Liver of CT Slice Localization and Segmentation Based on GPV levelset

2018 International Conference on Applied Mechanics, Mathematics, Modeling and Simulation (AMMMS 2018) ISBN: 978-1-60595-589-6

Liver of CT Slice Localization and Segmentation Based on GPV-levelset

Lu WANG

1

, Li-fang ZHOU

1,2,3,*

, Wei-sheng LI

1

,

Bang-jun LEI

2

and Hong-mei LI

3

1

Coll. of Computer Science and Technology, Chongqing Univ. of Posts and Telecommunications, Chongqing 400065, China

2_{Hubei Key Laboratory of Intelligent Vision Based Monitoring for Hydroelectric Engineering, China} Three Gorges University, Yichang 443002, China

3

Coll. of Software, Chongqing Univ. of Posts and Telecommunications, Chongqing 400065, China

*Corresponding author

Keywords: Location, Liver segmentation, GPV-levelset.

Abstract. Motivated by the goal of improving segmentation of challenging liver cases, which always contain weak boundary with neighboring organs and the presence of intrahepatic tumors as well as highly varied appearance between different subjects, a multi-level detection segmentation framework is presented. The Gaussian pseudo-variance based on local patch is utilized to improve the level set segmentation technique, which named as Gaussian pseudo-variance level set (GPV-levelset). Our method considers the liver scale, the spatial texture, and the changes of the energy functional over iterations. Therefore, the image with uneven gray scale and noise images can be processed effectively. We demonstrate the capabilities of the method in the domain of medical imaging for segmenting two public databases Sliver07 and 3Dircadb.

Introduction

Although Computed Tomography (CT) images have been extensively implemented in clinics, accurate liver segmentation from CT images is still a challenging task[1]. In abdominal medical images, there are several neighboring organs which share similar intensities, which lead to low contrast and weak boundary. Liver segmentation based on pixel methods is hard to detect the boundary accurately which may easily leak to neighboring organs. Hence, shape priors are advisable since they can prevent the results deviating from reasonable pattern shape[2].

One of the most popular shape prior modeling methods is to learn the prior shape information variations from many training samples by statistical shape models (SSM). It can be always integrated into level set[3] based method to improve the accuracy of segmentation. Payel et al.[4] incorporated derivative-free optimization for the level set function to segment prostate on pelvic of computed tomography and magnetic resonance images.

Method

The proposed method is a multi-stage segmentation approach which is shown in Figure 1. First, Faster RCNN extracts the liver patch from the original image, and the red liver area will be separated from the unrelated organs. Next, calculating the GMM-SDF of the liver patch and then the coarse segmentation result can be obtained. The darker the color, the greater the probability that the pixel belongs to the liver region. Finally, the GPV-level set is proposed to evolve the coarse contour to approach the liver boundary accurately.

Faster RCNN

GMM-SDF GPV-Level set

Orginal Image Liver Patch Coarse

Segmentation Segment result

Pliver

[image:2.595.150.454.182.301.2]

GMM SDF   

Figure 1. The architecture of Multi-level.

Faster RCNN

Faster RCNN is a general object detection algorithm based on deep learning network[6]. Detecting the specific location of the liver is one of the important step for fine segmentation. In detail, we utilize the Faster RCNN to detect the liver. 1500 labeled CT slices of the 3D-IRCADb dataset were trained. The framework is Tensorflow with a learning rate of 0.0005, a momentum of 0.9 and a batch size of 64.

GMM-SDF

Shape modeling. The shape is directly aligned according to the maximum overlap by the signed distance function (SDF). Let I₀ is the reference binary image ₀, where I₀

 

x 1 if ₀

 

x 0 and

 

0 x 0

  otherwise. Minimize the following energy function to align each SDF _i with ₀.







 



2



 





 



2





 





1, 2, 0 1 0 2 1

B T i T i T

F c c X I x c H  X I x c H  X dx







    (1)

whereH x

 

is Heaviside function. Minimizing the energy function F c c X_B



₁, ₂, _T



by iterating each

parameter alternately, all shapes can be aligned to the reference function ₀.

Let M 



 ₁, ₂,...,_n



is the n aligned training shape matrix. The eigenvalues and eigenvectors of

the covariance matrix shape matrix are  



 ₁, ₂,...,_m



 ₁  ₂  ... _m



and U 



u u₁, ₂,...,u_m



respectively. The varied pattern in the PCA shape space can be given as:

 

1

p

i i i i

u

   



  



(2)

where  



 ₁, ₂,...,p



is a vector of shape coefficients. There is no limitation to  to ensure that

the generating shapes is similar to original training shapes.

Matching. Although the liver morphology varies from patient to patient, the intensity of the same tissue is usually uniform in CT scanning. Therefore, the liver distribution can be coarse fitted by one of the Gaussian model in the GMM. Let x is a random variable. The GMM can be defined as

 



2



1

,

K

i i i

i

P x N x  



where_i is weight and

1

1, 0 1

K i i i      



. Kis the number of components. N

 

 is the Gaussian probability density function. The Expectation-Maximization (EM) algorithm [7] is used to estimate the parameters  



p₁,...,p_k,₁,..., _k, ₁2,...,_k2



and the liver-classified _GMM . With Eq. 2, _GMM can drive the average shape to reach the object boundary. Finally, the coarse segmentation result

GMM SDF

 _ can be obtained.

GPV-level set

In this section, we propose GPV-level set method to convergence boundary since the contour of coarse segmentation is not converged completely.

Edge Stop Function. LetP_con

 

x is the probability likelihood estimation of data samplex, where

i GMM SDF

x  _ . The edge stop function can be rewritten as

 

 



2



1

1 _{liver con}

g x

P P x



  (4)

The larger the value ofg x

 

, the faster the curve evolves. The value of g x

 

decreases and the

contour evolve slowly, when the gray of pixel has a large difference from the liver-classified.

GPV-levelset. To maintain the edge features and enhance the anti-noise ability, we propose Gaussian pseudo-variance level set. The pseudo-variance is the variance value of pixels at the evolutionary edge corresponding to the liver-classified area. We define the PV term by

 

     





2

1 2

g liver liver

PV g x P  _ I x H_   dx







 (5)

Where P_{liver is the probability density function of the evolutionary edge,} _liver is the mean value of

liver-classified, _

 

x is the Dirac delta function, and H_

 

x is the Heaviside function. The value of

the PV term and g x

 

are both minimized when the curve is closest to liver boundary.

GPV-Level set. For a level set function:   , the distance regularized level set evolution energy functional  _( ) is defined by





2

1

( ) ( ) ( ) ( )

2

p g g GMM SDF

R GPV A

           _ (6)

where the last term is the constraint of priori shape.   , ,  are the coefficients of the energy functionsR_p( ) , L_g( ) and A_g( ) , respectively. R_p( ) is the level set regularization term[8].

The energy function (6) can be approximated minimized by solving following gradient flow:

 





2

 



2

 



    



= div d_p + gP_liver I H I _liver + g x _{GMM SDF}

t   

              _

 _{     }

 (7)

Experimental Implementation

Quantitative Results

Figure 2 presents three segmentation results of our method. Ground truth is displayed in yellow curves. The red curves are the segmenting curves by our. From the left to right, each column corresponds to the original CT slice, liver-patch, initial segmentation, segmentation results and distance map, respectively. From Figure 2, the proposed method can successfully extract the liver from large intensity (b), and deal the shape variations (a), and handle the ambiguous boundaries (b), capture the long and narrow ravine in liver regions (c). From the distance map, we can see that the overall segmentation results are satisfactory.

0 mm 23.5 mm 0 mm 17.9 mm 0 mm 18.7 mm

a

b

c

Figure 2. Three segmentation results of the proposed method.

Comparison with State-of-the-art Methods

[image:4.595.97.498.192.378.2]

To evaluate the performance of the proposed liver segmentation framework, two experiments have been done to compare it with recently published methods based on the Sliver07 database and 3Dircadb database. The results of each measure represent the mean for the overall datasets. Table 1 shows the quantitative comparative results on SLIVER07 database. For all error comparison metrics, our method achieved much better performance than others. Therefore, the performance of our method performance is comparable to that of doctor which can be deployed for effective liver tissue segmentation.

Table 1.Quantitative analysis on SLIVER07. Table 2. Quantitative analysis on 3D-IRCADb.

Method VOE VD AVD MSD MXD Method VOE VD AVD SD MXD

Dou et

al.[10] 7.7 1.9 1.6 4.1 45.9 Lu et al.[13] 14.9 -0.6 1.9 5.9 44.8

Hu et al.[11] 5.4 0.3 1.0 1.8 19.2 Shi et al.[14] 8.7 2.4 1.4 2.6 26.9 Wu et al.[12] 7.78 1.31 1.29 2.5 23.6 Li et al.[15] 9.15 -0.07 1.55 3.15 28.22

Proposed 4.3 0.2 0.7 1.4 16.7 Proposed 5.7 0.6 1.2 2.5 22.1

Table 2 shows the quantitative comparative results on 3D-IRCADb database. Specifically, the mean AVD, VOE and MXD of our method are 1.2mm, 5.7% and 22.1mm, respectively. However, the VD of our method (0.6%) is slightly higher than Li's and method (0.07%), which means that our method tends to over-segment the liver tissue. These results indicate that our method is more accurate and more robust than other state-of-the-art methods.

Discussion and Conclusion

[image:4.595.55.542.548.627.2]

segmenting two public databases Sliver07 and 3Dircadb. The experiment results are competitive with state-of-the-art methods.

Although our method has better performance for most CT liver image segmentation, there are still some severe clutter images beyond our consideration due to organ diversity and tumor clutter. In future research, we will committe to seek more accurate characterization. Besides, our method is to segment the 2D CT slice and reconstruct them into 3D which may loss some information. Therefore, we will try to segment CT volumes directly to reduce the loss of spatial information.

Acknowledgement

This study was funded by National Natural Science Foundation of China (No. U1401252), Hubei Key Laboratory of Intelligent Vision Based Monitoring for Hydroelectric Engineering (2017SDSJ02) and Chongqing research and innovation project of graduate students (CYS18247).

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