorized into two main streams: edge-based model and region-based model. The edge-based model constructs an edge detector with edge information, which is usually the image gradient, to stop the contour evolution at object boundaries [8 –10]. However, the edge detector could not be halted at true boundary if the edge is too blurry. On contrary, the region-based model utilizes region statistical information to build an edge stopping function [11, 12]. Since region-based model is less sensitive to noise and is adapted to image blur, the algorithm has better performance in actual applications. Despite the robustness of region-based model in general images, the efficiency is limited by the heavy computational cost.

In 2010, Zhang developed the Selective Binary Gaussians Filtering Regularizing Level Set (SBGFRLS) model [13]. The model combines merits of both edge-based and region-based model by utilizing the statistical information inside and outside of the contour to build the signed pressure force (SPF) function. This hybrid method shows a better performance than classical one by stopping contour evolution at weak or blurred edge. The SBGFRLS is also benefited by the Gaussian regularized contour, in which re-initialization is unnecessary. The iteration process is thus computationally effective.

Another advantage of SBGFRLS is the intuitiveness of algorithm. The method could be further extended by modifying the SPF function. Many researchers have considered to relieve the assumption of image homogeneity. They have introduced new terms into SPF which merges both global and local statistics into SPF calculation, which makes the segmentation of heterogeneous object possible [14 –18]. However, the performance in brain tumor segmentation is unsatisfactory because of the high variance in tumor appearance.

Therefore, the objective of this study is to improve the robustness of SBGFRLS method for brain segmentation by modifying the SPF. New metric is introduced into SBGFRLS in order to become capable with clinical scenarios. Multiple images are incorporated in the proposed SPF to provide more information in defining the brain tumor region. By first discussing the merit and demerit of SBGFRLS model, the proposed algorithm with presented with detailed mathematical formulations. The effectiveness of new method will also be demonstrated and discussed with real clinicalimages.

2 Methods

2.1 Selective Binary Gaussians Filtering Regularizing Level Set (SBGFRLS)

SBGFRLS model combines the merits of Geodesic Active Contour (GAC) model [9] and Chan-Vese model [11]. It utilizes the mean intensity value of information I (x) inside and outside of the contour to constructs the SPF function, which acts as an edge stopping function. The level set formula φ is described as follows: $\frac{\partial φ}{\partial t} = spf (I (x)) \cdot α | \nabla φ |$ (1) where α is the propulsion force that controls the rate of expansion of the level set function. The SPF function is defined as follows: $spf (I (x)) = \frac{I (x) - \frac{c_{1} + c_{2}}{2}}{max | I (x) - \frac{c_{1} + c_{2}}{2} |}$ (2) where c₁ and c₂ are the global intensity mean inside and outside of the respective contour. The terms are described as follows: $\begin{matrix} c_{1} = \int_{Ω} \frac{I (x) \cdot H (φ) dx}{H (φ) dx} \\ c_{2} = \int_{Ω} \frac{I (x) \cdot (1 - H (φ)) dx}{(1 - H (φ)) dx} \end{matrix}$ (3) where Ω is the image domain and H (φ) is the Heaviside function that defines as follows: $H_{ɛ} (z) = \frac{1}{2} (1 + \frac{2}{π} \tan^{- 1} (\frac{z}{ɛ}))$ (4)

Heaviside function equal to zero when z is negative value and equal to 1 when z is positive value. A smaller ɛ corresponds to a steeper transition at z = 0. Heaviside function can then be interpreted as a unit step function with a very small ɛ, i.e. H_ɛ (z) equals to 1 when z is 1, otherwise equal to zero.

The SBGFRLS model is computational efficient and effective. The algorithm stops the contour evolution even with blurred edges without any priori training. However, the model assumes the region to be segmented is homogeneous, which is not occasionally seen in general clinical cases. The facing heterogeneous intensity distributions, the detection accuracy could fall significantly as the fundamental assumption is violated [17]. Moreover, the SBGFRLS model could easily trapped by local minima without proper initialization and results in poor segmentation performance.

2.2 The proposed model

Tumor regions could be enhanced by intravenous contrast agent injection. Owning to the vascularization and tissue activity, several regions could not be well separated from the normal brain tissue. Necrosis is one of example without contrast enhancement under MRI. The region thus cannot be segmented with conventional SBGFRLS method as the contour evolution favors hyper-intensity regions. In SBGFRLS model, contour evolution mainly depends on SPF. Positive SPF will expand the contour while negative SPF will shrink the contour. In the formula of SPF in original SBGFRLS, the SPF can only be positive if pixel intensity at point x (I (x)) has a higher value than average of mean intensity inside and outside the contour $(\frac{c_{1} + c_{2}}{2})$ so necrosis region, hypo-intensity region, have negative SPF and is excluded from the contour. Therefore we proposed to introduce new direction term f (x) in the SPF function. The metric act as a switch to control the sign of SPF. The modified SPF hence will be positive if the pixel intensity is closer to global mean intensity value inside contour (c₁) than global mean intensity value outside contour (c₂). Also, contour evolution is constrained within the brain region by setting SPF to be negative when the pixel is outside the brain region B (x). The modified SPF function spf′ can be expressed as: ${spf}^{'} (I (x)) = {\begin{matrix} \frac{(- 1)^{f (x)} | I (x) - \frac{c_{1} + c_{2}}{2} |}{max (I (x) - \frac{c_{1} + c_{2}}{2})} & , I (x) \in B (x) \\ - 1 & , otherwise \end{matrix}$ (5)

And $f (x) = {\begin{matrix} - 1 & , I (x) - c_{2} > I (x) - c_{1} \\ 1 & , otherwise \end{matrix}$ (6)

The modified level set formulation then becomes: $\frac{\partial φ}{\partial t} = {spf}^{'} (I (x)) \cdot α | \nabla φ |$ (7)

In the modified SBGFRLS method, initial contour act as the key factor to control the contour evolution and hence affects the final segmentation result. If the initial contour is set within hyper-intensity region, the contour tends to evolve to whole bright region, and vice versa. The robustness is believed to be improved when dealing with brain tumors with a board variation of appearance.

2.3 Multi-image level set method

The proposed method could be further extended by incorporating multiple images. Increasing number of images could help to deal with blur edge problem. General form is defined by following: $spf (I_{1} (x), I_{2} (x), . . . . I_{n} (x)) = {\begin{matrix} \frac{(- 1)^{f (x)} \sqrt{\sum_{j = 1}^{n} {(I_{j} (x) - \frac{c_{j 1} + c_{j 2}}{2})}^{2}}}{max (\sqrt{\sum_{j = 1}^{n} {(I_{j} (x) - \frac{c_{j 1} + c_{j 2}}{2})}^{2}})} & , I_{j} (x) \in B (x) \\ - 1 & , otherwise \end{matrix}$ (8)

With generalized direction term $f (x) = {\begin{matrix} - 1 & \sqrt{\sum_{j = 1}^{n} (I_{j} (x) - c_{j 2})^{2}} > \sqrt{\sum_{j = 1}^{n} (I_{j} (x) - c_{j 1})^{2}} \\ 1 & , otherwise \end{matrix}$ (9) where I_j are the collection of multiple aligned images, c_j1 and c_j2 are the global mean intensity value inside and outside of the contour of I_j.

In this study, two MR images are utilized to demonstrate the feasibility of proposed method. The two-image SPF is defined by following, $spf (I_{A} (x), I_{B} (x)) = {\begin{matrix} \frac{(- 1)^{f (x)} \sqrt{{(I_{A} (x) - \frac{c_{A 1} + c_{A 2}}{2})}^{2} + {(I_{B} (x) - \frac{c_{B 1} + c_{B 2}}{2})}^{2}}}{max (\sqrt{{(I_{A} (x) - \frac{c_{A 1} + c_{A 2}}{2})}^{2} + {(I_{B} (x) - \frac{c_{B 1} + c_{B 2}}{2})}^{2}})} & , I_{A} (x) \in B (x) & I_{B} (x) \in B (x) \\ - 1 & , otherwise \end{matrix}$ (10) with new directional term $f (x) = {\begin{matrix} - 1 & \sqrt{(I_{A} (x) - c_{A 2})^{2} + (I_{B} (x) - c_{B 2})^{2}} > \sqrt{(I_{A} (x) - c_{A 1})^{2} + (I_{B} (x) - c_{B 1})^{2}} \\ 1 & , otherwise \end{matrix}$ (11)

2.4 Data selection

Brain tumor MR data is downloaded from several online archives (The Tumor Cancer Imaging Archive, TCIA) 1 in DICOM format [19]. The public accessible collection Low & High Grade Glioma Collection “REMBRANDT”, is selected as test data. 97 sets of data are chosen in the first screening as they are acquired by the same MR machine. 46 sets are excluded due to incomplete data, motion artifact and insignificant tumor volume, resulting in 51 sets of data selected as the subject cohort.

T1 image and T1 with gadolinium-based contrast enhanced (T1+C) image are acquired with the following parameters: Echo Time (TE) = 14 ms, Repetition Time (TR) = 500 ms, Spacing = 0.938 mm×0.938 mm×3 mm, Dimension = 256×256×51. The chosen image data are further categorized into 5 different groups according to the appearance of tumor in T1+C image: non-enhanced (n = 13), homogeneously enhanced (n = 4), heterogeneously enhanced (n = 8), ring enhanced (n = 24), and diffuse (n = 2). One iconic slice from each category is display in Fig. 1.

2.5 Image preprocessing

Rigid registration is performed by maximizing the mutual information [20] between T1 and T1+C images for spatial alignment. Brain extraction is achieved by using brain extraction method developed by Oxford Centre for Functional MRI of the Brain (Analysis Group, FMRIB, Oxford, UK [21]). Rectangular ROI is manually adjusted to encompass the whole tumor region for image cropping in order to reduce the size of image domain to lower computation cost.

First, ACM requires the definition of an initial contour as the algorithm initialization. Figure 2 shows initial contours with different shapes and at different regions. Theoretically the contour initialization can be a simple geometry within or without target region. However, the evolution of contour is found to be affected by the initial contour in preliminary experiment. Improper placement of initial contour could cause a longer computation time or even trapped in the local extrema. As suggested by D. Gurari, a rough initial segmentation of target objects could generate a better result in level set method than using simple geometric shapes [22]. For such reason, we decide to apply manually labelling at tumor region for one single slice on T1+C image with ITK-SNAP (Penn Image Computing and Science Laboratory, University of Pennsylvania, PA, USA [23]). The roughly initialized label is then evolved in 3D using the proposed SBGFRLS.

In ring enhanced cases, the segmentation is divided into two separate labels, namely the necrosis region and active tumor region. The initialization is performed with K-mean clustering algorithm with cluster number k = 2 [24]. Figure 4 demonstrates one example for segregation of necrosis and active tumor region as level set initialization. The contour for necrosis and active tumor regions will then evolve separately with the proposed algorithm.

Second, to illustrate the ease of implementation of our modified SBGFRLS method, the main steps can be summarized as follows:

Initialize the level set function ψ, initial contour, using Equation. at t = 0,

φ (x, t = 0) = {\begin{matrix} - 1 & x \in Ω_{0} - \partial Ω_{0} \\ 0 & x \in \partial Ω_{0} \\ 1 & x \in Ω - Ω_{0} \end{matrix}

(12)

Compute global mean values c_A1, c_A2, c_B1, and c_B2.

Calculate direction term f (x) with Equation (11).

Calculate modified SPF function SPF (I_A (x) , I_B (x)) using Equation (10.)

Regularized the level set function by a Gaussian kernel.

Check if converge, otherwise go back to step (II)

2.6 Evaluation

We conduct evaluation on our proposed method and original SBGFRLS model by calculating sensitivity, specificity, Dice similarity coefficient and Jaccard similarity index by comparing the ground truth labelled by experienced medical students. The evaluation involves the estimation of the total pixel of true positive (TP), true negative (TN), false positive (FP) and false negative (FN) labels with following the definitions: $Sensitivity = \frac{TP}{TP + FN}$ $Specificity = \frac{TN}{TN + FP}$ $DICE = \frac{2 TP}{2 TP + FP + FN}$ $Jaccard = \frac{TP}{TN + FN + FP}$

Sensitivity measures the proportion of positives that are correctly identified while specificity measures the proportion of negatives that are correctly identified. The conformity between the result and the ground truth is positively proportional to the DICE similarity index and Jaccard similarity Index, i.e. the higher the index, the more overlapping between ground truth and result.

3 Results

The parameters in our experiment are carefully chosen for best optimization and guarantee robustness. The proposed method shares same parameter as the original SBGFRLS method. The propulsion term is set at 20 for 60 iterations. The algorithm is implemented in C++with Qt (Qt, version 5.6.1; The Qt Company, Espoo, Finland, https://www.qt.io/), Visualization Toolkit(VTK, versions 6.3.0; Kitware Inc., Los Alamos National Laboratory, Los Alamos, NM [25]) and Image and Segmentation Toolkit (ITK, versions 4.10.1; Kitware Inc., Los Alamos National Laboratory, Los Alamos, NM [26]) on a 8 threads personal computer (Intel(R) Core(TM) i7-4710, 2.5 GHz, 8 GB memory).

It is easy understanding that proposed method is computationally heavier than original SBGFRLS because modified SPF involves more images. More computation time is used to iterate over theadditional images. Both of the method can still meet the clinical acceptance and can finish within 10 seconds.

The comparisons between proposed method and original SBGFRLS are tabulated in Table 1. Both methods are showing high specificity, meaning that they can correctly identify the normal tissue. The proposed method gives a higher sensitivity in identifying tumor region. Both methods shows good performance in segmenting homogeneously-enhanced tumor while the proposed method has a great improvement in segmenting heterogeneously-enhanced tumor and ring-enhanced tumor.

Experimental result proved that with a modification in direction term in SPF, SBGFRLS can be successfully segment non-enhanced tumor. Both methods fail to segment diffuse tumor as the tumor intensity is similar to normal cerebral tissues.

4 Discussions

We have qualitatively compared our proposed method with original state-of- art model SBGFRLS on the selected data to demonstrate the improvement in accuracy and speed. Our model gives a more accurate result with similar computation time.

First, we compared the results generated by our modified method with the original SBGFRLS method. Table 1 shows a quantitative measurement of segmentation result using original SBGFRLS and proposed method compared with ground truth. In all categories, both methods show high specificity (>0.999), which indicate the accuracy to identify non-tumor tissue. Moreover, proposed method shows improvement in all categories. Apart from diffuse tumor, the performance of proposed method is satisfactory.

The homogeneously-enhanced tumor has a distinct and clear boundary. This tumor type is considered to be the most easy-to-segment among all categories. Both methods perform well with the proposed method give a slight better result (Sensitivity = 0.778, Jaccard = 0.725, DICE = 0.839) than original SBGFRLS (Sensitivity = 0.774, Jaccard = 0.715, DICE = 0.832).

In heterogeneously-enhanced tumor, due to the violation of object homogeneity assumption, original SBGFRLS gives a lower score in both Jaccard (0.693) and DICE (0.816) index. The proposed method tackles the problem of homogeneity assumption by providing SPF more statistical information to keep tumor as a homogeneous target and thus gives a significantly better result (Jaccard = 0.758, DICE 0.8606). It is worth noticing that sensitivity of proposed method is higher than original SBGFRLS, increases from 0.748 to 0.808, indicating that proposed method has superiority to identify heterogeneously-enhanced tumor. The heterogeneity problem will be further discussed in section “Sensitivity to Inhomogeneity”.

Proposed method shows the largest improvement in segmenting ring-enhanced tumor. When comparing to original tumor (Jaccard = 0.512, DICE 0.664), proposed method gives a more accurate result (Jaccard = 0.703, DICE = 0.823). The improvement comes from segmenting necrosis region with a step-wise level set method. Original SBGFRLS cannot segment necrosis region as necrosis region has a low pixel intensity. SPF of SBGFRLS favors high pixel intensity. Contour will be attracted to evolve over high pixel intensity, causing leakage. The addition of direction term considers the difference between absolute distance of pixel intensity and global intensity inside and outside contour which help contour to evolve over the necrosis region. The sensitivity can thus increase significantly.

No comparison can be made in non-enhanced tumor group as original SBGFRLS is unable to segment this category. The proposed method produces a satisfactory result (Jaccard = 0.559, DICE = 0.711) with high sensitivity (0.739). The advancement is mainly due to the introduction of directional term, in which will be further discussed in section “Sensitivity to Initial Contour”.

Both methods give dissatisfying score in segmenting diffuse tumor. Since the diffuse tumor has a similar intensity with gray matter, it is only distinguishable from the pattern but not by intensity. Although proposed method has improved result (Jaccard = 0.201, DICE = 0.330) compared to original one (Jaccard = 0.140, DICE = 226), the segmentation result is still disappointing. This is a common limitation of intensity-based segmentation method where pattern-based method may be a suitable substitute.

Level set method is considered to be unsuitable in segmenting edema regions. The reason is that differentiability between edema and normal tissue is low under T1 imaging. Contours may evolve into normal tissue and causing leakage of curve. A possible solution is by applying multi-parametric MR sequences with a better prominent on edema region, for example, T2 image.

Next, we investigated the sensitivity to initial contour. New SPF causes the level set contour evolves towards the intensity similar to initial contour due to the newly introduced direction term. It extends the method to segment non-enhanced tumor and necrosis region. Figure 5 shows that curve could evolve in different directions by changing the location of initial contour. In original SBGFRLS, the SPF term points to same direction in hyper-intensity region while the proposed directional term takes action in the hypo-intensity region. Necrosis region could be effectively segmented on necrosis region under T1 imaging. The initial contour becomes the key factor to control the extension of curve evolution. The initial contour can be coarsely defined as the contour will evolve for fine-tuning. In this study, we applied manual segmentation of one slice as the initial contour but one can use interactive segmentation [27] to minimize the effort in contour initialization.

Last, the proposed method shows better performances in segmenting heterogeneously-enhanced tumor. Without relieving the assumption of homogeneity, we consider tumor as homogeneous in nature using multiple image information. This composes one set of inhomogeneity intensity class. Multiple images could provide suitable information to the level set function to retain the segmented region as a homogeneous object. In Fig. 6c, the tumor is darker than normal gray matter under T1 image while it is heterogeneously-enhanced under T1+C image. In T1+C image, the tumor edge has lower intensity, which makes original SBGFRLS fail to identify. With the supplementary information from T1 image, proposed method has the ability to recognized inhomogeneity regions. However, some holes may still be observed caused in the segmented label. It may be caused by signal noise, variation in localized vascularization, or regional tissue necrosis. Dual image information is insufficient to retain a homogeneity distribution. Application of multiple images from various sequences could be a possible solution to the problem.

5 Conclusion

In this study, we present a novel brain tumor segmentation method in MR image. This method is a clinical-oriented method is fast, robust and accurate with minimal user interaction. By extending the SPF term of SBGFRLS method, the proposed method utilized the information from multiple images with an additional new directional metric to control level set curve evolution. It effectively segmented the homogeneously-enhanced, non-enhanced, heterogeneously-enhanced, and ring-enhancing tumor. Experimental results show the efficiency and robustness of our proposed method. Though the proposed method is still limited in application of identifying edema and diffuse tumor, several possible reasons are suggested to turn the curve evolution method into a fully functional clinical diagnostic tool.

Footnotes

Acknowledgments

This study was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No.: CUHK 14113214), a grant from the Science, Technology and Innovation Commission of Shenzhen Municipality (Project No.: CXZZ20140606164105361), grants from grant from the Innovation and Technology Commission (Project No.: GHP/028/14SZ, ITS/293/14FP), and grants from CUHK Technology and Business Development Fund (Project No.: TBF16MED002 and TBF16MED004).

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