HyperDense-Net: A hyper-densely connected CNN for multi-modal image segmentation

HyperDense-Net: A hyper-densely connected CNN for multi-modal image segmentation

Jose Dolz, Karthik Gopinath, Jing Yuan, Herve Lombaert, Christian Desrosiers, and Ismail Ben Ayed J. Dolz, K. Gopinath, H. Lombaert, C. Desrosiers and I. Ben Ayed are with the École de technologie Superieure, Montreal, Canada. email:jose.dolz@livia.etsmtl.caJ. Yuan is with the Xidian University, School of Mathematics and Statistics, Xi’an, China.Manuscript received XXX; revised XXX.
Abstract

Recently, dense connections have attracted substantial attention in computer vision because they facilitate gradient flow and implicit deep supervision during training. Particularly, DenseNet, which connects each layer to every other layer in a feed-forward fashion, has shown impressive performances in natural image classification tasks. We propose HyperDenseNet, a 3D fully convolutional neural network that extends the definition of dense connectivity to multi-modal segmentation problems. Each imaging modality has a path, and dense connections occur not only between the pairs of layers within the same path, but also between those across different paths. This contrasts with the existing multi-modal CNN approaches, in which modeling several modalities relies entirely on a single joint layer (or level of abstraction) for fusion, typically either at the input or at the output of the network. Therefore, the proposed network has total freedom to learn more complex combinations between the modalities, within and in-between all the levels of abstraction, which increases significantly the learning representation. We report extensive evaluations over two different and highly competitive multi-modal brain tissue segmentation challenges, iSEG 2017 and MRBrainS 2013, with the former focusing on 6-month infant data and the latter on adult images. HyperDenseNet yielded significant improvements over many state-of-the-art segmentation networks, ranking at the top on both benchmarks. We further provide a comprehensive experimental analysis of features re-use, which confirms the importance of hyper-dense connections in multi-modal representation learning. Our code is publicly available111https://www.github.com/josedolz/HyperDenseNet.

Deep learning, brain MRI, segmentation, 3D CNN, multi-modal imaging

1 Introduction

Multi-modal imaging enables the combination of different anatomical and functional information. Therefore, the joint analysis of multi-modal data has emerged as a natural approach to medical image analysis. Its use is becoming increasingly common for the study of a breadth of diseases [1], being of primary importance in developing comprehensive models of pathologies, as well as in increasing the statistical power of current imaging biomarkers. In multi-modal studies, images of the same target structures are acquired with different techniques. This combination of complementary information enables accurate visualization and delineation of the structures of interest.

Integrating several modalities provides solutions that overcome the limitations of independent imaging techniques. For instance, magnetic resonance imaging (MRI) depicts different tissue contrasts by varying the pulse sequences. On the one hand, MR-T1 (T1) yields a good image contrast between the gray matter (GM) and white matter (WM) tissues. On the other hand, MR-T2 weighted (T2) and proton density (PD) pulses are powerful in visualizing tissue abnormalities, such as lesions. A special case of T2 is the fluid attenuated inversion recovery (FLAIR) pulse sequence. This modality enhances the image contrast of white matter lesions (WMLs), such as multiple sclerosis [2]. Considering multiple MRI modalities can recover low tissue contrast, for example, between brain tissues (Fig. 1). This span of imaging possibilities has, therefore, led to an outstanding progress in exploring and understanding brain anatomy and brain-related disorders.

Fig. 1: Example of data from a training subject. Neonatal isointense brain images from a mid-axial T1 slice (left), the corresponding T2 slice (middle), and manual segmentation (right).

In general, the advances in multi-modal imaging have increased the quality of diagnosis, treatment and follow-up of various diseases. This comes, however, at the price of an inherently large amount of data produced by multi-modal studies, imposing a burden on disease assessments. Visual inspections of such an enormous amount of medical images are prohibitively time-consuming, prone to errors and unsuitable for large-scale studies. Therefore, automatic and reliable multi-modal segmentation algorithms are of high interest to the clinical community.

1.1 Prior work

The rapidly increasing use of multi-modal data prompted substantial research efforts in image segmentation algorithms that account for multi-modal scenarios, in various diseases or clinical studies. For example, PET-CT imaging has been widely used for joint tumor segmentation [3, 4, 5, 6, 7, 8, 9, 10, 11, 12]. Deformable, level-set models, which combine individual segmentations from PET and CT images, were used in some of these approaches [3]. In addition, textural features from CT images were extracted to distinguish cancerous tissue types, incorporating PET to this information [4, 7]. These methods have several limitations. In fact, independent segmentations do not fully account for all the available multi-modal information. The underlying assumptions oversimplify the complex relationships that may exist between different imaging modalities. For instance, finding the tumor structure independently in PET and CT implicitly assumes that tumor volume is identical in both modalities, which is not the case. In fact, assuming simple correspondences between anatomical and functional images may not be realistic. Furthermore, sub-optimal solutions to the individual problems, due to optimization issues, along with heavy computational loads, impeded significantly the use of these approaches in practice.

The studies in [5, 8] stated the problem as a Markov Random field (MRF) on a graph, which encodes the information from both modalities. The ensuing PET-CT co-segmentation algorithms seek the tumor structures concurrently in both modalities. For these models, discrete graph-cut optimization can achieve globally optimal solutions in low-order polynomial time.

Multi-modal image segmentation in brain-related applications has also received a substantial research attention, for instance, brain tumors [13, 14, 15, 16], brain tissues of both infant [17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27] and adult [28, 29], subcortical structures [30], among other problems [31, 32, 33]. Atlas-propagation approaches are commonly used in multi-modal scenarios [34, 35]. These methods rely on registering one or multiple atlases to the target image, followed by a propagation of manuals labels. When several atlases are considered, labels from individual atlases can be combined into a final segmentation via a label fusion strategy [18, 20, 23]. When relying solely on atlas fusion, the performance of such techniques might be limited and prone to registration errors. Parametric or deformable models [21] can be used to refine prior estimates of tissue probability [24]. For example, the study in [24] investigated a patch-driven method for neonatal brain tissue segmentation, integrating the probability maps of a subject-specific atlas into a level-set framework.

More recently, our community has witnessed a wide adoption of deep learning techniques, particularly, convolutional neural networks (CNNs), as an effective alternative to traditional segmentation approaches. CNN architectures are supervised models, trained end-to-end, to learn a hierarchy of image features representing different levels of abstraction. In contrast to conventional classifiers based on hand-crafted features, CNNs can learn both the features and classifier simultaneously, in a data-driven manner. They achieved state-of-the-art performances in a broad range of medical image segmentation problems [36, 37], including multi-modal tasks [38, 25, 14, 39, 26, 29, 27, 16, 15, 32, 33].

1.1.1 Fusion of multi-modal CNN feature representations

Most of the existing multi-modal CNN segmentation techniques followed an early-fusion strategy, which integrates the multi-modality information from the original space of low-level features [25, 39, 38, 15, 29, 33]. For instance, in [25], MR-T1, T2 and fractional anisotropy (FA) images are simply merged at the input of the network. However, as argued in [40] in the context of multi-modal learning, it is difficult to discover highly non-linear relationships between the low-level features of different modalities, more so when such modalities have significantly different statistical properties. In fact, early-fusion methods implicitly assumes that the relationship between different modalities are simple (e.g., linear). For instance, the early fusion in [25] learns complementary information from T1, T2 and FA images. However, the relationship between the original T1, T2 and FA image data may be much more complex than complementarity, due to significantly different image acquisition processes [26]. The work in [26] advocated late fusion of high-level features as a way that accounts better for the complex relationships between different modalities. They used an independent convolutional network for each modality, and fused the outputs of the different networks in higher-level layers, showing better performance than early fusion in the context infant brain segmentation. These results are in line with a recent study in the machine learning community [40], which investigated multimodal learning with deep Boltzmann machines in the context of fusing data from color images and text.

Work Modality Target Method
El Naqa et al., 2007  [3] PET-CT Lung and cervix cancer Multi-Level sets 2D/3D
Yu et al.,2009  [4] PET-CT Head and neck cancer Multi-Level sets 2D/3D
Han et al.,2011  [5] PET-CT Head and neck cancer Markov Random Field (MRF)
Bagci et al.,2012  [6] PET-CT Lung disease abnormalities Random Walker
Bagci et al.,2013  [9] PET-CT, PET-MRI, PET-CT-MRI Several lesions Random Walker
Markel et al.,2013  [7] PET-CT Lung carcinoma Decision tree with KNN
Song et al.,2013  [8] PET-CT Lung tumor Markov Random Field (MRF)
Ju et al.,2015  [11] PET-CT Lung tumor Random walker + Graph Cuts
Cui et al.,2016  [12] PET-CT Lung tumor Random walker

Prastawa et al., 2005  [17]
T1,T2 Infant brain tissue Multi-atlas
Weisenfeld et al., 2006  [18] T1,T2 Infant brain tissue Multi-atlas
Deoni et al., 2007  [30] T1,T2 Thalamic nuclei K-means clustering
Anbeek et al., 2008  [19] T2,IR Infant brain tissue KNN
Weisenfeld and Warfield, 2009  [20] T1,T2 Infant brain tissue Multi-atlas
Wang et al., 2011  [21] T1,T2,FA Infant brain tissue Multi-atlas + Level sets
Srhoj et al., 2012  [22] T1,T2 Infant brain tissue Multi-atlas + KNN
Wang et al., 2012  [23] T1,T2 Infant brain tissue Multi-atlas
Wang et al., 2014  [41] T1,T2,FA Infant brain tissue Multi-atlas + Level sets
Kamnitsas et al., 2015  [38] Flair, DWI, T1, T2 Brain lesion 3D FCNN + CRF
Zhang et al., 2015  [25] T1,T2,FA Infant brain tissue 2D CNN
Havaei et al., 2016  [14] T1,T1c,T2,FLAIR Multiple Sclerosis/Brain tumor 2D CNN
Nie et al., 2016  [26] T1,T2,FA Infant brain tissue 2D FCNN
Chen et al., 2017  [29] T1,T1-IR,FLAIR Brain tissue 3D FCNN
Dolz et al., 2017  [27] T1,T2 Infant brain tissue 3D FCNN
Fidon et al., 2017  [16] T1,T1c,T2,FLAIR Brain tumor CNN
Kamnitsas et al., 2017  [15]
T1,T1c,T2,FLAIR
MPRAGE,FLAIR,T2,PD
Brain tumour/lesions 3D FCNN + CRF
Kamnitsas et al., 2017  [32] MPRAGE,FLAIR,T2,PD Traumatic brain injuries 3D FCNN(Adversarial Training)
Valverde et al., 2017  [33] T1, T2,FLAIR Multiple-sclerosis 3D FCNN


TABLE I: A brief summary of existing methods for multi-modal medical image segmentation for some applications.

1.1.2 Dense connections in deep networks

Since the recent introduction of residual learning in [42], shortcut connections from early to late layers have become very popular in a breadth of computer vision problems [43, 44]. Unlike traditional networks, shortcut connections back-propagate gradients directly, thereby mitigating the gradient-vanishing problem and allowing deeper networks. Furthermore, they transform a whole network into a large ensemble of shallower networks, yielding competitive performances in various applications [45, 29, 46, 47]. DenseNet [48] extended the concept of shortcut connections, with the input of each layer corresponding to the outputs from all previous layers. Such a dense network facilitates the gradient flow and the learning of more complex patterns. DenseNet yielded significant improvements in accuracy and efficiency for natural image classification tasks [48]. However, the impact of dense connectivity in medical image segmentation, particularly in multi-modal problems, remains unexplored.

1.2 Contributions

We propose HyperDenseNet, a 3D fully convolutional neural network that extends the definition of dense connectivity to multi-modal segmentation problems. Each imaging modality has a path, and dense connections occur not only between the pairs of layers within the same path, but also between those across different paths; see the illustration in Fig. 2. This contrasts with the existing multi-modal CNN approaches, in which modeling several modalities relies entirely on a single joint layer (or level of abstraction) for fusion, typically either at the input (early fusion) or at the output (late fusion) of the network. Therefore, the proposed network has total freedom to learn more complex combinations between the modalities, within and in-between all the levels of abstractions, which increases significantly the learning representation in comparison to early/late fusion. Furthermore, hyper-dense connections facilitate the learning as they improve gradient flow and impose implicit deep supervision. We report extensive evaluations over two different222iSEG 2017 focuses on 6-month infant data, whereas MRBrainS 2013 uses adult data. Therefore, there are significant differences between the two benchmarks in term of image data characteristics, e.g, the voxel spacing and number of available modalities. and highly competitive multi-modal brain tissue segmentation challenges, iSEG 2017 and MRBrainS 2013. HyperDenseNet yielded significant improvements over many state-of-the-art segmentation networks, ranking at the top on both benchmarks. We further provide a comprehensive experimental analysis of features re-use, which confirms the importance of hyper-dense connections in multi-modal representation learning. Our code is publicly available333https://www.github.com/josedolz/HyperDenseNet.

A preliminary conference version of this work appeared at ISBI 2018 [49]. This journal version is a substantial extension, including (1) a much broader, more informative/rigorous treatment of the subject in the general context of multi-modal segmentation; and (2) comprehensive experiments with additional baselines and publicly available benchmarks, as well as a thorough investigation of the practical usefulness and impact of hyper-dense connections.

2 Methods and Materials

Convolutional neural networks (CNNs) are deep models that can learn feature representations automatically from the training data. They consist of multiple layers, each processing the imaging data at a different level of abstraction, enabling segmentation algorithms to learn from large datasets and discover complex patterns that can be further employed for predicting unseen samples. The first attempts to use CNNs in segmentation problems followed a sliding-window strategy, where the regions defined by the window are processed independently, which impedes segmentation accuracy and computational efficiency. To overcome these limitations, the network can be viewed as a single non-linear convolution, which is trained end-to-end, a process known as fully CNN (FCNN) [50]. The latter brings several advantages over standard CNNs. It can handle images of arbitrary sizes and avoid redundant convolution and pooling operations, enabling computationally efficient learning.

2.1 The proposed Hyper-Dense network

The concept of “the deeper the better” is considered as a key principle in deep learning [42]. Nevertheless, one obstacle when dealing with deep architectures is the problem of vanishing/exploding gradients, which hampers convergence during training. To address these limitations in very deep architectures, the study in [48] investigated densely connected networks. DenseNets are built on the idea that adding direct connections from any layer to all the subsequent layers in a feed-forward manner makes training easier and more accurate. This is motivated by three observations. First, there is an implicit deep supervision thanks to the short paths to all feature maps in the architecture. Second, direct connections between all layers help improving the flow of information and gradients throughout the entire network. Third, dense connections have a regularizing effect, which reduces the risk of over-fitting on tasks with smaller training sets.

Inspired by the recent success of densely-connected networks in natural image classification tasks, as well as in a few recent medical image segmentation works [51, 52, 53], we propose HyperDenseNet, a hyper-dense architecture for multi-modal image segmentation. We extend the concept of dense connectivity to the multi-modal setting: Each imaging modality has a path, and dense connections occur not only between layers within the same path, but also between layers across different paths; see Fig. 2 for an illustration.

Fig. 2: A section of the proposed HyperDenseNet in the case of two image modalities. Each gray region represents a convolutional block. Red arrows correspond to convolutions and black arrows indicate dense connections between feature maps.

Let be the output of the layer. In CNNs, this vector is typically obtained from the output of the previous layer by a mapping composed of a convolution followed by a non-linear activation function:

(1)

A densely-connected network concatenates all feature outputs in a feed-forward manner:

(2)

where denotes a concatenation operation.

Pushing this idea further, HyperDenseNet introduces a more general connectivity definition, in which we link the outputs from layers in different streams, each associated with a different image modality. In the multi-modal setting, our hyper-dense connectivity yields a much more powerful feature representation than early/late fusion as the network learns the complex relationships between the modalities within and in-between all the levels of abstractions. For simplicity, let us consider the scenario of two image modalities, although extension to modalities is straightforward. Let and denotes the outputs of the layer in streams 1 and 2, respectively. The output of the layer in a stream can then be defined as follows:

(3)

Figure 2 depicts a section of the proposed architecture, where each gray region represents a convolutional block. For simplicity, we assume that the red arrows indicate convolution operations only, whereas the black arrows represent the direct connections between feature maps from different layers, within and in-between the different streams. Thus, the input of each convolutional block (maps before the red arrow) is the concatenation of the outputs (maps after the red arrow) of all the preceding layers from both paths.

2.2 Baselines

To investigate thoroughly the impact of hyper-dense connections between different streams in multi-modal image segmentation, we considered several baselines. First, we extend the semi-dense architecture proposed in [27] to a fully-dense one, by connecting the output of each convolutional layer to all subsequent layers. In this network, we follow an early-fusion strategy, in which MR-T1 and T2 are integrated at the input of the CNN and processed jointly along a single path (Fig. 8, left). The connectivity setting followed by this model is explained in eq. 2. Second, instead of merging both modalities at the input of the network, we considered a late-fusion strategy, where each modality is processed independently in different streams and learned features are fused before the first fully connected layer (Fig. 1 right in supplemental materials). In this model, the dense connections are included within each path, assuming the connectivity definition described in Eq. 2 for each of the streams.

2.3 Network architecture

To have a large receptive field, FCNNs typically use full images as input. The number of parameters is then limited via pooling/unpooling layers. A problem with this approach is the loss of resolution from repeated down-sampling operations. In the proposed method, we follow the strategy in [15], where sub-volumes are used as input, avoiding pooling layers. While sub-volumes of size are considered for training, we used sub-volumes during inference, as in [15, 36]. This strategy offers two considerable benefits. First, it reduces the memory requirements of our network, thereby removing the need for spatial pooling. More importantly, it substantially increases the number of training examples and, therefore, does not need data augmentation.

Conv. kernel # kernels Output Size Dropout
conv_1 333 25 No
conv_2 333 25 No
conv_3 333 25 No
conv_4 333 50 No
conv_5 333 50 No
conv_6 333 50 No
conv_7 333 75 No
conv_8 333 75 No
conv_9 333 75 No
fully_conv_1 111 400 Yes
fully_conv_2 111 200 Yes
fully_conv_3 111 150 Yes
Classification 111 4 No
TABLE II: The layers used in our architectures and the corresponding values with an input of size . In the case of multi-modal images, the convolutional layers (conv_x) are present in any network path. All the convolutional layers have a stride of one pixel.

The network parameters are optimized via the RMSprop optimizer, using cross-entropy as cost function. Let denotes the network parameters (i.e., convolution weights, biases and from the parametric rectifier units), and the label of voxel in the -th image segment. We optimize the following:

(4)

where is the softmax output of the network for voxel and class , when the input segment is .

To initialize the weights of the network, we adopted the strategy proposed in [54], which yields fast convergence for very deep architectures. In this strategy, a zero-mean Gaussian distribution of standard deviation is used to initialize the weights in layer , where denotes the number of connections to the units in that layer. Momentum was set to 0.6 and the initial learning rate to 0.001, being reduced by a factor of 2 after every 5 epochs (starting from epoch 10). The network was trained for 30 epochs, each composed of 20 subepochs. At each subepoch, a total of 1000 samples were randomly selected from the training images and processed in batches of size 5.

3 Experiments and results

The proposed HyperDenseNet architecture is evaluated on two challenging multi-modal image segmentation tasks, using publicly available data provided by two MICCAI challenges: infant brain tissue segmentation, iSEG444http://iseg2017.web.unc.edu, and adult brain tissue segmentation, MRBrainS555http://mrbrains13.isi.uu.nl. Quantitative evaluations and comparisons with the state-of-the-art methods are reported for each of these applications. First, to evaluate the impact of dense connectivity on performance, we compared the proposed HyperDenseNet to the baselines described in section 2.2 on infant brain tissue segmentation. Then, our results, compiled by the iSEG challenge organizers on testing data, are compared to those from the other competing teams. Second, to juxtapose the performance of HyperDenseNet to other segmentation networks under the same conditions, we provide a quantitative analysis of the results of current state-of-the-art segmentation networks for adult brain tissue segmentation. This includes comparison to the participants the MRBrainS challenge. Finally, in section 3.3, we report a comprehensive analysis of feature re-use.

3.1 iSEG Challenge

The focus of this challenge was to compare (semi-) automatic stat-of-the-art algorithms for the segmentation of 6-month infant brain tissues in T1- and T2-weighted brain MRI scans. This challenge was carried out in conjunction with MICCAI 2017, with a total of 21 international teams participating in the first round.

3.1.1 Evaluation

The MICCAI iSEG-2017 organizers used three metrics to evaluate the accuracy of the competing methods: Dice Similarity Coefficient (DSC) [55], Modified Hausdorff distance (MHD), where the 95-th percentile of all Euclidean distances is employed, and Average Surface Distance (ASD). The first measures the degree of overlap between the segmentation region and ground truth, whereas the other two evaluate boundary distances.

3.1.2 Results

We report infant brain tissue segmentation results using MR-T1w and MR-T2w images. Table III compares the performance achieved by HyperDenseNet to those of the baselines introduced in Section 2.2, for CSF, GM and WM brain tissues. The first observation that we can make from these results is that the late fusion of the high-layer features of independent paths did not provide a clear improvement over the single-path version. While the dual-path baseline reported better results for DC and ASD, processing both modalities in a single path achieved a better performance for MHD. HyperDenseNet outperformed both baselines, yielding better DC and ASD accuracy values for all cases, and better MHD values in two out of the three tissues. It achieved a lower MHD for the GM and WM tissues. Considering standard deviations, HyperDenseNet showed lower variances than the baselines, in the GM and WM regions. The difference in performance might be explained by the fact that our hyper-dense connectivity allows the network to access any feature map from almost any point in the architecture, both in depth and in width, thanks to the use of multiple inter-connected streams. This enable the network to freely learn features from several image modalities, at any level of abstraction, thereby identifying more complex patterns.

DC MHD ASD
CSF
Single-Path Baseline 0.953 (0.007) 9.296 (0.942) 0.128 (0.016)
Dual-Path Baseline 0.953 (0.008) 9.354 (1.242) 0.128 (0.018)
HyperDenseNet 0.957 (0.007) 9.421 (1.392) 0.119 (0.017)
Gray Matter
Single-Path Baseline 0.916 (0.009) 7.131 (1.729) 0.346 (0.041)
Dual-Path Baseline 0.918 (0.008) 7.643 (1.698) 0.343 (0.041)
HyperDenseNet 0.920 (0.008) 5.752 (1.078) 0.329 (0.041)
White Matter
Single-Path Baseline 0.895 (0.015) 6.903 (1.140) 0.406 (0.051)
Dual-Path Baseline 0.896 (0.013) 7.434 (1.571) 0.397 (0.045)
HyperDenseNet 0.901 (0.014) 6.659 (0.932) 0.382 (0.047)
TABLE III: Performance measures provided by the iSEG Challenge organizers for the analyzed methods. The best performance for each metric is highlighted in bold.

Figure 3 depicts a comparison of the training and validation accuracy between the baselines and HyperDenseNet. In these figures, the mean DC for the three brain tissue is evaluated on training (Top) and validation (Bottom) data after each sub-epoch. One can see that, in both cases, HyperDenseNet outperforms the baselines, achieving better results in lesser epochs. This might be attributed to two factors. The first is the high number of direct connections between different layers, which facilitates back-propagation of the gradient to shallow layers. The second is the freedom of the network to explore more complex patterns thanks to the combination of several image modalities at any level of abstraction.

Fig. 3: Training (top) and validation (bottom) accuracy plots for the proposed architecture and the baselines.

Figure 4 depicts visual results for the subject used in validation. It can be observed that HyperDenseNet recovers thin regions better than the baselines, which can explain the improvements observed in the distance-based metrics. As confirmed in Table III, this effect is most prominent in the boundaries between the gray and white matter. Furthermore, HyperDenseNet produces fewer false positives for WM than the baseline, which tend to over-estimate the segmentation in this region.

Fig. 4: Qualitative results of segmentation achieved by the baselines and HyperDenseNet on the validation subject. The red squares indicate some spots, where HyperDenseNet successfully reproduced the ground-truth whereas the baselines failed.

Comparing these results to those of all the methods in the first round of the iSEG Challenge (Table IV), one can see that HyperDenseNet achieved a state-of-the-art accuracy for this task. It obtained the best performance in 7 out of the 9 metrics. A noteworthy point is the general decrease in performance, among all the methods, for the segmentation of GM and WM, with lower DC and larger ASD values. This suggests that the segmentation of these tissues is challenging due to the unclear boundaries between them.

Method CSF GM WM
DSC MHD ASD DSC MHD ASD DSC MHD ASD
Bern_IPMI 0.96 9.62 0.13 0.92 6.46 0.34 0.90 6.78 0.40
LIVIA(Ensemble) 0.96 9.13 0.12 0.92 6.06 0.34 0.90 7.45 0.41
MSL_SKKU 0.96 9.07 0.12 0.92 5.98 0.33 0.90 6.44 0.39
nic_vicorob 0.95 9.18 0.14 0.91 7.65 0.37 0.89 7.15 0.43
TU/e IMAG/e 0.95 9.43 0.15 0.90 6.86 0.38 0.89 6.91 0.43
HyperDenseNet (Ours) 0.96 9.42 0.12 0.92 5.75 0.33 0.90 6.66 0.38
TABLE IV: Results on the iSEG-2017 data for HyperDenseNet and the methods ranked in the top-5 at the first round of submissions (in alphabetical order). The bold fonts highlight the best performances. For additional details, we refer the reader to the challenge’s website.

3.2 MRBrainS Challenge

This MRBrainS challenge was carried out in conjunction with MICCAI 2013, and a total of 47 international teams have participated up to date. The focus is on adult brain tissue segmentation in the context of aging, and three modalities have been used for this purpose, MR-T1, MR-T1 Inversion Recovery (IR) and MR-FLAIR.

3.2.1 Evaluation

The organizers used three types of evaluation measures: a spatial overlap measure (DC), a boundary distance measure (MHD) and a volumetric measure (the percentage of absolute volume difference).

3.2.2 Architectures for comparison

We start by comparing HyperDenseNet to the state-of-the-art networks in medical image segmentation. The first architecture is a 3D fully convolutional neural network with residual connections [56], which we denote FCN_Res3D. Then, U-Net [57] with residual connections in the encoder and 3D volumes as input, referred to as UNet3D, is evaluated. Finally, DeepMedic [15], which has shown an outstanding performance in brain lesion segmentation, is included in the comparison. The implementation details are described in the supplemental materials.

3.2.3 Results

We performed a leave-one-out-cross-validation (LOOCV) on the training set to compare the proposed network to the state-of-the-art architectures listed above, using four subjects for training and one for validation. This process was repeated for 3 different subjects, and an average was computed. For this set of comparisons, we used all the three modalities, MR-T1, MR-T1 IR and FLAIR, for all the competing methods. In a second set of experiments, we assessed the impact of integrating multiple imaging modalities on the results of HyperDenseNet using all the possible combinations of two modalities as input.

Method Mean DSC (std dev)
CSF GM WM
FCN_Res3D [58]  (3-Modalities) 0.7685 (0.0161) 0.8163 (0.0222) 0.8607 (0.0178)
UNet3D [57]  (3-Modalities) 0.8218 (0.0159) 0.8432 (0.0241) 0.8841 (0.0123)
DeepMedic[15]  (3-Modalities) 0.8292 (0.0094) 0.8522 (0.0193) 0.8884 (0.0137)
HyperDenseNet  (T1-FLAIR) 0.8259 (0.0133) 0.8620 (0.0260) 0.8982 (0.0138)
HyperDenseNet  (T1IR-FLAIR) 0.7991 (0.0181) 0.8226 (0.0255) 0.8654 (0.0087)
HyperDenseNet  (T1-T1IR) 0.8191 (0.0297) 0.8498 (0.0173) 0.8913 (0.0082)
HyperDenseNet  (3-Modalities) 0.8485 (0.0078) 0.8663 (0.0247) 0.9016 (0.0109)
TABLE V: Comparison to several state-of-the-art 3D networks on the MRBrainS challenge.

Table V reports the mean DSC and standard-deviation values, with FCN_Res3D exhibiting the lowest mean DSC, a performance that might be explained by the transpose convolutions in FCNRes3D, which may cause voxel misclassification within small regions. Furthermore, the downsampling and upsampling operations in FCN_Res3D make the feature maps in hidden layers sparser than the original inputs, causing a loss of the image details. This limitation is overcome by skip connections, which propagate information at different levels of abstraction between the encoding and decoding paths, as in UNet3D. This is reflected in the results, where the latter clearly outperformed FCN_Res3D in all the metrics. DeepMedic obtained better results than its competitors, yielding a performance close to the different two-modality configurations of HyperDenseNet. The dual multiscale path is an important feature of DeepMedic, which gives the network a larger receptive field via two paths, one for the input image and the other processing a low-resolution version of the input. This, in addition to the removal of pooling operations in DeepMedic, could explain the increase in performance with respect to FCN_Res3D and UNet3D.

The two-modality versions of HyperDenseNet yielded competitive performances, although there is a significant variability between the three configurations. Notice that using MR-T1 and FLAIR already places HyperDenseNet first for two DSC measures (GM and WM), and second for the remaining measure (CSF), even though the competing methods used all three modalities. HyperDenseNet with three modalities yielded significantly better segmentations, obtaining the highest mean DSC values for all three tissues. These results confirm the importance of handling image modalities in separate paths with dense connections within and in-between the paths, facilitating the flow of information.

The MRBrainS challenge organizers compiled the results and a ranking of 47 international teams666http://mrbrains13.isi.uu.nl/results.php. In Table VI, we report the results of the top-10 methods, with HyperDenseNet ranked first. This performance confirms, again, the importance of hyper-dense connections for multi-modal segmentation

Method GM WM CSF Sum
DSC HD AVD DSC HD AVD DSC HD AVD
HyperDenseNet (ours) 0.8633 1.34 6.19 0.8946 1.78 6.03 0.8342 2.26 7.31 48
VoxResNet [29] + Auto-context 0.8615 1.44 6.60 0.8946 1.93 6.05 0.8425 2.19 7.69 54
VoxResNet [29] 0.8612 1.47 6.42 0.8939 1.93 5.84 0.8396 2.28 7.44 56
MSL-SKKU 0.8606 1.52 6.60 0.8900 2.11 5.54 0.8376 2.32 6.77 61
LRDE 0.8603 1.44 6.05 0.8929 1.86 5.83 0.8244 2.28 9.03 61
MDGRU 0.8540 1.54 6.09 0.8898 2.02 7.69 0.8413 2.17 7.44 80
PyraMiD-LSTM2 0.8489 1.67 6.35 0.8853 2.07 5.93 0.8305 2.30 7.17 83
3D-UNet [57] 0.8544 1.58 6.60 0.8886 1.95 6.47 0.8347 2.22 8.63 84
IDSIA [59] 0.8482 1.70 6.77 0.8833 2.08 7.05 0.8372 2.14 7.09 100
STH [60] 0.8477 1.71 6.02 0.8845 2.34 7.67 0.8277 2.31 6.73 112
TABLE VI: Results of the MICCAI MRBrainS challenge of different methods (DC, HD (mm) and AVD). Only the top-10 methods are included in this table. More details on the results of 47 international teams can be found in the MRBrainS Challenge Website.

A typical example of the obtained segmentation result is depicted in Fig. 5. In these images, red arrows indicate regions where the two-modality versions of HyperDenseNet fail in comparison to the three-modality version. Most of the errors of these networks occur at the boundaries between the GM and WM, which makes sense given the very weak contrast between these tissues; see the images in Fig. 1, for example. We can observe how HyperDenseNet with three modalities can handle thin regions better than its two-modality versions. This example demonstrates how the integration of correlated information can overcome the limitations or weaknesses of single modalities.

Fig. 5: A typical example of the segmentations achieved by the proposed HyperDenseNet in a validation subject (Subject 1 in the training set) for 2 and 3 modalities. The red arrows indicate some of the differences between the segmentations. For instance, one can see here that HyperDenseNet with three modalities can handle thin regions better than its two-modality versions.

3.3 Analysis of features re-use

Dense connectivity enables each network layer to access feature maps from all its preceding layers, strengthening feature propagation and encouraging feature re-use. To investigate the degree of usability of features in a trained network, we performed additional experiments. For each convolutional layer, we computed the average L-norm of its filter weights assigned to the connections to the previous layers from any stream. This serves as a surrogate for the dependency of a given layer on its preceding layers. We normalized the values between 0 and 1 to facilitate visualization. Fig. 6 depicts the weights of HyperDense-Net trained with two modalities, for both iSEG and MRBrainS challenges. As the MRBrainS data set contains three modalities, we have three different two-modality configurations. Fig 7 depicts the average weights for the case of three modalities. A dark square in these plots indicates that the target layer (on x-axis) makes a strong use of the features produced by the source layer (on y-axis).

An important observation that one can make from both figures is that, in most cases, all layers spread the importance of the connections over many previous layers, not only within the same path, but also from the other streams. This indicates that features extracted by shallower layers are directly used by deeper layers from both paths, which confirms the usefulness of hyper-dense connections in facilitating information flow and in learning complex relationships between the modalities within different levels of abstractions.

Looking into the details of each particular application, we can observe that, for HyperDenseNet trained on iSEG (top row of Fig 6), immediate previous layers have typically higher impact on the connections from both paths. Furthermore, the connections having access to the MR-T2 features typically have the strongest values, which may indicate that MR-T2 is more discriminative than T1 in this particular situation. We can also observe some regions with high (0.5) feature re-usability patterns from shallow to deep layers. The same behaviour is observed for HyperDenseNet trained on two modalities from the MRBrainS challenge, where immediate previous layers have a high impact on the connections within and in-between the paths. The re-use of low-level features by deeper layers is more evident than in the previous case. For example, in HyperDenseNet trained with T1-IR and FLAIR, the deep layers in the T1-IR path make a strong use of the features extracted in shallower layers in the same path, as well as in the path that processed the FLAIR modality. This strong re-use of the features extracted early in the network from both paths occurred across all the configurations. The same pattern is observed when using three modalities (Fig 7), with a strong re-use of shallow features from the last layers in the network. This reflects the importance of allowing the deepest layers in the network to access to the early-extracted features. Additionally, it demonstrates that learning how and where to fuse information from multiple sources is a better strategy than combining image modalities in early or late stages.

Fig. 6: The average of the L1-norm of the filters from HyperDenseNet trained on the iSEG (top) and MRBrainS (from 2 to 4 rows) challenges with two modalities. The color at each location encodes the average L1 norm of the weights connecting a convolutional-layer source to a convolutional-layer target. These values were normalized between 0 and 1 by accounting for all the values within each layer.

Fig. 7: The average of the L1-norm of the filters from HyperDenseNet trained on the MRBrainS challenge with three modalities (MR-T1, FLAIR and MR-T1 IR). The color at each location encodes the average L1 norm of the weights connecting a convolutional-layer source to a convolutional-layer target. These values were normalized between 0 and 1 by accounting for all the values within each layer.

4 Discussion

We presented a novel densely connected network, HyperDenseNet, which makes efficient use of multiple imaging modalities in the context of segmentation. In our model, each imaging modality has a path, and dense connections occur not only between the pairs of layers within the same path, but also between those across different paths.

We presented extensive experiments on two challenging public brain segmentation benchmarks, one focusing on 6-month infant data and the other on adult images, with significant differences in the image characteristics between the two benchmarks. HyperDenseNet yielded state-of-the-art performances on both. Considering several baselines, we showed experimentally the positive impact of hyper-dense connections between different streams in multi-modal segmentation. It is worth mentioning that the architecture and hyper-parameters were unchanged through the experiments of both challenges, showing the flexibility of the proposed model in brain related problems. We anticipate that our model has a much larger applicability scope, going beyond brain tissue regions, in a breadth of other multi-modal volumetric medical image segmentation problems.

The accuracy improvements that HyperDenseNet brings might be explained by several factors. First, the network has total freedom to learn complex combinations between the modalities, within and in-between all the levels of abstraction, which increases significantly the learning representation. Second, it implicitly imposes deep supervision from the loss function that individual layers receive via the dense connections. The benefits of such deep supervision have been observed previously in the different context of deeply-supervised nets [61], which impose explicit layer-wise supervision by associating a classifier to each of the hidden layers. Finally, hyper-dense connections facilitate gradient flow, allowing feature re-use throughout the network, as evidenced by our experimental analysis. In fact, shallow layers typically operate at a fine-grained scale, to extract low-level features, while deeper layers extract coarse-scale information so as to infer the global context. Both scales are important, but occur at different levels in the network. Including dense connections alleviates this problem by facilitating the information flow between the different scales.

We evaluated the impact of the number of modalities on the performance and found that, even with less modalities, HyperDenseNet yields competitive performances in comparison to several state-of-the-art segmentation networks under the same conditions. An important finding in this experiment was that DeepMedic outperformed two versions of HyperDenseNet, when the latter is trained with only two modalities instead of three: T1-T1_IR and T1_IR-FLAIR. In fact, DeepMedic explicitly uses multi-scale information, incorporating larger receptive fields via two paths, one for the input image and the other processing a low-resolution version of the input. This suggests that integrating hyper-dense connections with explicit multi-scale information and larger receptive fields might further improve the network performance. Indeed, Huang et al. [62] investigated the use of dense connections in a multi-scale branch network, Multi-Scale Dense Net (MSDN), for image classification, showing that the multi-scale version outperforms its predecessor DenseNet.

Our experimental analysis of feature re-use revealed a strong information flow between the deep and shallow layers, particularly at the high levels of abstraction, an observation aligned with the findings in [48]. This indicates that the early-layer features are directly used by the deep layers. Our feature re-use study has an important benefit: it may allow us to remove useless connections, keeping only those having a strong information flow. This will ideally generate a computationally efficient model, without affecting performance.

5 Conclusion

This study investigated a hyper-densely connected 3D fully CNN, HyperDenseNet, with applications to brain tissue segmentation in multi-modal MRI. Our model leverages dense connectivity beyond recent works, exploiting the concept in multi-modal problems. Dense connections occur not only within each single-modality stream, but also across the streams, which increases significantly the learning representation in multi-modal problems: The network has total freedom to explore complex combinations between the different modalities, within and in-between all the levels of abstraction. We reported comprehensive evaluations and comparisons using the benchmarks of two highly competitive challenges, iSEG-2017 for 6-month infant brain segmentation and MRBrainS for adult data, showing state-of-the-art performances of HyperDenseNet on both. The experiments presented in this work provided new insights on the inclusion of short-cut connections in deep neural networks for segmentating medical images, particularly in multi-modal scenarios. HyperDenseNet demonstrated its potential to tackle multi-modal volumetric medical image segmentation problems.

Acknowledgments

This work is supported by the National Science and Engineering Research Council of Canada (NSERC), discovery grant program, and by the ETS Research Chair on Artificial Intelligence in Medical Imaging. The authors would like to thank both iSEG and MRBrainS organizers for providing data benchmarks and evaluations.

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Supplemental Materials

Dataset iSEG:

The images were acquired at the UNC-Chapel Hill on a Siemens head-only 3T scanner with a circular polarized head coil, and were randomly chosen from the pilot study of the Baby Connectome Project (BCP)777http://babyconnectomeproject.org. During scan, infants were asleep, unsedated and fitted with ear protection, with the head secured in a vacuum-fixation device. T1-weighted images were acquired with 144 sagittal slices using the following parameters: TR/TE = 1900/4.38 ms, flip angle = 7 and resolution = 111 mm. Likewise, T2-weighted images were obtained with 64 axial slices, TR/TE = 7380/119 ms, flip angle = 150 and resolution =1.251.251.95 mm. T2 images were linearly aligned onto their corresponding T1 images. All the images were resampled into an isotropic 111 mm resolution. Standard image pre-processing steps were then applied using in-house tools, including skull stripping, intensity inhomogeneity correction, and removal of the cerebellum and brain stem. For this application, subjects were employed for training and 1 for validation.

Dataset MRBrainS:

20 subjects with a mean age of 71 4 years (10 male, 10 female) were selected from an ongoing cohort study of older ( years of age), functionally-independent individuals without a history of invalidating stroke or other brain diseases [63]. To test the robustness of the segmentation algorithms in the context of aging-related pathology, the subjects were selected to have varying degrees of atrophy and white-matter lesions, and the scans with major artifacts were excluded. The following sequences were acquired and used for the evaluation framework: 3D T1 (TR: 7.9 ms, TE: 4.5 ms), T1-IR (TR: 4416 ms, TE: 15 ms, and TI: 400 ms) and T2- FLAIR (TR: 11000 ms, TE: 125 ms, and TI: 2800 ms). The sequences were aligned by rigid registration using Elastix [64], along with a bias correction performed using SPM8 [65]. After the registration, the voxel size within all the provided sequences (T1, T1 IR, and T2 FLAIR) was 0.960.963.00 mm. Five subjects that were representative for the overall data (2 male, 3 female and varying degrees of atrophy and white-matter lesions) were selected for training. The remaining fifteen subjects were provided as testing data. While ground truth was provided for the 5 training subjects, manual segmentations were unknown for the testing data set. The following structures were segmented and were available for training: (a) cortical gray matter, (b) basal ganglia, (c) white matter, (d) white matter lesions, (e) peripheral cerebrospinal fluid, (f) lateral ventricles, (g) cerebellum and (h) brainstem. These structures can be merged into gray matter (a-b), white matter (c-d), and cerebrospinal fluid (e-f). The cerebellum and brainstem were excluded from the evaluation.

Dice similarity coefficient (DSC):

Let and be, respectively, the reference and automatic segmentations of a given tissue class and for a given subject. The DSC for this subject can be defined as:

(5)

DSC values are within a range, 1 indicating perfect overlap and 0 corresponding to a total mismatch.

Modified Hausdorff distance (MHD):

Let and denote the sets of voxels within the reference and automatic segmentation boundary, respectively. MHD is given by:

(6)

where is the point-to-set distance defined by: , with denoting the Euclidean distance. Low MHD values indicate high boundary similarity.

Average surface distance (ASD):

Using the same notation as the Hausdorff distance above, the ASD corresponds to:

(7)

where denotes the cardinality of a set. In distance-based metrics, smaller values indicate higher proximity between two point sets and, thus, a better segmentation.

Absolute Volume Differences
(8)

where and are the volume of the segmentation result and reference, respectively. These measures were used to evaluate the following brain structures in each of the fifteen test datasets: GM, WM, CSF, brain (GM + WM), and intracranial volume (GM + WM + CSF). The brainstem and cerebellum are excluded from the evaluation.

Implementation:

We extended our 3D FCNN architecture proposed in [36], which is based on Theano. The source code of this architecture is publicly available888https://github.com/josedolz/SemiDenseNet. Training and testing was performed on a server equipped with a NVIDIA Tesla P100 GPU with 16 GB of RAM memory. Training HyperDenseNet took around 70 min per epoch, and around 35 hours in total for the two-modality version. With three image modalities, training each epoch took nearly 3 hours. Inference on a whole 3D MR scan took on average from 70-80 to 250-270 seconds, for the two- and three-modality versions, respectively.

Single Dense Path    Dual Dense Path

Fig. 8: Section of baseline architectures: single-path dense (left) and dual-path dense (right). While in the first case both modalities are concatenated at the input of the network, each modality is analyzed independently in the second architecture, and features fused at the end of the streams. Each gray region represents a convolutional block. Red arrows correspond to convolutions and black arrows indicate dense connections between feature maps. Dense connections are propagated through the entire network.

FCN_Res3D: The architecture of FCN_Res3D consists on 5 convolutional blocks with residual units on the encoder path, with 16, 64, 128, 256 and 512 kernels. The decoding path contains 4 convolutional upsampling blocks, each composed of 4 kernels, one per class. At each residual block, batch normalization and a Leaky ReLU with a leakage value of 0.1 are employed before the convolution. Instead of including max-pooling operations to re-size the images, stride values of 2 2 2 are used in layers 2, 3 and 4. Volume size at the input of the network is 64 64 24. The implementation of this network is provided in [58] 999https://github.com/DLTK/DLTK.

UNet3D: Although quite similar to FCN_Res3D, UNet3D presents some differences, particularly in the decoding path. It contains 9 convolutional blocks in total, 4 in the encoding and 5 in the decoding path. The number of kernels in the encoding path are 32, 64, 128 and 256, with strides of 2 2 2 at layers 2, 3 and 4. In the decoding path, the number of kernels are 256, 128, 64, 32 and 4, from the first to the last layer. Furthermore, skip connections are added at the convolutional blocks of the same scale between the encoding and decoding paths. As in FCN_Res3D, batch normalization and a Leaky ReLU with a leakage value of 0.1 are employed before the convolution at each block. Volume size at the input of the network is also 64 64 24. The implementation is provided in [58].

DeepMedic: We used the default architecture of DeepMedic in our experiments. This architecture includes two paths with 8 convolutional blocks: 30, 30, 40, 40, 40, 40, 50, 50 kernels of size 333. At the end of both paths, two fully connected convolutional layers with 150 111 filters each are added, before the last classification layer. The second path is used with a low-resolution version of the input at the first path, for a larger receptive field. The input patch size is 272727 and 353535 for training and segmentation, respectively. The official code 101010https://github.com/Kamnitsask/deepmedic is employed to evaluate this architecture.

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