Segmentation of Kidneys from Computed Tomography Using 3D Fast GrowCut Algorithm Gao-Yuan Dai, Zhi-Cheng Li, Jia Gu, Lei Wang, Xing-Min Li
Abstract— This paper proposes a fast GrowCut (FGC) algorithm and applies the new algorithm in three-dimensional (3D) kidney segmentation from computed tomography (CT) volume data. Users could mark the object of interest with different labels in CT slices. FGC propagates the labels using monotonically decreasing function and gray features to derive an optimal cut for a given data in space. The gray features play a great role in comparing wi th neighborhood cells. The with experimental results clearly demonstrate the superiority of FGC uracy and speed. in acc accuracy Fast Grow Cut (FGC), three dimensional Index Terms—Fast segmentation, kidney segmentation.
I. INTRODUCTION Medical images segmentation refers to the process of deriving meaningful regions from medical images that are homogeneous with respect to local image features such as edges, texture, color, etc [1]. The three-dimension (3D) segmentation of kidneys from computed tomography (CT) or magnetic resonance (MR) is an important task in several specific therapies of renal diseases, such as surgical planning and navigation in kidney tumor ablation or Percutaneous Nephrolithotomy (PCNL), and volume assessment for patients with kidney transplants or chronic kidney diseases [2]. Segmenting 3D structures from medical images is difficult due to the sheer size of the datasets and the complexity and variability of the anatomic shapes of interest [3]. On the other hand, the sampling artifacts, spatial aliasing and noise typical of sampled data could cause the boundaries of structures to be indistinct and disconnected [4]. More complications will arise when it comes to segment the kidney from CT, as the gray value of kidney is often similar with nearby tissues such as liver and spleen. Furthermore, obtaining accurate and repeatability segmentation of kidney is often subject to intra-operator and inter-operator variability [5]. Many different methods have been studied for segmentation of structures or organs of interest. The commonly-used methods include region growing, statistical shape models and level set segmentations [6]. Region Growing approaches exploit the fact that pixels within Gao-Yuan Dai, Zhi-Cheng Li, Jia Gu and Lei Wang are with Shenzhen Key Laboratory for Low-cost Healthcare, Key Lab for Health Informatics, Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences, Xueyuan Avenue 1068, Shenzhen 518055, China (e-mail:
[email protected],
[email protected],
[email protected],
[email protected]). Gao-Yuan Dai, Xing-min Li are with Computer School South China Normal University. Zhongshan Road 80, Guangzhou 510631, China(e-mail:
[email protected],
[email protected])
978-1-4799-2341-0/13/$31.00 ©2013 IEEE
specific organ are often have similar gray values. [7, 8, 9]. Statistical shape model-based methods often constrain itself from catching details during deformations. This is because the number of eigenvector cannot exceed the number of training samples. [10, 11, 12]. The level set method is able to handle topological changes naturally. However, it is sensitive to the initial placement of the contour and often time-consuming [13, 14, 15, 16]. Besides, Growcut is based on Cellular Automaton while the graph cut (GC) is applied with multi-selection of seed labels to provide the hard constraint. A good medical image segmentation method requires the algorithm yields accurate and repeatable result within acceptable time. In this paper, we propose a Fast GrowCut algorithm (FGC) for 3D CT image segmentation. For every pixel, the proposed FGC algorithm propagates the labels using monotonically decreasing function and gray features to derive an optimal cut for a given data in space. The main differences between FGC and traditional GrowCut are: 1. We improve the three dimensions GrowCut algorithm and apply it to kidney segmentation from CT images. The segmentation results were directly obtained in the form of volume data without calculating slice by slice. 2. The proposed FGC is fast as it propagates the labels based on monotonically decreasing function and gray features. This feature is important as it reduces computational time in 3D image segmentation. This paper is organized as follows. In section II, we describe the details of proposed FGC method. In section III, the proposed method is evaluated via experiment of CT kidney segmentation. The summary and conclusion are presented in section IV. II. METHODS A. Original GrowCut The GrowCut algorithm was first proposed by Vladimir Vezhnevets in 2005[17]. In original GrowCut,given a small number of user-labeled pixels, the rest of the image is segmented automatically by a Cellular Automaton (CA) which is the key of GrowCut algorithm. CA was introduced by Ulam and von Neumann in 1966. Typically, a CA consists of some pre-defined state-transition rules, determining the value of each cell based on the value of its neighborhood cells [18]. In case of kidney segmentation from CT volume data, the state transition rules are applied iteratively to update the value of each pixel. Considering the computation load, we found it is difficult to segment 3D images with traditional GrowCut algorithm, because 1) too many seed points are needed to be selected manually, 2) the running time is too
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ICIP 2013
long. Therefore, we next propose FGC in order to segment 3D structures. B. Proposed method: FGC The FGC is also based on cellular automaton. A cellular automaton is defined using a triple ( S , N , δ ) , where S is a non-empty state set, N is the neighborhood system, and δ : S N → S is the local transition function. This function defines the rule of calculating the cell’s state at t + 1 time step, using the states of the states of the neighborhood cells at previous time step t . The main aim of the proposed FGC is to reduce user interaction and reduce operation time. The flowchart of the kidney segmentation using FGC is shown in Figure 1.
Segmentation is over,output the label data as result NO
At tim e T,Obtain the value and state of neighborhood cells around the seed pixels
Those neighborhoods which fulfill the rule will be labeled and become the new seed pixels
YES
YES
If there are neighborhood around
If Function judgment and t h e v alu e o f pending pixel similar With se e d
strength values are assigned with 1. Otherwise, the strength values are assigned with 0. Step 3. If there is neighborhood cell around the seed point, we obtain the value of neighborhood cell. The neighborhood system we use is called Moore neighborhoods Zn is the integer space. （1） N ( p) = {q ∈ Z n : p − q ∞ := max pi − qi = 1} i =1,n
g ( I p − I q ) ⋅ θ qt > θ tp . The advantages include the reduction
NO Traverse the remaining pixe ls
final goal of the segmentation is to assign each pixel one of the possible labels. The states of all the pixels are considered as the state of cellular automation. We set the initial states as: l p = 0, θ p = 0, I p = Intensity . For the labeled pixels, the
In this paper, we will compare the 26-neighborhood system (26 cube-around) with 6-neighborhood system (up, down, left, right, front, and back) around the seed pixel. Step 4.The labeling process starts from the seed pixels and try to occupy their surrounding pixels. At each step, each cell tries to attack its neighbors. When the value of neighbor’s strength multiply a monotonically decreasing function g ( x) ∈ [0,1] is larger than defending-cell strength and their values is belong to the scope of kidney gray value, the label and strength of defending-cell will be replaced by its neighbors. The competition will go on until automaton converges to stable configuration. In particular, FGC propagates the labels using monotonically decreasing function and gray features. Considering the fact that value of kidney images is similar with surrounding tissue, the seeds marked by users may be not always correct. Therefore, we add the contrat of gray value I p − SEED ∈ [0,12] to the condition of
The abdominal CT image series
The initial seed pixels marked by u se r
vector, for gray scale images, I p is the pixel intensity. The
All the labeled pixels will be the initial seed in time T+1
of required human interaction and computing time. Step 5.After traversing all pixels, we will get the volume data of labels as segmentation result.
Figure 1: The flowchart of kidney segmentation
Step 1. The abdominal CT volume data is used as the algorithm input. The volume data is a 3D array of m × n × l pixels Step 2. The segmentation starts with selecting seeds manually. Here we define three types of pixels in CT slices: the object of interest, the background, and the neutral territory. The object of interest is marked by user as ”1”,while the background is marked as ”-1”. The unmarked area belongs to neutral territory, which is marked by user as ”0”. In order to pick seed points in the volume data easily, users are allowed to draw continuous curves with different colors in CT slice instead of set point. For example, the red curve is used to mark the region of interest, while the blue curve is used to mark the background. The label-marking can be finished within a few minutes. The state of pixel p in volume data is given by three triple (l p , θ p , I p ) where l is the label, θ p is the strength of the current cell, we assume that θ p ∈ [0,1] , I p is the cell feature
III．RESULTS The medical data used for algorithm evaluation consists of 3D abdominal CT data from 10 different healthy patients of mixed gender (5 Men, 5 Women) and age(18 to 48 years old). The data was acquired using Siemens CT scanners Sensation 16 with a resolution in x/y/z from 0.6/0.6/5 to 0.75/0.75/5 (in mm) and provided in DICOM format. The image dimension is 288 × 288 ×104 . The algorithm was run on the 64-bit HP Z800 workstation, with Inter(R) Xeon(R) CPU and 24.0 GB RAM. The evaluation and experimental results obtained are described below. The proposed segmentation method was evaluated in terms of accurate, processing time and repeatability. The kidney pairs were manually segmented slice by slice and approved by a nephrologist. The manual segmentation results were used as the gold standard in all experiments,as shown in Figure 2. The evaluation of the FGC is based on the comparison with the gold standard. Specifically, the accuracy was
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evaluated in terms of the difference between the FGC segmentation and the gold standard.
Figure 4. The result of FGC
Figure 2 :The result of Gold standard .
Assume that the gold standard data is { g1 , g 2 ,⋯ , g N , i ∈ [1, N ]} , Then, the accuracy in terms of mean square error was calculated as: 1 A= ( g1 − x1 ) 2 + ( g 2 − x 2 ) 2 ⋯ + ( g i − xi ) 2 ⋯ + ( g N − x N ) 2 N i ∈ [1, N ] （2） The algorithm speed is estimate by the execution time. In addition, we estimate the robust R using the variance of accurate A . Assume that A is the average value of { A , A , ⋯ , A } . Then the variance is: 1
2
Here, we compare the result of Fast GrowCut with traditional GrowCut and region growing. The results are shown in Table1. 6N denotes that 6 neighborhood system was used while 26 represents the 26 neighborhood system. RG means region grow segmentation results. Table1:Compare between different methods
10
1 [( A1 − A) 2 + ( A2 − A) 2 + ⋯ + ( A10 − A) 2 ] （3） 10 Before the experiment begins, users specify seeds with different colorful curves slice by slice. The red curves represent object of interest (number of label is 1). The blue curves represent background (number of label is -1). The unmarked areas are the neutral territory(number of label is 0).It took about two minutes on average to mark hundreds seed points. Figure 3 is one of the marked image.
TIME(s)
SEED
ACCU
ROB
GrowCut 6N
179. 2
862
0. 0098
0. 015
GrowCut 26N
306. 8
862
0. 0012
0. 012
3D RG 6N
143. 7
1
0. 1265
0. 031
3D RG 26N
158. 8
1
0. 1079
0. 029
FGC
173. 7
357
0. 0026
0. 005
Manual-segment
2096. 2
15873
0
0
R=
In Talbe1, the running time of manual-segment is 2096.2s as 15873 seed points need to be picked. The running time and required seed-numbers of FGC are between region growing and traditional GrowCut. It shows that the accuracy and repeatability of region growing are worse than traditional GrowCut. The segmentation result of given data is also influenced by the number of neighborhood cells around seed points. Generally, more seed points yield more accurate segmentation. However, the accurate changes slowly when there are enough seeds. The relationship between the number of neighborhood cells and accuracy is shown in Figure 5.
Figure 3:One slice of original image
After the user specify seed points, FGC finishes the segmentation process in 173.7s. The result is shown in Figure 4.
Figure 5: The accuracy of results versus the number of seed points
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The relationship between neighborhood cells and time is shown in Figure 6. It is quite clear that the running time increases with the number of seed points.
[4]
[5]
[6]
[7]
[8]
[9] Figure 6: The running time with different seed points [10]
IV. CONCLUSION We propose a 3D segmentation algorithm named FGC based on cellular automaton and apply it to segment kidney form CT. The segmentation results of 3D FGC method are better than the results of existing 3D segmentation methods, for example, region growing. The algorithm complexity is independent of the image size, the number of image features and neighborhood cells. For the number of neighborhood cells considered by 6-neighborhood method considers is not many as 26-neighborhood, the result of 26-neighborhood is better while 6-neighborhood is faster.
[11]
[12]
[13]
[14] [15]
ACKNOWLEDGMENT This work is supported in part by grants from National Natural Science Foundation of China (No.61102086, No. 81171402), NSFC Joint Research Fund for Overseas Research Chinese, Hong Kong and Macao Young Scholars (30928030), Image guided high-risk surgical series products (No.2012AA021105), National Basic Research Program 973 (2010CB732606) from Ministry of Science and Technology, China, Guangdong Innovative Research Team Program (No. 2011S013), China.
[16]
[17]
[18]
References [1] [2]
[3]
Tian, J , Medical Image Processing and Analysis , in Chinese, Publishing House of Electronics Industry, 2003, pp. 35–95. Zhicheng Li, Kai Li, Ken Chen and et al, Comparison of 2D and 3D Ultrasound Guided Percutaneous Renal Puncture, in Proc. World Congress on Medical Physics and Biomedical Engineering, May 2012. (Oral Presentation) J. Z. Chen, G. S. Tracton, M. Rao, S. Joshi, E. L. Chaney, and S. M. Pizer, "Comparison of automatic and human segmentation of
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kidneys from CT images", Int. J. Radiation Oncology Biology Physics, vol. 54, pp. 82. 2002 K. H. Zou, S. K. Warfield, A. Bharatha, C. M. C. Tempany, M. R. Kaus, S. J. Haker, W. M. Wells III, F. A. Jolesz, and R. Kikinis, "Statistical validation of image segmentation quality based on a spatial overlap index 1: Scientific reports", Acad. Radiology, vol. 11, pp. 178 -189 2004 . B. Tsagaan, A. Shimizu, H. Kobatake, K. Miyakawa, and Y. Hanzawa, "Segmentation of kidney by using a deformable model, " in Int. Conf. Image Processing, vol. 3, Thessaloniki, Greece, 2001, pp. 1059-1062. Martin Spiegel, Dieter A. Hahn, Segmentation of kidneys using a new active shape model generation technique based on non-rigid image registration, Computerized Medical Imaging and Graphics, 2009. J. Wu, S. Poehlman, M. D. Noseworthy, and M. V. Kamath, "Texture Feature based Automated Seeded Region Growing in Abdominal MRI Segmentation, " presented at International Conference on BioMedical Engineering and Informatics, Hainan, China, 2008. N. A. Mat-Isa, M. Y. Mashor, and N. H. Othman, "Seeded Region Growing Features Extraction Algorithm; Its Potential Use in Improving Screening for Cervical Cancer, " International Journal of The Computer, the Internet and Management, vol. 12, pp. 61-70, 2005. U. K. Ngah, N. A. Mat Isa, and M. M. Noor, “Automated Seed-based Region Growing using the Moving K-means Clustering for the detection of Mammographic Microcalcifications, ” Proceedings, paper no. 154, the World Congress on Medical Physics and Biomedical Engineering (WC 2003), Sydney, Australia, 2003. D. L. Pham, C. Xu, and J. L. Prince, "Current methods in medical image segmentation, " Annu. Rev. Biomed. Eng. , vol. 2, pp. 315-338, 2000. Hao Chen, Zhicheng Li, Qingsong Zhu and et al, “Development and Evaluation of Ultrasound-based Surgical Navigation System for Percutaneous Renal Interventions”, in Proc. International Symposium on Bioelectronics and Bioinformatics (ISBB), Nov. 2011. (Oral Presentation) T. F. Cootes, C. J. Taylor, D. Cooper, and J. Graham. "Active Shape Models - their training and application. " Computer Vision Image Understanding, 61(1): 38-59, 1995. R. Kimmel , A. Amir and A. Bruckstein "Finding shortest paths on surfaces using level set propagation", IEEE Trans. Pattern Anal. Mach. Intell. , vol. 17, no. 6, pp. 635 -640 1995 Christophe Samson,Laure Blanc-Féraud,Gilles Aubert,Josiane Zerubia. A Level Set Model for Image Classification[J] ,2000 J. A. Sethian "A fast marching level set method for monotonically advancing fronts", Proc. Nat. Acad. Sci. , vol. 93, no. 4, pp. 1591 -1595 1996 C. Li , C. Xu , C. Gui and M. Fox "Level set evolution withoutre-initialization: A new variational formulation", Proc. IEEE Conf. Comput. Vis. PatternRecognit. , pp. 430 -436 2005 V. Vezhnevets and V. Konouchine, Grow-Cut - Interactive Multi-Label N-D Image Segmentation, Proc. Graphicon, pp. 150– 156, 2005. Payel Ghosh, Sameer K. Antani, L. Rodney Long, George R. Thoma, Unsupervised Grow-Cut: Cellular Automata-based Medical Image Segmentation, 2011 First IEEE International Conference on Healthcare Informatics, Imaging and Systems Biology.
