Liver segmentation plays a crucial role in liver structural analyses, volume measurements, and clinical operations (e.g., surgical planning). For clinical usage, the accurate segmentation of a liver is one of the key components of automated radiological diagnosis systems. The manual or semi-automatic segmentation of the liver is an impractical task because of its large shape variability and unclear boundaries. Unlike other organs, ambiguous boundaries with heart, stomach, pancreas, and fat make liver segmentation difficult. Thus, for a computer-aided diagnosis system, the fully automatic and accurate segmentation of the liver plays an important role in medical imaging.
Multiple methods have been proposed to segment a liver [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. The simplest and most intuitive approaches to perform liver segmentation are thresholding and region growing [1, 2]. Active contour model approaches [3, 4] have also been reported, mainly using intensity distributions. However, such a local intensity-based approach easily fails owing to the great variability of shapes and intensity contrasts. Shape-prior-based methods such as active shape model, statistical shape model, and registration-based methods have been developed to overcome such difficulties [7, 5, 6, 11, 12, 13, 10]. Shape-based methods are more successful than simple intensity-based methods owing to embedded shape priors. However, the shape-based methods suffer from limited prior information because of the difficulty of embedding all inter-patient organ shapes. Thus, the number of training statistical models directly affects the model matching performance.
In recent years, deep neural networks (DNNs) have widely been used for various imaging applications [14, 15, 16, 17, 18, 19, 20, 21, 22]. For imaging applications, the convolutional neural network (CNN) is the most effective used network with respect to image classification [14, 15, 16], segmentation [17, 18, 19, 20, 22], and enhancement [21, 23]. Various active studies have successfully applied CNNs to medical image segmentation [24, 25, 26, 27, 28, 29, 30, 31, 22, 32, 33, 34]. The U-net applies contracting and expanding paths together with skip connections, which successfully combines both low and high-level features . However, the U-net is not suitable for volumetric image segmentation as it is a fully convolutional network (FCN) based on 2D images. A 2D network architecture cannot leverage complex 3D anatomical information. The 3D U-net has been used to overcome the limitation of the original U-net architecture to extract 3D contextual information via 3D convolutions with sparse annotations . However, the 3D U-net presents limitations of slice-based annotations. In , a full 3D-CNN-based U-net-like architecture was reported to segment volumetric medical images using a dice coefficient loss metric and overcome the class imbalance issue. The deep contour-aware network  has been developed to depict clear contours with a multi-task framework. The VoxResNet has performed brain tissue segmentation using a voxelwise residual network 
. A residual learning mechanism has been used to classify each voxel. Subsequently, an auto-context algorithm  has been employed to further refine the voxelwise prediction results. Deeply supervised networks  have been developed to hierarchically supervise multiple layers and segment medical images . Deep supervision has allowed effective fast learning and regularization of the network. A fully connected conditional random field model has been applied as a post-processing step to refine the segmentation results . In 
, the incorporation of global shape information with neural networks was presented. A convolutional autoencoder network was constructed to learn anatomical shape variations from training images.
Herein, we propose a deeply self-supervising CNN with adaptive contour features. Instead of learning explicit ground-truth contour features such as in reference , we guide a neural network to learn complementary contour region that can aid the accurate delineation of the target liver object. The main objective for learning partially significant contour is that, unlike other segmentation problems (e.g., glands), the contour of a liver is difficult to obtain accurately, even with DNNs, because of its ambiguous boundaries. Learned partial contours are later fused with a global shape prediction to derive the final segmentation (Fig. 1). As shown in Fig. 1
, the network can be interpreted as a contour embedded shape estimation that uses three discriminative features: shape, contour, and deep features. Similar to the method presented in reference, the proposed base network architecture was designed as a densely connected V-net structure . The number of parameters and layers are effectively reduced using a densely connected network architecture  and separable convolutions while preserving the network capability. Finally, the learned DNN was used for automatic segmentation of the liver from CT images.
The remainder of this article is organized as follows. In Section 2, several CNN models that are closely related to the proposed method are reviewed. The proposed method is described in Section 3. The experimental results, discussion, and conclusion are presented in Sections 4, 5, and 6, respectively.
Ii Related Work
In this section, the CNN mechanism is reviewed and three major related works that contribute to key steps of our method are described: the V-net , deeply supervising networks (DSNs) [36, 31], and densely connected convolutional networks (DenseNets) .
The V-net is a volumetric FCN used for medical image segmentation . The U-net architecture  was extended to a volumetric convolution (i.e., 3D convolution), and U-net-like downward and upward transitions (i.e., convolutional reduction and de-convolutional expanding of feature dimensions ) were adopted together with multiple skip connections via an element-wise summation scheme. The dice loss was first presented to overcome the class imbalance issue.
A DSN was proposed to supervise a network to a deep level 
. Accordingly, a loss function penetrates through multiple layers in a DNN. The deeply supervising scheme makes intermediate features highly discriminative so that the final classifier can easily be a more accurate discriminative classifier for the output. Another aspect of the DSN is that training difficulties due to exploding and vanishing gradient issues can be alleviated by direct and deep gradient flows. In, a 3D deep supervision mechanism was adapted to volumetric medical image segmentation. The explicit supervision was exploited to hidden layers, and the auxiliary losses were integrated to the final loss with the last output layer to back-propagate gradients.
A DenseNet  connects each layer to every other layer in a feed-forward manner. The main advantage of the presented architecture is that the gradient directly flows to deep layers, accelerating the learning procedure. The feature reuse also strongly contributes to a substantial reduction of the number of parameters. This structure can be viewed as an implicit deep supervision network similar to the explicit version . The layer obtains the concatenation of all outputs of the preceding layers as follows :
where is the output of the layer, is the concatenation of the feature-maps produced in the previous layers, and
is a non-linear transformation at the
layer (e.g., composition of the convolution and non-linear activation function). The feature-reusing scheme of the DenseNet, which causes the reduction of the parameters, is an effective feature for the 3D volumetric neural network as the volume data lack GPU memory for DNNs.
The base architecture of the network is composed of several contracting, expanding paths, and skip connections, similar to the V-net . The key feature of the proposed network is that two different deep-supervisions are embedded in the network: contour and shape transition layers (i.e., the red and blue dotted boxes in Fig. 2). Deeply supervised contour and shape features are sequentially concatenated for the final segmentation result. There are three different non-linear modules in the proposed model: a D_Block (Fig. 3) and deep and out-transition layers (Fig. 4
). Each module comprises a convolution, batch normalization39], and skip connections. The details of the architecture and deep supervisions are described in the following subsections.
Iii-a Base Network Architecture
As shown in Fig. 2, the D_Block is the base non-linear module of the network. The D_Block is composed of non-linear transformation series: a convolution, batch normalization, and ReLU non-linear activation function (Fig. 3). These transformations are densely connected for feature reuse. Unlike the previous research reported in reference , depth-wise separable convolutions  are introduced in the densely connected block instead of bottleneck layers  or compression layers  for a more efficient use of the parameters.
The base network uses a D_Block as a non-linear module and performs several contracting (i.e., down-transition), expanding (i.e., up-transition) paths, and concatenating skip connections. For the down-transition layers (i.e., down-sampling feature dimensions; circled red lines in Fig. 2
), the feature map is down-sampled by a factor of 2 for each dimension via convolutions with stride 2. The number of features of the input is preserved. For the up-transition layers (i.e., up-sampling feature dimensions; squared blue lines in Fig.2), de-convolution (i.e., transposed convolution) is used, restoring the number of features as that of the skip connected upper layer for feature summation. Each up-transitioned layer is summed with previous feature outputs (i.e., element-wise summation in Fig. 2) and passes through a D_Block unit. The feature outputs of the lower layers are up-scaled (i.e., orange lines in Fig. 2) and concatenated for further propagation of the layers. At the final stage, the contour and shape features are sequentially concatenated to the out-transition layers (Fig. 2).
The final prediction of the network is achieved by integrating the three major features: 1) deep features from the base network (i.e., stack of D_Block), 2) contour features from the contour transition branch (i.e., the red-dotted box in Fig. 2), and 3) shape features from the shape transition branch (i.e., the blue-dotted box in Fig. 2
). The two deep transition layers are deeply supervised for each feature extraction.
Iii-B Deeply Supervised Transition Layers
The transition layers (Fig. 4) are also composed of non-linear transformation series such as the D_Block. In the transition layers, however, separable convolutions are not used. The deep transition layers (Fig. (a)a) perform down- and up-transitions (i.e., the red- and blue-circled arrows in Fig. (a)a) as in the base network. By contracting and expanding paths, the deep transition layer can extract more multi-scaled features (i.e., higher receptive field) with respect to the contour and shape features. The out-transition layers simply forward the feature maps with dense connections followed by a convolution (Fig. (b)b). There are two out-transition layers in the network for integrating features at the final stage.
As shown in Fig. 2, we applied two different deep supervision mechanisms in the proposed model: shape and contour transitions. The shape supervision is applied to the output feature map of the two shape transition layers (i.e., the blue-dotted box in Fig. 2
). Two identical transitions were applied separately to learn the complementary residuals. The final shape estimation was performed by a simple subtraction between the two feature maps. Using this method, a compact shape estimation architecture that constitutes two complementary feature extractors was successfully designed and could be used to aid the prediction. The effectiveness of the residual connection is evaluated in Section 4.
where is an element-wise multiplication operator and is a binary image with respect to the threshold value, :
is the output probability prediction of the proposed network for a given iteration. That is, the ground-truth contours (i.e., foreground voxels in) were automatically erased if our network successfully delineated the corresponding labels at the output. This adaptive self-supervision procedure aids the contour transition layer to effectively delineate the misclassified contour region with respect to low-level features (e.g., edge). The discriminative feature of the contour transition was later combined with the shape prediction for the final liver object delineation.
), padding (), and dilation value () is specified.
Iii-C Overall Loss Function
represent the input image and ground-truth label, respectively. The task of the given learning system is to model a conditional probability distribution,. To effectively model the probability distribution, the proposed network model was trained to map the segmentation function by minimizing the following loss function:
where , , and indicate the output features of out, shapes, and contour transitions, respectively. is the binary ground-truth label and is the set of parameters of the network. indicates the dice loss , and indicates softmax-cross-entropy loss,
Iii-D Data Preparation and Augmentation
In total, 160 subjects were acquired: 90 subjects from a publicly available dataset111DOI:http://doi.org/10.5281/zenodo.1169361 in , 20 subjects from the MICCAI-Sliver07 dataset , 20 subjects from 3Dircadb222https://www.ircad.fr/research/3dircadb, and an additional 30 annotated subjects with the help of clinical experts in the field. In the dataset, the slice thickness ranged from 0.5 to 5.0mm, and the pixel sizes ranged from 0.6 to 1.0mm.
For the training dataset, all abdominal computed tomography images were resampled by . The image was pre-processed using fixed windowing values: level = 10 and width = 700 (i.e., clipped the intensity values under and over ). After re-scaling, the input images were normalized into the range [0-1] for each voxel. On-the-fly random affine deformations were subsequently applied to that dataset for each iteration with 80% probability. Finally, the cutout image augmentation  was performed with 80% probability. The position of the cutout mask was not constrained with respect to the boundaries. A randomly sized zero mask was applied in the range , where and are the lengths of the mask and the image in each dimension, respectively. To the best of our knowledge, this is the first study applying a cutout  augmentation to an image segmentation problem. The effect of the cutout augmentations is presented in Section 4.
Iii-E Learning the Network
was set to 1 until 100 epochs, and decayed by multiplying 0.9 for every 10 epochs until 0.5 (i.e., the minimum value of). For the dense block unit, and were used as parameters for the D_Block. The Adam optimizer was used with a batch size of 4 and learning rate 0.001. The learning rate was decayed by multiplying 0.1 for every 50 epochs. The network was trained for 300 epochs using an Intel i7-7700K desktop system with a 4.2 GHz processor, 32 GB memory, and Nvidia Titan Xp GPU machine. It took 10 h to complete all the training procedures.
Iv Experiments and Results
In the proposed experiments, the learning curves and results of the proposed network were evaluated by comparing them with those of other FCN-based models. A DSN , VoxResNet , DenseVNet , and the proposed network, CENet, were used for performance evaluation.
Iv-a Learning Curve
A learning curve with the dice loss is plotted in Fig. 5
. All hyperparameters (such as learning rate and optimizer) were set as specified in the original studies. An eight-fold cross-validation was first designed for performance evaluation (i.e., 140 training images and 20 validation images). The plot in Fig.(a)a indicates that our proposed network achieved the most successful training result. The other networks could not minimize the validation errors. The quantitative results are presented in Tables I and II. A special experimental setting was have additionally designed with 10 training images and 150 validation images (Figs. (b)b and (c)c
). This experimental setting approximately proxies the real-life deep learning problem and shows an extremely generalized regularization analysis. The overall validation errors increased in a special cross-validation with 10 training images (Fig.(b)b). Moreover, the proposed network did not over-fit (i.e., lowest generalization error) to the training images compared to other networks. Fig. (c)c shows the least accurate generalization curve without a cutout augmentation , indicating that the cutout augmentation greatly aids the network training to be generalized. Comparing all training experiments, the proposed network made the fastest convergence, showed the lowest loss value, and resulted in the best generalization.
Iv-B Contour and Shape Feature Layers
The output feature map of the contour transition layer (i.e., ) is displayed in Fig. 8. The contour feature map of a fully supervised network (i.e., using ground-truth contour supervision without modification (2)) was activated within all contour regions (Fig. 8a). Fig. 8a demonstrates that even with full training, the network failed to extract full contour features accurately (i.e., a part of the low softmax responses on the ground-truth contour region). Moreover, with a self-supervised network, the contour feature map was activated in the local contour regions that can further aid the accuracy of the segmentation (Fig. 8b). As shown in Fig. 8b, the contour transition layer successfully learned discriminative contours excluding ambiguous regions that can be better delineated by global shape prediction (i.e., , presented in Fig. 9). The quantitative evaluation between the two methods is presented in the following section.
The effects of the residuals in the shape transition layers are shown in Fig. 9. Both shape transition layers learned complementary features (Figs. (a)a and (b)b) for accurate shape delineation by subtraction.
|Methods||DSC||HD [mm]||ASSD [mm]||Sensitivity||Precision|
|Metric||DSN ||VoxResNet ||DenseVNet ||CENet|
MEAN AND STANDARD DEVIATION OF THE EIGHT-FOLD CROSS-VALIDATION
Iv-C Quantitative Evaluations
The segmentation results were evaluated using the dice similarity coefficient (DSC), 95% Hausdorff distance (HD), average symmetric surface distance (ASSD), sensitivity (S), and precision (P). The DSC is defined as follows:
where is the cardinality of a set. is defined as a set of surface voxels of a set , the shortest distance of an arbitrary voxel is defined as follows :
Thus, HD is defined as follows :
Defining the distance function as
the ASSD can be defined as follows :
The sensitivity and precision are defined as follows:
where , , and are the numbers of true positive, false negative, and false positive voxels, respectively. In (8), 95% of the voxels in (7) were calculated to exclude 5% of the outlying voxels. This allows to obtain a generalized evaluation of the distance without portal vein variations (Fig. 11). An eight-fold cross-validation is used to obtain the quantitative results in Tables I and II. The visual box plot of Table II is presented in Fig. 10. The proposed CENet showed the best segmentation results within all evaluations. In particular, the DenseVNet failed to segment the liver accurately owing to two significant issues: 1) the network resolution is too low and 2) the shape prior has a weak representative power. Thus, for images with excessively coarse dimensions, the segmentation result suffers from the accurate delineation of an object in the original domain. Furthermore, the resolution of the shape prior is too small and the training images must be accurately and manually cropped to fully utilize the learned shape prior. There is no specific metric presented in the previous research reported in reference  to crop testing images automatically.
The proposed experiments were extended with network variants: the CENet without self-supervised contour learning (i.e., using the full ground-truth contour instead of the adaptively modified ; CENet-A), without contour transition layer (i.e., removing the red box in Fig. 2; CENet-C), without shape transition layer (i.e., removing the blue box in Fig. 2; CENet-S), and without the residual shape estimation layer (i.e., removing the black box in Fig. 2; CENet-R). In the case of the CENet-R, two shape transition layers were sequentially stacked for the shape estimation. The accuracy of our network variants was slightly lower than that of the original CENet. The DSC, sensitivity, and precision scores of the variants were preserved while the distance errors (i.e., 95% HD and ASSD) slightly increased. The CENet-S showed the lowest distance errors among the variants, while the CENet-R showed the highest distance errors. This indicates that the residual shape estimation process is critical for an accurate shape estimation. When using the CENet-R network, the feature was similar to that shown in Fig. (a)a which leads to an inaccurate output result. Without residuals, the design of more complex and deep transition layers is required for the shape estimation, which may lead to an over-fitting. The result of the CENet-C indicates that the contour transition part plays a key role in the accurate delineation of an object. However, the performance of the CENet-A was poorer than that of the CENet-C with respect to the HD and ASSD measurements, indicating that enforcing the network to learn the full ground-truth contour image has a negative effect on the performance.
The visual result of an example liver subject is presented in Fig. 11. As it is clearly visualized, the proposed CENet successfully segmented the liver with accurate guidelines of the contour and shape estimation. Segmenting the portal vein entry region accurately was difficult to achieve with all the networks, including the proposed one. However, our training database (i.e., clinically annotated ground-truth images) presented serious internal variations in the portal vein entry region. Several clinicians included the vessels but others excluded the major entry vessel region. A concurrent and integrated liver and vascular system segmentation framework could be built in the future to overcome the variability of annotations. In the case of the DenseVNet, the inaccurate shape prior seriously affected the final output, as shown in Fig. (d)d.
The segmentation of organs in medical imaging is a challenging issue. The edge is unquestionably the most important feature for accurate object segmentation in the perspective of contour delineation. However, the full contour is hard to identify in various cases, such as unclear boundaries and false edges in contrast-enhanced vessels. Even with the strong capability of the neural network, it is difficult to classify ambiguous regions. Thus, the proposed network avoids learning the full contour features that are unnecessary in this study. The proposed method guided (i.e., self-supervised) the neural network to learn the sparse but essential contour that can be a great complementary feature to be later fused with the global shape estimation. Two major neural network branches were used: contour and shape estimations. This network may be seen as a multi-task learning framework. However, the network was not enforced to explicitly inference multiple tasks. The proposed network internally guides weights to represent the object contour features without supervising the entire contour image. The network was self-supervised with modified contour images for each iteration. The main underlying principle of the proposed network is to concentrate the contour delineation pass on the missing contour part of an object (i.e., fine details of an object that are easily misclassified using the end-to-end learning). There are two main reasons for using the proposed method: 1) even with a powerful deep neural network, unclear boundaries are challenging to be discriminated as a contour and 2) contour regions in unclear boundaries can be delineated by global shapes. Finally, we merged three strong discriminative features (i.e., shape, contour details, and deep features) to obtain accurate segmentation results. The proposed network can be intuitively interpreted as a robust contour guided shape estimation.
For the effective modification of the proposed network to other applications, the parameters of the dense block (Fig. 3) and (i.e., the threshold value to determine the misclassified voxels) should be modified. The parameters and in the dense block adjust the complexity of the network and adjusts the workload of the contour transition. The higher the value of , the larger the contour region required to be delineated in the contour estimation pass. Herein (i.e., liver segmentation), the parameter was not sensitive to the presented results.
In this work, an FCN was designed for image segmentation with a self-supervised contour-guiding scheme. The proposed network combined the shape and contour features to accurately delineate the target object. The contour features were learned to delineate the complementary contour region in a self-supervising scheme. The network was divided into two big branches for shape and complementary contour estimations. The proposed network demonstrated that the critical and partial contour features, instead of the fully-supervised contour, could effectively improve the performance of the segmentation result. The quantitative experiments showed that our method performed 2.13% more accurately than the state-of-the-art method with respect to the dice score. The deep contour self-supervision was automatically performed by the output of the network without any manual interactions. The building block of our network was a densely connected block with separable convolutions, which made the network more compact and representative. The proposed network successfully performed the liver segmentation without deepening or widening the neural network, unlike the state-of-the-art methods.
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