Gerard Sanroma
email: gerard.sanroma@upf.edu

Víctor Andrea

Oualid M Benkarim

José V Manjón

Pierrick Coupé

Oscar Camara

Gemma Piella

Miguel A González Ballester

Early Prediction of Alzheimer's Disease with Non-local Patch-based Longitudinal Descriptors

Keywords: early AD prediction, non-local patch-based label fusion, longitudinal analysis

Alzheimer's disease (AD) is characterized by a progressive decline in the cognitive functions accompanied by an atrophic process which can already be observed in the early stages using magnetic resonance images (MRI). Individualized prediction of future progression to AD, when patients are still in the mild cognitive impairment (MCI) stage, has potential impact for preventive treatment. Atrophy patterns extracted from longitudinal MRI sequences provide valuable information to identify MCI patients at higher risk of developing AD in the future. We present a novel descriptor that uses the similarity between local image patches to encode local displacements due to atrophy between a pair of longitudinal MRI scans. Using a conventional logistic regression classifier, our descriptor achieves 76% accuracy in predicting which MCI patients will progress to AD up to 3 years before conversion.

Introduction

Alzheimer's disease (AD) is characterized by a progressive decline of the cognitive abilities. Before being diagnosed as probable AD, patients usually go through a mild cognitive impairment (MCI) stage. The earliest signs of neurodegeneration can be observed using magnetic resonance images (MRI) already at the MCI stage [START_REF] Frisoni | The clinical use of structural MRI in Alzheimer disease[END_REF]. Machine learning techniques have taken advantage of this fact to characterize individuals at different stages of the disease. Cuingnet et al. [START_REF] Cuingnet | Automatic classification of patients with Alzheimer's disease from structural MRI: A comparison of ten methods using the ADNI database[END_REF] presented a comparison of 10 methods for discrimination of healthy controls (HC) and AD patients with different degrees of neurodegeneration. The most common MRIbased features used for discrimination include tissue probability maps, cortical thickness, hippocampal morphometry or a combination of them [START_REF] Wolz | Multi-Method Analysis of MRI Images in Early Diagnostics of Alzheimer's Disease[END_REF].

Among the personalized medicine approaches related to AD, the discrimination between patients that will remain stable in the MCI stage (i.e., s-MCI) and the ones that will progress to AD in the future (i.e., p-MCI) is possibly the one with most potential impact. Successful early identification of p-MCI patients opens up the possibility for improving clinical trials aimed at assessing preventive care treatments. Moradi et al. [START_REF] Moradi | Machine learning framework for early MRI-based Alzheimer's conversion prediction in MCI subjects[END_REF] specifically focused on the discrimination of p-MCI vs. s-MCI patients up to 3 years prior to conversion. Tong et al. [START_REF] Tong | A Novel Grading Biomarker for the Prediction of Conversion From Mild Cognitive Impairment to Alzheimer's Disease[END_REF] also identified p-MCI subjects depending on their similarity with a pre-defined dictionary containing both HC and AD subjects. This latter work was inspired by an hippocampal grading method by Coupé et al. [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF] (i.e., SNIPE) that assessed hippocampal abnormality based on local similarities to a pre-defined training library. The grade produced by SNIPE could discriminate s-MCI vs. p-MCI with high accuracy.

The structures in the medial temporal lobe (MTL), including the hippocampus, are among the first ones to be atrophied during the early stages of AD [START_REF] Thompson | Dynamics of gray matter loss in Alzheimer's disease[END_REF]. Strictly speaking, atrophy can only be measured using repeated acquisitions from the same subject over time (rather than using a single MRI, as in the above methods). Several approaches agree in finding atrophy rates in the MTL structures following the trend AD > MCI > HC [START_REF] Cash | Assessing atrophy measurement techniques in dementia: Results from the MIRIAD atrophy challenge[END_REF][START_REF] Chincarini | Integrating longitudinal information in hippocampal volume measurements for the early detection of Alzheimer's disease[END_REF]. However, these approaches are not designed for personalized predictions at the individual level and can only reveal the general trends in the population.

We propose a novel method to describe, with a high level of detail, the atrophy patterns across a pair of MRI scans from the same subject at different time points. The proposed descriptor is suitable for being used by machine learning techniques for personalized medicine. Inspired by patch-based label fusion in multi-atlas segmentation [START_REF] Coupé | Patch-based Segmentation using Expert Priors: Application to Hippocampus and Ventricle Segmentation[END_REF], our descriptor computes local patch-wise similarities between baseline and follow-up images. Therefore, one-to-many correspondences are used to encode local displacements. For the early prediction of AD, we feed the proposed high-dimensional descriptors extracted from the hippocampal region to a conventional logistic regression classifier.

Other learning-based methods use longitudinal data to predict AD in the first stage of the pathology. Zhu et al. [START_REF] Zhu | Early Diagnosis of Alzheimer's Disease by Joint Feature Selection and Classification on Temporally Structured Support Vector Machine[END_REF] proposed a constrained SVM specifically designed for longitudinal data. Jie et al. [START_REF] Jie | Temporally-Constrained Group Sparse Learning for Longitudinal Data Analysis in Alzheimer's Disease[END_REF] proposed a constrained regression for the prediction of the evolution of cognitive scores in AD patients. The main difference between these methods and the proposed one is that the former ones propose longitudinally-aware classifiers that use conventional MRI images, whereas we propose longitudinally-specific descriptors that can be used by conventional classifiers.

Method

We present an atrophy descriptor between a pair of baseline B i and follow-up F i images for the i-th patient, aimed at capturing the subtle atrophy patterns discriminating s-MCI and p-MCI patients. In order to bring the pair of images into correspondence while still preserving the local differences due to atrophy, we affinely register the follow-up image to its baseline. We use the notation F →B i to denote that the follow-up image has been registered to its corresponding baseline. In the case that we have more than one follow-up image per patient, we can divide the entire sequence into a set of pairs baseline / follow-up and treat them independently. The proposed method is divided in the following steps: (i) defining the region-of-interest (ROI), (ii) computing the patch-based similarity maps, (iii) building the atrophy descriptor and (iv) learning the classifier.

Region of Interest

We extract the high-dimensional atrophy descriptors from a ROI around the hippocampus. As shown in the literature, the hippocampus is among the first regions to be atrophied due to AD [START_REF] Thompson | Dynamics of gray matter loss in Alzheimer's disease[END_REF] and therefore it is a reasonable choice as ROI for early prediction of AD [START_REF] Coupé | Patch-based Segmentation using Expert Priors: Application to Hippocampus and Ventricle Segmentation[END_REF][START_REF] Cuingnet | Automatic classification of patients with Alzheimer's disease from structural MRI: A comparison of ten methods using the ADNI database[END_REF]. We propagate the hippocampal ROI, denoted as Ω, from a template image T onto each baseline B i using spatial warpings T T →Bi obtained via non-rigid image registration. The hippocampal ROI in the template was computed by dilating (with a structuring element of 3 × 3 × 3) the hippocampal segmentation obtained through multi-atlas segmentation [START_REF] Coupé | Patch-based Segmentation using Expert Priors: Application to Hippocampus and Ventricle Segmentation[END_REF]. Fig. 1 shows the hippocampal ROI (in red) overlaid onto the template. Finally, let us denote as B i (x) , F →B i (x) , x ∈ Ω i , the pair of voxel intensities at corresponding location x within the ROI Ω i in the baseline and follow-up images of a given subject.

Patch-based Similarity Maps

We encode the atrophy patterns as one-to-many correspondences between each point in the baseline x ∈ Ω i and the neighboring points in the follow-up x ∈ N x , where N x is a cubic neighborhood of size s 3 around point x. This gives highdimensional information about local displacements undergone by each point between the two scans. We use the similarity between image patches to compute the local correspondences, where the patches centered at x and x in the baseline and follow-up images are defined respectively as P B i (x) , P F i (x ). In our experiments we use a patch size of 3 × 3 × 3.

For each subject, we compute a set of similarity maps W (j) i , j = 1 . . . s 3 , one for each offset in the cubic neighborhood N x , as follows:

W (j) i (x) = exp -P B i (x) -P F i (N x (j)) 2 2 h 2 (1)
where N x (j) is the j-th offset in the cubic neighborhood and we use the exponential of the negative sum of squared differences as measure of patch similarity with a normalization constant h = j P B i (x)-P F i (N x (j)) 2 . Fig. 2 shows examples of similarity maps across each neighbor offset in a cubic 27-neighborhood. Fig. 2. Each of the 27 tiles shows the similarity map for a different neighbor, with red and blue denoting higher and lower similarities, respectively. We have used a cubic neighborhood of size s 3 = 3 × 3 × 3 = 27. Tiles in each group of 9 are coherently placed according to their neighborhood offset within the sagittal plane. The three groups correspond to neighbors along the sagittal axis.

Atrophy Descriptors

The proposed atrophy descriptors are built by encapsulating the similarity maps W (j) i into feature vectors according to the following steps:

1. We spatially align to a reference space the similarity maps, denoted as W (j) i , using the inverse non-rigid transformations between template and baselines T -1

T →Bi (recall that similarity maps originally lie in the space of their baseline images). 2. To compensate for moderate registration errors, we smooth the warped similarities using a Gaussian kernel of width σ. 3. We build the longitudinal atrophy descriptor for i-th subject, denoted as z i , by concatenating the similarities across ROI locations and neighbors, i.e., W (j) i (x) |x ∈ Ω, j = 1 . . . s 3 (in practice, we subsample the locations with a step size ρ along each dimension in order to reduce redundancy and decrease the vector's length).

The length of the final vector is approximately |Ω|•s 3 /ρ 3 . In our experiments we set σ = 1.0, s 3 = 27 and ρ = 2.

Learning

Given the atrophy descriptors computed in the previous section in a population of training subjects {z i , i = 1 . . . n}, we learn a logistic regression classifier to predict the future outcome of each patient, denoted as y i = {-1, 1}, for s-MCI and p-MCI, respectively. Prior to learning, we select the most important features by training a random forest classifier with 1000 trees on the future outcome of each patient. As input to the logistic regression classifier, we only use the features with an importance above 0.5 • µ, where the importance is computed according how much a feature decreases the average impurity on the forest and µ is the average importance across features6 . After the feature selection step, we train a logistic regression classifier by minimizing the empirical loss over our training data subject to some regularization constraint. We define the optimization as:

min v,b n i 1 1 + exp (-y i (v z i + b)) + λ v 1 , (2)
where v and b are the parameters of the logistic regression classifier and z i is the vector of selected features from the i-th subject. The first term penalizes the classification errors and the second term, modulated by the scalar λ, enforces the sparseness of the coefficients-vector v through the L 1 -norm. The sparsity regularization is suitable when the number of features is much larger than the number of training samples, as in our case. Given the atrophy descriptor extracted from a new testing subject z, first we obtain z by picking the most important features as determined during training and then we classify it as p-MCI or s-MCI according to the output of the function: sign (f (z ; v, b)), where f (•) is the learned logistic regression classifier.

Experiments

We evaluate our method in classification experiments between MCI patients that remain stable (i.e., s-MCI) and MCI patients that will progress to AD in the following 3 years (i.e., p-MCI). We use the same subset of ADNI7 as in [START_REF] Moradi | Machine learning framework for early MRI-based Alzheimer's conversion prediction in MCI subjects[END_REF][START_REF] Tong | A Novel Grading Biomarker for the Prediction of Conversion From Mild Cognitive Impairment to Alzheimer's Disease[END_REF], containing 164 p-MCI and 100 s-MCI subjects 8 . We use the first scan (i.e., baseline, B i ) and second scan (i.e., follow-up F i ) of each subject in order to compute the atrophy descriptors. Images are corrected for inhomogeneities with the N4 algorithm [START_REF] Tustison | N4ITK: Improved N3 Bias Correction[END_REF] and their histograms linearly matched to a reference template [START_REF] Nyúl | On standardizing the mr image instensity scale[END_REF]. Follow-up images F i are affinely registered to their respective baselines B i with ANTs [START_REF] Avants | Symmetric diffeomorphic image registration with cross-correlation: Evaluating automated labeling of elderly and neurodegenerative brain[END_REF]. Subsequently, also with ANTs, we compute non-rigid spatial transformations from the MNI152 template to each of the baselines T T →Bi .

For each subject, we build the atrophy descriptors as follows:

1. The hippocampal ROI is propagated from the template to each of the baselines B i , as described in Sec. 2.1. 2. Similarity maps W (j) i are computed using baseline and registered follow-up scans, as described in Sec. 2.2. 3. Atrophy descriptors z i are built after smoothing and subsampling the warped similarity maps W (j) i , as described in Sec. 2.3.

Alternatively, we also compute more compact representations by decomposing the similarities at each point through PCA. We took the first 10 components explaining > 90% of the variance of the data.

Table 1 shows the average classification accuracy obtained by logistic regression with the proposed atrophy descriptors in 10-fold cross-validation experiments (with and without PCA decomposition) for a range of regularization strengths λ. 1. Accuracy of the proposed method in 10-fold cross-validation classification of s-MCI and p-MCI subjects for increasing regularization strenghts. First row corresponds to the original proposed descriptor. Second row corresponds to the proposed descriptor with an additional PCA decomposition step.

As we can see in Table 1, the additional PCA decomposition step degrades the discrimination accuracy, thus suggesting that some important information may be lost after the linear decomposition in the present application. Note that, even we only sacrifice 10% of the variance of the data in the PCA decomposition, we may also lose some structure imposed by the normalization of the similarities (i.e., similarities may not add up to one after the reconstruction).

For comparison, in Table 2 we show the results reported by state-of-the-art methods in s-MCI vs. p-MCI classification using MRI features (including some methods using the same dataset as ours).

Comparing results in Table 2, we can see that our method achieves state-ofthe-art performance. Our results are directly comparable to [START_REF] Moradi | Machine learning framework for early MRI-based Alzheimer's conversion prediction in MCI subjects[END_REF][START_REF] Tong | A Novel Grading Biomarker for the Prediction of Conversion From Mild Cognitive Impairment to Alzheimer's Disease[END_REF], since we use the same dataset. It is worth noting that [START_REF] Moradi | Machine learning framework for early MRI-based Alzheimer's conversion prediction in MCI subjects[END_REF][START_REF] Tong | A Novel Grading Biomarker for the Prediction of Conversion From Mild Cognitive Impairment to Alzheimer's Disease[END_REF] use the whole brain whereas we only use the hippocampal ROI. On the other hand, we use a pair of baseline and follow-up scans whereas [START_REF] Moradi | Machine learning framework for early MRI-based Alzheimer's conversion prediction in MCI subjects[END_REF][START_REF] Tong | A Novel Grading Biomarker for the Prediction of Conversion From Mild Cognitive Impairment to Alzheimer's Disease[END_REF] 2. Perfomance in s-MCI vs. p-MCI classification of state-of-the-art methods using only MRI features. The former 4 methods in the table use only a single baseline MRI for classification whereas the latter 3 use at least one longitudinal follow-up as well. See the main text for details about performances reported as an interval. Methods with an asterisk (*) have been evaluated in the same dataset as the proposed method.

AD classification [START_REF] Thompson | Dynamics of gray matter loss in Alzheimer's disease[END_REF]. As another difference, results of [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF][START_REF] Wolz | Multi-Method Analysis of MRI Images in Early Diagnostics of Alzheimer's Disease[END_REF] correspond to early prediction of up to 4 years before conversion, whereas our results (as well as those in [START_REF] Moradi | Machine learning framework for early MRI-based Alzheimer's conversion prediction in MCI subjects[END_REF][START_REF] Tong | A Novel Grading Biomarker for the Prediction of Conversion From Mild Cognitive Impairment to Alzheimer's Disease[END_REF]) correspond to prediction up to 3 years before conversion. The rest of longitudinal methods (i.e., [START_REF] Zhu | Early Diagnosis of Alzheimer's Disease by Joint Feature Selection and Classification on Temporally Structured Support Vector Machine[END_REF][START_REF] Jie | Temporally-Constrained Group Sparse Learning for Longitudinal Data Analysis in Alzheimer's Disease[END_REF]) use at least 4 follow-up scans for each subject, whereas we use only 1 baseline and 1 follow-up scan. Zhu et al. [START_REF] Zhu | Early Diagnosis of Alzheimer's Disease by Joint Feature Selection and Classification on Temporally Structured Support Vector Machine[END_REF] discriminate between progression to AD at intervals 18, 12, 6 and 0 months with accuracies 0.76, 0.81, 0.83 and 0.84, respectively, hence the interval 0.76 -0.84 in the table.

Conclusions

We have presented a high-dimensional atrophy descriptor for early AD prediction using longitudinal MRI data. We achieve state-of-the-art performance by feeding our proposed descriptor to a conventional logistic regression classifier. Results suggest that our descriptor is suitable for capturing subtle atrophic patterns distinguishing s-MCI and p-MCI patients up to 3 years before conversion. Indeed, the hippocampal ROI is a suitable region for prediction in the early stages because it is among the first areas revealing atrophy due to AD [START_REF] Thompson | Dynamics of gray matter loss in Alzheimer's disease[END_REF]. Other methods have also focused in this ROI, achieving comparable performance to methods using the whole brain [START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF]. Effective ways to reduce the dimensionality should be explored in order to extend the use of the proposed descriptor to larger areas of the brain. Results in [START_REF] Zhu | Early Diagnosis of Alzheimer's Disease by Joint Feature Selection and Classification on Temporally Structured Support Vector Machine[END_REF] suggest room for improvement in using the full sequence of follow-up scans (instead of the first 2 ones). Possible lines of future work include combining our descriptor extracted from full follow-up sequences with longitudinally-aware classifiers.

Fig. 1 .

 1 Fig. 1. Hippocampal ROI (in red) overlaid onto a template image.

λ

  = 0.1 λ = 1.0 λ = 10 λ = 50 λ = 100 λ = 200 λ = 300 λ = 500 original 0.

  only use single baseline scan for classification. Coupé et al.[START_REF] Coupé | Scoring by nonlocal image patch estimator for early detection of Alzheimer's disease[END_REF] also focused on the hippocampal ROI (including enthorinal cortex), suggesting that this area might convey important information for early

			Cross-sectional			Longitudinal
	Method	Moradi [9] *	Tong [12] *	Coupé [4]	Wolz [14]	Zhu [15]	Jie [8]	proposed
	Perform. 0.747	0.789	0.74	0.68	0.76-0.84 0.757	0.766
	Table

This is implemented in the feature importance attribute of the random forest classifier in scikit-learn package in Python

http://www.adni-info.org/

More details at: https://sites.google.com/site/machinelearning4mcitoad/

Acknowledgements The first author is co-financed by the Marie Curie FP7-PEOPLE-2012-COFUND 462 Action. Grant agreement no: 600387


José V Manjón

Pierrick Coupe

Hippocampus subfield segmentation using a patch-based boosted ensemble of autocontext neural networks

The hippocampus is a brain structure that is involved in several cognitive functions such as memory and learning. It is a structure of great interest in the study of the healthy and diseased brain due to its relationship to several neurodegenerative pathologies. In this work, we propose a novel patch-based method that uses an ensemble of boosted neural networks to perform the hippocampus subfield segmentation on multimodal MRI. This new method minimizes both random and systematic errors using an overcomplete autocontext patch-based labeling using a novel boosting strategy. The proposed method works well on high resolution MRI but also on standard resolution images after superresolution. Finally, the proposed method was compared with a similar state-of-the-art methods showing better results in terms of both accuracy and efficiency.

Introduction

The hippocampus (HC) is a complex gray matter structure located under the surface of each temporal lobe. It is involved in many cognitive functions such as memory and spatial reasoning [START_REF] Milner | Psychological defects produced by temporal lobe excision[END_REF]. It has been largely studied in the last years to understand its healthy evolution across the lifespan in normal aging [START_REF] Petersen | Memory and MRI-based hippocampal volumes in aging and AD[END_REF] but also due to its key role in several dysfunctions such as epilepsy [START_REF] Cendes | MRI volumetric measurement of amygdala and hippocampus in temporal lobe epilepsy[END_REF], schizophrenia [START_REF] Altshuler | Amygdala enlargement in bipolar disorder and hippocampal reduction in schizophrenia: an MRI study demonstrating neuroanatomic specificity Arch[END_REF] or Alzheimer's disease [START_REF] Braak | Neuropathological stageing of Alzheimer-related changes[END_REF].

The hippocampus is composed of multiple subfields that can be divided into sections called the dentate gyrus, the cornu ammonis (CA) and the subiculum. The CA is also subdivided in sub-sections CA1, CA2, CA3, CA4, layers alveus, stratum oriens, stratum pyramidale, stratum radiatum, stratum lancosum and stratum moleculare. These layers present a high neuron density and are very compact so high resolution imaging is required to identify them.

Due to this morphological complexity and MR related image resolution limitations, mainly whole hippocampus volume analysis has been performed in the past by segmenting it as a single object [START_REF] Chupin | Fully automatic hippocampus segmentation and classification in Alzheimer's disease and mild cognitive impairment applied on data from[END_REF]. Even with this limitations whole HC volume has been shown to be a good biomarker for Alzheimer's disease [START_REF] Van Leemput | Automated segmentation of hippocampal subfields from ultra-high resolution in vivo[END_REF]. However, hippocampus subfields have shown to be affected differently by AD and normal aging in ex-vivo studies [START_REF] Braak | Neuropathological stageing of Alzheimer-related changes[END_REF] which makes them excellent candidates for early diagnosis.

Although high resolution MRI is becoming more accessible in research scenarios, manual segmentation, which is the most accurate analysis method, is not a feasible option since it is a highly time consuming procedure which requires expert trained raters taking many hours per case.

To overcome this problem some automated segmentation solutions have been developed in the last years. One of the first methods was proposed by Van Leemput et al. using a statistical model of MR image formation around the hippocampus to produce automatic segmentation [START_REF] Van Leemput | Automated segmentation of hippocampal subfields from ultra-high resolution in vivo[END_REF]. Recently, Iglesias et al. pursued this work and replaced the model by a more accurate atlas generated using ultra-high resolution ex-vivo MR images [START_REF] Iglesias | A computational atlas of the hippocampal formation using ex vivo, ultrahigh resolution MRI: Application to adaptive segmentation of in vivo MRI[END_REF]. Chakravarty et al. proposed a multiatlas method based on the estimation of several non-linear deformations and a label fusion step [START_REF] Chakravarty | Performing label-fusion-based segmentation using multiple automatically generated templates[END_REF]. Also using a multiatlas approach, Yushkevich proposed a method where a multiatlas approach is combined with a similarity-weighted voting and a learning-based label bias correction [START_REF] Yushkevich | Automated volumetry and regional thickness analysis of hippocampal subfields and medial temporal cortical structures in mild cognitive impairment[END_REF] and Romero et al also proposed a multiatlas multispectral method [21].

In this work, we propose a fast and accurate patch-based method to segment the hippocampus subfields using an ensemble of boosted neural networks. In the next sections, we will describe the method details as well as some experiments to demonstrate the accuracy and efficiency of the proposed approach.

Material and Methods

Image data

In this paper, we used a High Resolution (HR) dataset composed of 25 cases with T1weighted and T2-weighted images to construct a library of manually labeled cases. This dataset includes 25 subjects from a public repository (http://www.nitrc.org/projects/mni-hisub25) (31 ± 7 yrs, 12 males, 13 females) with manually-drawn labels dividing the HC in three parts (CA1-3, DG-CA4 and Subiculum). MRI data from each subject consist of an isotropic 3D-MPRAGE T1-weighted (0.6x0.6x0.6 mm 3 ) and anisotropic 2D T2-weighted TSE images (0.4×0.4×2 mm 3 ). Images underwent automated correction for intensity non-uniformity, intensity standardization and were linearly registered to the MNI152 space. T1w and T2w images were resampled to a resolution of 0.4 mm 3 (Figure 1). To reduce interpolation artifacts, the T2w data was upsampled using a non-local superresolution method [START_REF] Coupé | Collaborative patch-based super-resolution for diffusion-weighted images[END_REF]. For more details about the labeling protocol see the original paper [START_REF] Kulaga-Yoskovitz | Multi-contrast submillimetric 3Tesla hippocampal subfield segmentation protocol and dataset[END_REF].

Preprocessing

All the images (T1 and T2) were first filtered with a spatially adaptive non-local means filter [START_REF] Manjón | Adaptive non-local means denoising of MR images with spatially varying noise levels[END_REF] and inhomogeneity corrected using the N4 method [START_REF] Tustison | N4ITK: improved N3 bias correction[END_REF]. Later, they were linearly registered to the Montreal Neurological Institute space (MNI) using the ANTS package [START_REF] Avants | Advanced normalization tools (ANTS)[END_REF] and the MNI152 template. Next, we left-right flipped the images and cropped them to the right hippocampus area to produce 50 right hippocampus crops. After that, we non-linearly registered the cropped images to the cropped MNI152 template to better match the hippocampus anatomy. Finally, we normalized the image intensities using Nyúl and Udupa [START_REF] Nyúl | On standardizing the MR image intensity scale[END_REF] method. Hippocampus labels were spatially registered to the same space.

Proposed method

After the described preprocessing, a region of interest (ROI) is computed fusing all manual segmentations of the library and dilating the resulting region with a 5x5x5 voxels kernel to create a HC candidate region. For each voxel of this candidate region a feature set is created to be used to train a classifier. Several classifiers can be used to relate the image features and the corresponding labels. Lately high performance classifiers such as random forest [START_REF] Serag | SEGMA: An Automatic SEGMentation Approach for Human Brain MRI Using Sliding Window and Random Forests[END_REF] have been used. In our proposed method, we have used a neural network-based classifier [START_REF] Manjón | HIST: HyperIntensity Segmentation Tool. PatchMI workshop[END_REF].

• Features: The features used to train the network were three 3D patches per image modality of different size around the voxel/s to be classified, the x, y and z voxel coordinates of the center voxel of the patches and a value representing the a priori label probability. This apriori label probability map was obtained computing the average of all training label masks (convolved with a 5 mm 3 Gaussian kernel). In our experiments, we used a P 1 of size 3x3x3, a P 2 of 7x7x7 and P 3 of 9x9x9 voxels (however, for efficiency, we subsampled the patches P 2 and P 3 so we took only 27 samples uniformly spaced in all three dimensions). This leads to a feature vector X of 166 elements (i.e. 27 for P 1, 27 for P 2 and 27 for P 3 on T1, the same for T2, x, y and z coordinates and the prior probability).

• Network topology: A feedforward multilayer perceptron with two hidden layers was used. The network that we used had 166x85x55x27 weights. The network output is a patch of the same size of P 1. Note that an overcomplete approach was used so each voxel has contributions from several adjacent patches. This improves segmentation accuracy (more votes per voxel) and enforces the final label regularity.

To further improve classification results a second autocontext network is trained using an expanded feature vector constructed concatenating the original feature vector X with the output of the first network. This leads to a feature vector X a of 193 elements (166 + 27). Final classification is obtained from the output of network 2. Note that both networks are independently trained (Figure 2) .

Ensemble-based classification

A common approach for improving classification results is the use of the so-called ensemble learning. Ensemble methods (i.e. combination of several classifiers) allow in general to improve classification results by minimizing random and systematic errors.

In our proposed method, we have used a boosting strategy to leverage classification accuracy. Boosting [START_REF] Schapire | The strength of weak learnability[END_REF] is an algorithm that combines the output of several classifiers to minimize the variance and bias of the final classification. In boosting, each classifier is trained using the information of the previous one to minimize the errors of the current prediction. This is done giving more weight to the samples wrongly classified by the previous classifier or performing a non-random selection on the training dataset selecting with higher probability samples wrongly classified previously. While typically each network uses random initial weights (network reset) we decided to use the weights of the previous network as done in transfer learning which improves ensemble classifier accuracy while minimizing training time due to faster convergence. Finally, the different classifier outputs are combined according to their accuracy.

We trained four ensembles of M autocontext modules (figure 2) (one ensemble per subfield plus the background) over the whole hippocampus region and each voxel was labeled with the class of higher network output.

Experiments and results

In this section, a set of experiments are presented to show the performance of the proposed method. All the experiments have been done by processing the cases from the described library splitting the 50 cases first into a 30 training cases set and 20 test cases and later switching training and test datasets to evaluate the whole dataset.

Ensemble training

We explored two variants of ensemble training, the classical one with network reset and one without reset. For these experiments, we trained M=10 autocontext networks using only 10000 samples randomly selected from the candidate regions of the training dataset. All resulting networks outputs were averaged according to the accuracy to produce the final output.

We evaluated the impact of the two boosting variants (with and without reset) and estimated the optimal number of neural networks. In figure 3 (left), the evolution of the DICE coefficient (during training without reset) as a function of the number of individual and averaged trained networks is shown. In figure 3 (right), the same results with reset option are also shown.

As can be noticed, both boosting variants improved the classification results reaching a plateau at around 10 networks. However, no-reset boosting produced a more pronounced improvement compared to classical reset approach (0.9091 versus 0.9052). To understand the improved results we can look at the accuracy of each individual network of the ensemble. As can be noticed, reseted networks show a pseudo stable behaviour while non-reseted networks show maintained improvements as long as the number of ensemble networks increases. In fact, non-reseted last individual networks almost reach the accuracy of the whole ensemble.

Figure 3. Left: Dice coefficient in function of the number of networks for each network in nthe ensemble and for the ensemble prediction with the proposed boosting. Right:

Same results with classical boosting. Note that using previous network in the embeding not only improves overall ensemble accuarcy but also produces more accurate individual networks.

DICE

Results with reset

Independent Ensemble

With this settings, we trained the final network ensemble (M=10) using randomly selected sets of 1000000 samples from the total population of 2600000 patches. To train the 4 ensembles took around 8 hours while the time to segment a new case is around 10 seconds. To evaluate all 50 cases we trained two ensemble sets (one using the 30 training cases and applied to the remaining 20 cases and another trained on the 20 cases and applied to the 30 cases). We could do a leave-one-out approach to further improving the results but this would result on a large training time of around two weeks. Table 1 shows the dice coefficient of the different subfields for the 50 cases. We have also included the results when using only the best network instead of the ensemble (thus requiring only 1 second to perform the segmentation).

Standard resolution vs High resolution

High resolution MR images are not widely available, especially in clinical environments. For this reason, we analyzed the effectiveness of the proposed method on upsampled standard resolution images. For this purpose, we reduced the resolution of the library HR images by a factor 2 by convolving the HR images with a 2x2x2 boxcar kernel and then decimating the resulting image. The down-sampled images were upsampled by a factor 2 using BSpline interpolation and a superresolution method called Local Adaptive SR (LASR) [START_REF] Coupé | Collaborative patch-based super-resolution for diffusion-weighted images[END_REF]. Results are shown in Table 2. As can be noticed, segmentations performed on images upsampled with SR were better than using BSpline interpolation. Moreover, this experiment shows that the proposed method is able to produce competitive results even when using standard resolution images.

Comparison

We compared our method with other recent methods applied to hippocampus segmentation using the same number of structures and labeling protocol. The compared methods are called ASHS [START_REF] Yushkevich | Automated volumetry and regional thickness analysis of hippocampal subfields and medial temporal cortical structures in mild cognitive impairment[END_REF] and Surfpatch [START_REF] Caldairou | A Surface Patch-Based Segmentation Method for Hippocampal Subfields[END_REF]. Table 3 shows that the proposed method obtained higher DICE coefficients for all the structures. In terms of computation efficiency, our method requires only few seconds while ASHS and Surfpatch have an execution time of several hours per case.

Discussion

In this paper, we present a new hippocampus subfield segmentation method based on a boosted ensemble of autocontext neural networks. The proposed method achieves state-of-the-art accuracy very efficiently. Furthermore, the proposed method has been shown to perform well on standard resolution images, obtaining competitive results on typical clinical data. This fact is very important because it will allow analyzing large amounts of legacy data. Finally, it has been also shown that the proposed method compares well to another related state-of-art method obtaining better results in terms of both accuracy and reduced execution time.

Figure 1 :

 1 Figure 1: Example of an HR MRI case. Figure shows T1w and T2w images and its corresponding manual segmentation.

Figure 2 :

 2 Figure 2: Autocontext neural network. Original feature vector x used to train network 1 is expanded using the output of the network (posterior probabilities) to train network 2.

Table 1 :

 1 Mean DICE and standard deviation for each structure segmentation using two variants of the proposed method. Best results in bold.

	Structure	Proposed (best network)	Proposed (ensemble)
	Average	0.8681	0.8695
	CA1-3	0.8992	0.9001
	CA4\DG	0.8384	0.8404
	Subiculum	0.8667	0.8678
	Hippocampus	0.9518	0.9523

Table 2 :

 2 Mean DICE for each structure segmentation using the high resolution library and applying BSpline interpolation and LASR to the previously downsampled image to be segmented. Best results in bold.

	Structure	BSpline	LASR	HR
	Average	0.8595	0.8662	0.8695
	CA1-3	0.8930	0.8981	0.9001
	CA4\DG	0.8250	0.8349	0.8404
	Subiculum	0.8605	0.8655	0.8678
	Hippocampus	0.9480	0.9513	0.9523

Table 3 :

 3 Mean DICE in the native space for each structure. Segmentation performed by ASHS, SurfPatch, proposed method and human rater (intra-rater and inter-rater). Best results (for automatic segmentation) in bold.

	Structure	ASHS	SurfPatch	Proposed	Inte-rater	Intra-rater
	Average	0.8513	0.8503	0.8584	0.8833	0.9113
	CA1-3	0.8736	0.8743	0.8903	0.8760	0.9290
	CA4\DG	0.8254	0.8271	0.8283	0.9030	0.9000
	Subicu-	0.8548	0.8495	0.8565	0.8710	0.9050
	lum

Acknowledgements

This research was supported by the Spanish UPV2016-0099 grant from Universitat Politécnica de Valencia. This study has been also carried out with financial support from the French State, managed by the French National Research Agency (ANR) in the frame of the Investments for the future Program IdEx Bordeaux (ANR-10-IDEX-03-02, HL-MRI Project) and Cluster of excellence CPU and TRAIL (HR-DTI ANR-10-LABX-57).