

ORIGINAL ARTICLE 

Year : 2019  Volume
: 5
 Issue : 2  Page : 8589 

Active contour model for medical sequence image segmentation based on spatial similarity
Chencheng Huang^{1}, Denglan Lei^{1}, Zhaofei Li^{2}
^{1} College of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing, China ^{2} College of Automation and Information Engineering, Sichuan University of Science and Engineering, Sichuan, China
Date of Web Publication  23Sep2019 
Correspondence Address: Chencheng Huang Chongqing Technology and Business University, Chongqing China
Source of Support: None, Conflict of Interest: None  Check 
DOI: 10.4103/digm.digm_11_19
Background and Objectives: Image segmentation is the basic problem in computer vision and pattern recognition. This study mainly focuses on the segmentation of medical sequence images. Materials and Methods: In this article, we considered the spatial similarity of the medical sequence image in active contour model (ACM) for segmentation. First, by utilizing the similarity of object contour between adjacent slices of medical images, and then using the segment result of the former slice as the initial contour of the next image to segmentation. The proposed model can automatically obtain a better initial contour location and reduce the computing cost for segment processing. Second, to improve the accuracy of image segmentation, we considered the similarity of the object contour between adjacent slices, and introduce a punishment term in localized ACM. Results: We compared our model and other methods for segmenting medical brain magnetic resonance slices, and the experimental results on synthetic medical sequence images validate the effectiveness of the proposed method. Conclusions: By utilizing the similarity of object contour between adjacent slices of medical images, and using the segment result of former slice as the initial contour of the next image to segment, the proposed model can obtain better initial contour location for segmentation sequence images and reduce the computing cost for whole medical sequence image segmentation process.
Keywords: Active contour model, image segmentation, medical sequence image, spatial similarity
How to cite this article: Huang C, Lei D, Li Z. Active contour model for medical sequence image segmentation based on spatial similarity. Digit Med 2019;5:859 
Introduction   
Image segmentation is the basic problems in computer vision and pattern recognition. It is an important way to extract specific tissues for medical images and do some quantitative analysis in medical diagnosis. When comparing with ordinary images, medical images often are characterized by fuzziness and inhomogeneity.^{[1]} To accurately distinguish the structure and pathological tissue of normal tissue, it is necessary to segment various tissues in medical images. In the process of medical diagnosis, the image of the lesion location is usually given in the form of sequence. Therefore, to get the more accurate volume measurement and location of the pathological tissue, it is necessary to divide the medical sequence images and display the threedimensional (3D) image, and then, doctors can make the correct diagnosis. At present, the active contour models (ACMs)^{[2]} based on curve evolution are widely and successfully applied in image processing. Moreover, the level set method (LSM) proposed by Malladi et al.,^{[3]} and Osher and Fedkiw^{[4]} can represent the shape of objects in images flexibly. ACM with LSM is widely used in image segmentation such as medical, industry, and other applications.^{[5],[6],[7]}
One of the most popular ACM is the curriculum vitae (CV) model,^{[5]} which use the whole image statistical information of inside and outside of the evolution curve, to construct the energy functional. When giving an initial contour, the curve can automatically move to the object boundaries. The CV has been successfully applied in images with intensity homogeneous. However, for images with intensity inhomogeneity, CV model may not go well.^{[6],[7]}
For images with intensity inhomogeneities, many models were proposed and discussed. Chan and Vese^{[8]} proposed the piecewise smooth model. Li et al.^{[6],[7]} proposed the regionscalable fitting (RSF) model or local binary fitting (LBF) model, which utilizes the local image information as constraints, can well segment objects with intensity inhomogeneities. RSF (LBF) model was successfully used in medical image segmentation such as magnetic resonance (MR) and computed tomography images.
In this article, we propose an ACM to segment medical sequence images, which has less computing cost and more accuracy. For medical sequence images, we consider the spatial similarity of adjacent slices and construct the energy functional by using the difference between the adjacent objects as a constraint of the energy functional which can obtain more accurate object contour and by utilizing the final contour of object as the initial contour of the next adjacent slice, which can reduce the time of curve evolution and the computing cost for whole medical sequence image segmentation process.
The rest of the article is organized as follows. In section materials and methods, we review some classic models and indicate their limitations and describe our model and its variational formulation. In section results, we validate our method by various experimentations on synthetic and real images.
Materials And Methods   
Background
CV model
Chan and Vese^{[5]} proposed an ACM to segmentation image with two phases. Let Ω be a region, I: Ω → R be an input image, and c be a closed curve; they defined the energy functional as follows:
Where, λ_{1},λ_{2}, and μ are fixed nonnegative constants, in(C), out(C) represent the region inside and outside of the curve C, and c_{1}, c_{2} are two constants which represent the approximately intensity values of I inside and outside of C. L(C) represents the length c. The first two terms of the right side in Eq. (1) were called the data terms, which play an important part in segment objects; the last terms were called the smooth term.
By using LSM, they obtain the following functional:
Where, φ is a level set function, and φ = 0 represent the curve C, μ_{i} (φ) (i = 1,2) is the membership function of φ, δ (φ)represents the Dirac function. The gradient flows^{[8]} were used to minimize the Eq. (2), and they obtain the curve evolution equation as follows:
Where, c_{1}, c_{2} can be calculated by:
From Eq. (4), c_{1}, c_{2} are two constants which represent the mean intensities inside and outside the curve C. Moreover, the CV model has good performance in segment image with two phases and can obtain a larger convergence range and less sensitive to the initialization. However, for images with intensity inhomogeneity, the intensities inside or outside of the curve c are not homogeneous, the constants, c_{1}and c_{2} may not suitable for approximate the mean intensities inside and outside the curve of C. Hence, the CV model may fail to segment image with intensity inhomogeneity.^{[5],[6]}
Regionscalable fitting model
To segment images with intensity inhomogeneity, Li et al. proposed the RSF or LBF model.^{[5],[6]} They considered the local region of image and defined the following energy functional:
Where, λ_{1},λ_{2}, and μ are fixed nonnegative constants, y is a point belong to the local region of x, x–y≤ (ρ > 0)), K σ(x) is a truncation Gaussian kernel function with standard deviation σ, and f_{1}, f_{2} are the fitting functions in the local region of two sides of curve C. Using LSM, they obtain the following functional:
To avoid the reinitialize of level set function, they add the following regularize term:
Then, the level set energy functional of RSF equation can be written as follows:
Where f_{i} (x) can be calculated by:
Using the gradient flows, we have the following level set function evolution equation:
Here,
The RSF model can obtain desirable segmentation results of the image with intensity inhomogeneity because of using the local intensity information. However, the computational cost of the RSF model is still very high^{[9]} and is sensitive to initialization to some extent^{[10]} which limits its practical applications.
Our method
In this section, we present and discuss the details of the medical sequence image segmentation based on spatial similarity model. In most medical image segmentation, the active model usually segments the single image or 3D volume data directly, that may cost more computing time. For 3D image segmentation, the slices interval of volume data may affect the segmentation results. Hence, we consider the medical sequence segmentation. We utilize the spatial similarity of objects between the adjacent slices to construct the energy functional based on the RSF model. As we see from [Figure 1], objects contour had high similarity in three adjacent slices of MR brain images.
As we discussed in section 2, the RSF model was successfully applied in medical image segmentation. However, for localized models, the segmentation results may be sensitive to the initial contours [Figure 2].
Assume that there are n medical image slices, we defined the following penalty term:
Where, φ represents the level set function of the ith slices, φ^{*}_{i}(i = 1, 2, …., n) is the final level set function (segment result) of the ith slices, and φ^{*}_{0} is the initial contour of the first slices.
By combining with RSF model, we have the following segmentation model for medical sequence images (for 2 phases):
 Note 1: We use the spatial similarity of objects between the adjacent slices. The penalty term cannot allow the differences of level set function between adjacent slices become larger, and make the segmenting model obtain more accurate object boundaries.
 Note 2: There implies an initial contour location in our model, which is very important for localized models. As the difference of φ^{*}_{i}_{1} and φ^{*}_{i} are similar, then we can use φ^{*}_{i}_{1} as the initial contour of the ith slices, and the φ^{*}_{i}_{1} is really located near the object boundaries of the ith slices. This way of initialization can reduce the computing cost of the ith slices.
Minimizing the Eq.(13), we have the following level set function evolution function (2 phases):
Where,
Results   
We compare RSF and our model for segment 145 medical brain MR slices; the initial contour is the same location of each slice [Figure 3] row 1, columns 1]. [Figure 3] is the partial segmentation results of RSF and our model. The first rows are the results of RSF, and the second rows are the results of our method. The columns 1 are the initial contours, the columns 2 are the results of the 70th slices, and columns 3 are the results of the 71th slices. We can see from [Figure 3] that both RSF and our model can obtain the right boundaries of the objects in the 70th slices; but for the 71th slices, RSF fail to obtain the object boundary (upper left of row 1, columns 3). As the use of the spatial similarity of adjacent slices, we use the 70th slices finallevel set function as the initial contour of the 71th slices (row 2, columns 1); our model can successfully obtain the object boundary.  Figure 3: Partial segmentation results of brain MR images of RSF and our method
Click here to view 
We also compare the computing cost between RSF and our model for segmentation 145 MR brain sequence. We use Matlab 2016a to run the algorithm, and the experimental environment is based on Win 7, 64 bit, Core 2 2.4GHz CPU, 4GB RAM. The CPU times of RSF and our method are shown in [Table 1]. As we see from [Table 1], RSF may use 150 iter number to get the final results, and our model can largely reduce the convergence time (only 30 iter numbers). That means, our model has more efficiency in segmentation medical image sequence.
Discussion   
In this article, [Figure 1] shows the space similarity of the object in adjacent slices, which is very important for sequence images segmentation in the proposed model. [Figure 2] demonstrates that the better result of the segment model can be obtained depending on the suitable location of initial contours. [Figure 3] demonstrates the comparison between the proposed method and RSF model for segmenting the sequence of the brain images. The proposed method can get better segment result because of utilizing the space similarity for objects between two adjacent slices. [Table 1] shows compting cost of the proposed method and RSF model for segment squence images.
This article proposed an ACM for segment medical sequence images utlizing space similarity of the image slices. The proposed model not only can get more accurate segment results but also can greatly reduce the computing cost of segmenting.
Conclusions   
This article presents an ACM for medical sequence image segmentation based on spatial similarity. We utilize the similarity of object contour between adjacent slices of medical images and use the segment result of the former slice as the initial contour of the next image to segment; the proposed model can obtain better initial contour location for segmentation sequence images and reduce the computing cost for whole medical sequence image segmentation process. To keep the accuracy of segment results, we introduce a punishment term in localized ACM. Experimental results on synthetic medical sequence images prove that the proposed model can obtain more accurate segmentation result and much less computing cost.
Acknowledgments
This work is supported by the Natural Science Foundation of Sichuan University of Science & Engineering (2015RC49, 2014RC11, 2015RC16).
Financial support and sponsorship
Nil.
Conflicts of interest
There are no conflicts of interest.
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[Figure 1], [Figure 2], [Figure 3]
[Table 1]
