 Research
 Open Access
Automatic liver segmentation in computed tomography using generalpurpose shape modeling methods
 Dominik Spinczyk^{1}Email authorView ORCID ID profile and
 Agata Krasoń^{1}
 Received: 20 February 2018
 Accepted: 23 May 2018
 Published: 29 May 2018
Abstract
Background
Liver segmentation in computed tomography is required in many clinical applications. The segmentation methods used can be classified according to a number of criteria. One important criterion for method selection is the shape representation of the segmented organ. The aim of the work is automatic liver segmentation using general purpose shape modeling methods.
Methods
As part of the research, methods based on shape information at various levels of advancement were used. The single atlas based segmentation method was used as the simplest shapebased method. This method is derived from a single atlas using the deformable freeform deformation of the control point curves. Subsequently, the classic and modified Active Shape Model (ASM) was used, using medium body shape models. As the most advanced and main method generalized statistical shape models, Gaussian Process Morphable Models was used, which are based on multidimensional Gaussian distributions of the shape deformation field.
Results
Mutual information and sum os square distance were used as similarity measures. The poorest results were obtained for the single atlas method. For the ASM method in 10 analyzed cases for seven test images, the Dice coefficient was above 55\(\%\), of which for three of them the coefficient was over 70\(\%\), which placed the method in second place. The best results were obtained for the method of generalized statistical distribution of the deformation field. The DICE coefficient for this method was 88.5\(\%\)
Conclusions
This value of 88.5 \(\%\) Dice coefficient can be explained by the use of generalpurpose shape modeling methods with a large variance of the shape of the modeled object—the liver and limitations on the size of our training data set, which was limited to 10 cases. The obtained results in presented fully automatic method are comparable with dedicated methods for liver segmentation. In addition, the deforamtion features of the model can be modeled mathematically by using various kernel functions, which allows to segment the liver on a comparable level using a smaller learning set.
Keywords
 Liver segmentation
 Single atlas based segmentation
 Active Shape Model
 Gaussian Process Morphable Models
Background
Liver segmentation has been the subject of research by various authors for many years and is required in many clinical applications [1–3]. The most popular imaging mode is computed tomography (CT) or the contrastenhanced CT, which are used for computer aided diagnosis (CAD) [4, 5] and planning and support of computer assisted interventions (CAI) of primary and secondary tumors in liver [6–9]. Precise liver segmentation is also crucial for selective internal radiation therapy (SIRT) [10].
The segmentation methods used can be classified according to a number of criteria. One important criterion for the division is the method of using information about the shape of the organ by a given method [11]. Simple segmentation methods that do not use shape information can be applied to different objects with a uniform intensity distribution and clearly separate the object of the interest from neighboring bodies. Such methods can be applied by selecting the values of several general parameters of the method, which can be selected on the basis of representative examples. In turn, more complex methods contain many parameters that use knowledge in the field of the shape of a segmented object.
The aim of the work is automatic liver segmentation using general purpose shape modeling methods. A new element in the work is the application of the generalized statistical model of the shape deformation method presented in [12].
Methods
As part of the research, methods based on shape information at various levels of advancement were used. The single atlas based segmentation method was used as the simplest shapebased method. This method is derived from a single atlas using the deformable freeform deformation of the control point curves [13, 14]. Subsequently, the classic and modified Active Shape Model (ASM) was applied, using the medium body shape models and organ model [15]. The most advanced method used was generalized statistical shape models, which are based on multidimensional Gaussian distributions of the shape deformation field [12].
Simple atlas method
An atlasbased segmentation method propagates the segmentation of an atlas image using the image registration technique (Fig. 1).
Classic and modified Active Shape Model
In the 1990s, Tim Cootes and Chris Taylor introduced a new segmentation technique called the Active Shape Model (abbreviated as ASM). This method makes it possible to create a medium model of the shape of the object based on the training set, and then iteratively deform and move its boundaries so that it fits the new case as well as possible. The ASM algorithm can be divided into three main stages, which consists of: determining the training set, estimating the average (statistical) shape model, and optimizing the obtained shape model. The classic ASM method uses the point distribution model (PDM), by means of which the pattern of the segmented object is created [16]. The steps necessary to create a shape model are shown in Fig. 2

Creating a series of hypotheses giving approximate locations of model points,

Refining each hypothesis and choosing the best one.

In every set of points there must be n corresponding landmarks,

Each landmark must lie in the image on the edge of the object the model is created,

Each set of n points must form a spatial grid consisting of polygons (creating a verticesfaces representation).
In this paper the ASM with the optimal features is used. This is an alternative to the classic ASM abandoning the creation of the GrayLevel Appearance Model using standardized derivative profiles and without estimating the cost function based on the Mahalanobis distance in favor of the algorithm which allows you to move the landmarks towards a better location during optimization along a perpendicular direction to the object edge [15]. The authors assumed that the best location is one for which everything on one side of the profile is outside the object, and everything on the other side is in the middle of the object. In order to determine whether a given location is in or outside the object, the probability is determined for the area around each landmark, on the basis of which the classification is made. The decision on the best new location of the point is made by the nonlinear classifier of the knearest neighbors classifier (kNNclassifier).
The authors of the article [19] proposed using the iterative closest point method (ICP) to generate a training set. Behiels et al. [20] proposed to improve the way the shape of the model is adjusted to the new case in ASM. In classic ASM, the position and shape parameters are corrected at each iteration by minimizing the sum of the squares of differences between model points and points estimated in a given iteration. This criterion of matching with the smallest squares is sensitive to outliers, which results in poorer results. When the outlying points attract further points towards it, the location of the landmarks can longer be improved in the next iteration. For this reason, it has been proposed to correct the suggested dX displacements before updating the position and shape parameters.
In order to prepare the data, all the images were subjected to the initial phase of data processing resulting in the generation of volumes on which the liver is visible in 60 crosssections. The initial processing phase can be divided into two stages. In the process of creating models of liver shape, prepared, segmented images were used. Based on these images, the edge of the liver was marked. Then 20–100 points lying on the designated border were selected. For the first four and last liver crosssections, the number of landmarks changed by 20 points, while for others the number was constant and amounted to 100. Three image resolution coefficients were used in the calculations: 0.25, 0.5 and 1. For each of them, five iterations with unchanged parameters were made. During results generation, the length of the profiles was 8 pixels, the number of determined landmark positions was 6 and the limits of the own values to 3.
Generalized statistical shape model

Rigid registration of input images

Finding correspondence in example sample vectors

Building a statistical shape model based on sample shapes

Segmenting of a new case
Rigid registration of input images
The data collection of abdominal CT reference images together with the expert outlines of the liver organ is subjected to a rigid registration of the similarity based on the minimization of MI, which brings the entire set to one common coordinate system. This is a necessary step because the generalized statistical model simulates shape deformations.
Finding correspondence in example shape vectors
 1.
Selecting of one of the shapes as a reference shape.
 2.
Building a Gaussian process on a reference model using the kernel function for a smooth deformation model.
 3.
Distributing the Gaussian process to r KarhunenLoe ve coefficients.
 4.
Registering of the model to individual shapes from the training set using the model development as a function of regularization in the registration task consisting of minimizing the distance measure.
Building a statistical shape model based on sample shapes
Segmentation of a new case
After constructing a generalized model of probabilistic distribution of shape deformation based on shapes from the training set, such a model can be used to segment the object in a new input image. In this case, the properties of a continuous multidimensional Gaussian process. The algorithm adjusting the model minimizes the Mahalanobis distance between the given and the average profile along the normal direction to the model. The main difference between ASM and GPMM is the generation of candidates for the new location of the points matching the image of the model. In the classic ASM approach, candidates are found along the normal vector to a model with a given length parameter. In the case under consideration, candidates are generated as samples from the Gaussian distribution of liver shape deformation built on the training set. Therefore, the new position of the model point does not have to be on the normal vector, but results from the probability distribution of the shape deformation field. In order to preserve the possibility of comparing the results in the considered scenarios, the same number of model points was used as in the case of the classical ASM algorithm.
Input data set
For the liver segmentation, 20 CT images of the abdominal cavity with a resolution of 512 by 512 pixels available in the SILVER07 database were used [22]. The number of crosssections on the images ranged from 64 to 394, while their thickness ranged from 0.7 to 3 cm. Each volume also contained a binary image with a segmented liver organ made with the help of radiologists (experts).
Quantifying segmentation quality
Ground truth, which are usually manually segmented by a human expert, is necessary to quantify segmentation accuracy.

Dice similarity coefficient (DICE) defined as:where \(I_{FSeg},I_{MSeg}\) present two segmentations and \(\cdot\) denominates the number of voxels inside the segmentation,$$\begin{aligned} DICE(I_{FSeg},I_{MSeg}(T))= 2\frac{I_{FSeg} \cap I_{MSeg}(T)}{I_{FSeg}+I_{MSeg}(T)}*100\% \end{aligned}$$(13)

Mean surface distance (MSD) is defined as:where \(n_{X},n_{Y}\) represent the number of voxels on the two segmentation surfaces respectively, and d are the closest distances from each voxel on the surface to the other surface. The value of this measure helps to identify distance between registered surfaces.$$\begin{aligned} MSD(I_{FSeg},I_{MSeg}(T))= \frac{1}{n_{X}+n_{Y}}\sum _{i=1}^{n_X} d_i\sum _{j=1}^{n_y} d_j \end{aligned}$$(14)

Hausdorff distance is defined as:where \(N_{X},N_{Y}\) represent the voxels on the two segmentation surfaces respectively, and \(d_i\) and \(d_j\) are the closest distances from each voxel on the surface to the other surface.$$\begin{aligned} H(I_{FSeg},I_{MSeg}(T))= \max \left\{ \sup _{x\in N_X}\inf _{y\in N_Y}d(x,y),\sup _{y\in N_Y}\inf _{x\in N_X}d(x,y)\right\} \end{aligned}$$(15)
Results
The segmentation quality measures defined above (DICE, MSD, Hausdorff) were used to present the results. Table 1 presents a quantitative summary of the obtained results. Statistical analysis of the results of the DICE coverage coefficient was performed. After demonstrating the lack of normal distribution (ShapiroWilk test), the Wilcoxon test was used to verify the median equality. Statistically significant differences in median DICE coefficient for the method of generalized statistical form factor in relation to Active Shape Model based on medium shape and a single atlas were demonstrated. The graphical representation of the results below presents the best and worst result of liver organ segmentation (according to the criterion of the DICE—Fig. 4).
Quantifying segmentation results according using methods  shape model points was limited to 10,000 and to 10 cases in training set
Similarity measure  Single atlas SSD  Single atlas MI  Classical ASM  Modified ASM  GPMM 10,000 pts  GPMM 19,000 pts  GPMM 40,000 pts 

MSD (mm)  3.49  3.08  2.91  2.85  2.79  1.95  1.7 
H (mm)  6.02  4.65  574.29  572.95  4.32  3.7  2.9 
DICE (%)  0.49  0.59  0.57  0.57  0.74  0.85  0.885 
Discussion
Liver segmentation using the methods used (singleatlas method, ASM and generalized statistical model of shape deformation) showed differences in results depending on the approach used (Table 1). The more complex the shape model used, the better the results. The poorest results were obtained for the single atlas method, with the measure of MI from the SSD measure being a better measure of similarity. In the case of the ASM method, in 10 analyzed new cases for seven test images, the DICE coefficient was obtained above 55\(\%\), of which for three of them the coefficient was over 70\(\%\), which placed the method in second place.The best results were obtained for the method of generalized statistical distribution of the deformation field. The best results had a DICE of 75\(\%\). Various specialized methods of liver segmentation are described in the literature [2, 23, 24]. They present DICE coefficients between 85 and 95 \(\%\). The lower value of DICE in the presented approach can be explained by the use of generalpurpose shape modeling methods, with a large variance of the shape of the modeled object—the liver. Due to the database of contoured expert cases, the training set was limited to 10 cases and number of shape model points was limited to 10,000.
To confirm the competitiveness of the proposed method, the approach used was compared with the three best methods dedicated to liver segmentation indicated in the MICCAI challenge [22]. In these studies we demonstrated the scalability of the proposed method. We increased the number of model points holding four times with an average DICE rating of 88.5\(\%\) and scoring according to the MICCAI Challenge criterion 65 pts. The authors of these articles shared the results they obtained. The best methods [25–27] scored 73, 59 and 43 pts respectively. Compared with the dedicated methods for liver segmentation with MICCAI challenge [22], the method took the 2nd place. The first place was taken by a method containing both a deformation based on FreeForm Segmentation statistics and shape statistics. However, this method required advanced assumptions and calculations related to Constrained FreeForm Deformation for a typical intensity distribution around the liver. In addition, the model the statistical was built on a four times larger training set [25]. The presented method does not contain any stages characteristic for the liver and is also fully automatic. In addition, the deforamtion features of the model can be modeled mathematically by using various kernel functions [12], which allows to segment the liver on a comparable level using a smaller learning set.
In the future, it is planned to create a deformation model on a larger training set.
Conclusions
The aim of the work is automatic liver segmentation using general purpose shape modeling methods. A new element in the work is the application of the generalized statistical model of the shape deformation method presented in [12]. Due to the clinical relevance of the problem of automatic liver segmentation and the existence of many highly specialized methods and the development of generalpurpose methods of statistical shape modeling, research on the effective use of generalpurpose methods to support clinical goals seems to be one of the many significant directions of development of modern biomedical engineering.
In the presented approach, a DICE of 88.5\(\%\) potentially indicates an the possibility of effective use of the modern generalpurpose methods while building the most representative dictionaries that cover the variability of anatomical shapes in the patient population. The obtained results in presented fully automatic method are comparable with dedicated methods for liver segmentation. In addition, the deforamtion features of the model can be modeled mathematically by using various kernel functions, which allows to segment the liver on a comparable level using a smaller learning set.
Declarations
Authors' contributions
Conception and design of the work, Drafting the article, Final aproval of the article: DS. Data analyis: AK. All authors read and approved the fnal manuscript.
Acknowledgements
We want to thanks Andre Woloshuk for English language corrections.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The data that support the findings of this study are available as part of the workshop 3D Segmentation in the Clinic: A Grand Challenge, on October 29, 2007 in conjunction with MICCAI 2007 [22].
Consent for publication
Not applicable.
Ethics approval and consent to participate
Bioetic Commission for this study is not necessary.
Funding
There is no founding for presented research.
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Authors’ Affiliations
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