Computational Vision and Medical Image Processing pp 229246  Cite as
A Novel TemplateBased Approach to the Segmentation of the Hippocampal Region
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Abstract
The work described in this document is part of a major work aiming at a complete pipeline for the extraction of clinical parameters from MR images of the brain, for the diagnosis of neurodegenerative diseases. A key step in this pipeline is the identification of a box containing the hippocampus and surrounding medial temporal lobe regions from T1weighted magnetic resonance images, with no interactive input from the user. To this end we introduced in the existing pipeline a module for the segmentation of brain tissues based on a constrained Gaussians mixture model (CGMM), and a novel method for generating templates of the hippocampus. The templates are then combined in order to obtain only one template mask. This template mask is used, with a mask of the grey matter of the brain, for determining the hippocampus. The results have been visually evaluated by a small set of experts, and have been judged as satisfactory. A complete and exhaustive evaluation of the whole system is being planned.
Keywords
Magnetic resonance Image analysis Hippocampus segmentation1 Introduction
The hippocampus is a structure of the Medial Temporal Lobe (MTL) that plays an essential role in the learning and memory capabilities of the brain. It is involved in Alzheimer’s disease (AD) and other neurodegenerative diseases (see [7, 12, 17, 22]). For this reason the hippocampus is targeted in the analysis of neuroimages. In particular, the analysis of the shape of the hippocampus is a well accepted indicator in the diagnosis of the Alzheimer’s disease, and the analysis of its changes over time can be useful for controlling the evolution of the disease. The problem to find relations between the hippocampus and clinical variables has been studied for some time already: [1, 2, 5, 11, 20].
A step preliminary to the analysis of the shape of the hippocampus is the segmentation of the hippocampus in MRIs, that in the last years has been tackled by many researchers following different approaches. Among the various works more interesting to the realisation of an automated system are two classes of methods: semiautomated and fully automated methods.
An interesting example of semiautomated method is described in [15]: a pipeline that combines the use of lowlevel image processing techniques such as thresholding and holefilling with the technique of the geometric deformable models [13, 16]. This process is regarded as semiautomated since the starting step is the labelling of some points on the hippocampal contour by the user; this is necessary to constrain the segmentation process to avoid the inclusion of some other grey matter structures, as the amigdala, in the hippocampal region. This kind of intervention by an expert is also present in [18].
A fully automated approach to the hippocampus segmentation based on the a priori anatomical knowledge of the hippocampus is described in [6]. The a priori knowledge is modelled by statistical information on the shape [14, 18] and by the deformation on a single atlas [8].
The approaches just mentioned are too sensible to the initialisation step, in the first case (i.e. the semiautomated methods), the labelling of the deformation constraints (landmarks) by the user is not exhaustive to describe the morphological variability of the hippocampal shape and is sensible to the specific MRI modality.
In the case of the fully automated method, the use of a single atlas to obtain the a priori knowledge not take in account the anatomical variability between various degrees of the atrophy of the hippocampus.
The work presented in this document is part of a pipeline, see [3, 4], the goal of which is the extraction of clinical variables from the hippocampus automatically segmented in MR images. What is presented in this document is a method for the segmentation of the brain tissues based on a constrained Gaussians mixture model, and a method for the generation of templates of the hippocampus that is novel respect to what was done in the pipeline presented in previous papers [3, 4].
In the remainder of this document first we will review the system implemented (Sect. 2); Sect. 3is dedicated to the brain tissues segmentation module based on a constrained Gaussian mixture model; then we will give details of the novel procedure for generating the hippocampus templates (Sect. 4), and finally we will show some results; the last section is left to some final remarks.
2 The Pipeline
In this section we briefly review how the pipeline implemented works. Further details can be found in [3, 4].
The pipeline consists of three main modules. The first one extracts from the MR two boxes containing the left and the right hippocampus plus a portion of the adjacent tissues and cavities. The second module, still under development, performs the automatic segmentation of the hippocampus, using a set of template masks manually segmented by expert radiologists. The last one, that is being studied, is dedicated to the computation of clinical variables that are related to the atrophic state of the hippocampus.
The pipeline accepts MR images and extracts two hippocampal boxes (HB) containing respectively the left and the right hippocampus, plus a portion of the adjacent tissues and cavities. This is achieved by a rigid registration between the input MR and a set of template boxes previously determined. These template boxes result from a rather long and computational intensive extraction procedure, described hereafter.
The templates extraction basically relies on the fact that the grey level contrast displayed by the complex hippocampal formation plus contiguous ventricles and adjacent structures is so characteristic as to be unique all over the brain. No other structure exists in the brain mimicking the same grey level distribution. Therefore, a procedure can be prepared which, on the basis of some suitably chosen examples, is able to identify the hippocampal region unambiguously.
2.1 Images Dataset
2.2 Extraction of the Hippocampal Boxes
The success of the registration of each moving image to the fixed image is quantified by the minimum reached in distance values. With a moderate computational effort, one could extract all the 100 remaining right HBs by using the first manually defined HB alone, but the quality of the results is not homogeneously good. In fact the fixed image is successful in extracting the HBs which are not too dissimilar from it. However, due to the ample morphological variability contained in the population of MR images, some HBs exist which are unsatisfactorily extracted or not found at all. Therefore, a more exhaustive approach is required.
The population of the remaining 99 MR images is registered to the fixed image. Thus, for each given image j(2 ≤ j≤ 99) this operation produces the value of the score d _{1, j }, stored in the first row of an upper triangular matrices. We remark that no actual HB extraction is performed at this stage. On the basis of the presently available score list (the first row of matrix d), the second box is extracted from MR\({}_{({j}^{{_\ast}})}\)where j ^{∗}is the index of the minimum (non zero) value of δ_{1, j }. Once the second HB is available, the remaining 98 moving images are registered on this new fixed image, and a new set of scores are obtained and stored in the second row of the matrix. The second extracted HB is selected from MR\({}_{({k}^{{_\ast}})}\)where now k ^{∗}is given by the index of the minimum (non zero) value of d _{1, j }and d _{2, j }, not taking into account the scores of the already extracted HBs. The procedure for the progressive extraction of all HBs follows this scheme and the extension to an increasing number of HB examples is obvious.
The illustrated procedure is able to detect hippocampi at any atrophy stage and to extract the corresponding HBs. Except for the extraction of the first HB, the whole process runs automatically, without requiring any manual intervention, and no appreciable drift affecting hippocampus orientation or positioning in the HB is noticeable during the extraction process. Visual assessment by an expert reader of the whole set of 100 exhaustive extracted HBs shows that the level of spatial registration of similar anatomical structures is very high. Such stability is not surprising if one considers the way the whole procedure works. At the beginning, the early extractions exhaust the set of the HBs which are very similar to the manually defined HB. Then, the procedure starts extracting HBs which are progressively different from the first ones, but diversity creeps into the growing HB database very slowly thanks to the relevant size of the population of the available MR images. Thus the orientation and position of the essential geometrical features of the hippocampal formation are preserved during the whole process of HB extraction.
2.3 Selection of Templates
As far as computational costs are concerned, this procedure is rather demanding and it is unreasonable to run it over again for extracting the two HBs of any new MR image. Instead of proposing scenarios of nHBs hunting for the n+ 1th HB, we show that the same hunt can be successfully performed by a decidedly smaller number of properly chosen HBs, in the following named HB Templates (HBTs). The HBTs are selected among all HBs as representative cases of the wide morphological variability of the MTL in a large population of elderly people. This idea is consistent with the fact that in the research field on atrophy progression affecting the medial temporal lobe usually only five scores are considered on the basis of visual MRI inspection: absent, minimal, mild, moderate and severe.
The basic idea of the HBTs selection process is to create groups of HBs, or clusters. To classify the nHBs in homogeneous clusters we used hierarchical clustering. The centroid for each cluster is then used as representative (template). To determine the optimal number of templates we increased the number of clusters k, starting from k= 3 to k= 20. We then evaluated the performance of the different sets of HBTs in extracting all the n= 100 right HBs. The test consisted in extracting all nHBs from all MR images given the set of kHBTs. Each MR image was registered to all the kHBTs and actual HB extraction was performed on the basis of the best score obtained (among the kavailable scores). The test was repeated for \(k = 3/20\). The procedure generated eighteen sets of nHBs (for each \(k = 3/10\)) to be compared to the original set extracted with the exhaustive procedure. To quantify the capability of the HBT sets in extracting the nHBs, we calculated the average distance between the newly extracted elements and the original ones. As the average distance decreases as the number of templates gets larger and larger, we chose the minimum number of templates whose extraction performance (average distance) is less than a given threshold.
With these templates we find the right and left hippocampal formations in any new MR image, using statistical indicators to assess the precision on this volume extraction. MR images ranging from normality to extreme atrophy can be successfully processed. We plan to obtain a set of clinical parameters useful for monitoring the progress of the disease from the analysis of the hippocampal formations.
A different analysis performed directly on the hippocampal boxes can allow the diagnosis of the disease. The boxes are analysed both with linear and non linear methods such as Voxel Based Morphometry and neural networks classifiers. The computed features are chosen to maximise the area under the ROC curve between Normal and AD cohorts. The same features are then used to classify MCI patients into likely AD converters and nonconverters. The procedure predictions are subsequently verified by clinical followups data, and the sensitivity/specificity against early detection of AD is computed.
3 Constrained Gaussian Mixture Model Segmentation oftheBrain

Number of tissues in which we want to segment the MRI box, in our case we are interested to cerebrospinalfluid (CSF), grey matter (GM) and white matter (WM).

Number of Gaussians used for modelling the distribution of the intensity feature.

Number of clusters associated to each Gaussian.

Number of Gaussians which model each tissue.
4 Hippocampal Mask Template Generation
Since there is no statistical atlas of the hippocampus, a set of template masks, i.e. HBs where the hippocampus has been manually segmented, can be used for the segmentation. What we present here is a method for combining the set of template masks in order to obtain only one template mask. The template mask thus found is then used together with a mask of the greymatter for determining the hippocampus in the input hippocampal box. The greymatter mask is obtained by a three class classifier (white matter, grey matter). Our pipeline includes different classifiers for performing this task.
More precisely our problem is to create only one hippocampal mask template from a set M= { M _{1}, M _{2}, …, M _{ n }} of nmanually segmented raw hippocampal boxes (RHB) [3], and use this derived mask for the hippocampus segmentation from the current hippocampal box H _{0}.
The first step is to warp all the M _{ i }s onto H _{0}(using the Thirion’s Demons registration algorithm [19]). This produces a set of nmorphed RHB M ^{ ′ }{M _{1} ′, M _{2} ′, …, M _{ n } ′} and a set of nvectorial fields which can measure the magnitude of the deformation. At this point we want to generate the template representative of the set M′. Toachieve this we adopted the STAPLE algorithm.
4.1 STAPLE
STAPLE (Simultaneous Truth and Performance Level Estimation) [21] is an algorithm for the simultaneous ground truth and level performance of various classifiers. A probabilistic estimation of the ground truth is produced with an optimal combination of all classifiers weighting any classifier with his performance level. The algorithm is formulated as an instance of Expectation Maximisation ( EM) where:

The segmentation of any classifier for all voxels is an observable.

The “true” segmentation is an hidden binary variable for all voxels.
 The performance level is represented by the sensitivityand specificityparameters:

sensitivity p: true positives rate.

specificity q: true negatives rate.

The Algorithm

p= (p _{1}, p _{2}, …, p _{ R })^{ T }is a column vector Relements, where each element is the sensitivity of the corresponding classifier.

q= (q _{1}, q _{2}, …, q _{ R })^{ T }is a column vector Relements, where each element is the specificity of the corresponding classifier.

Dis a matrix N×Rof the classifiers decisions for any of Nvoxel of the Rsegmentations.

Tis a vector of Nelements which represent the hidden true segmentation.

(D, T): the complete data.

f(D, T∣p, q): the probability function of the complete data.

θ_{ j }= (p _{ j }, q _{ j })^{ T } ∀j∈ 1…R: the performance parameters of the classifier j.

θ = [θ_{1}θ_{2} …θ_{ R }]: the complete set of performance parameters.

f(D, T∣θ) : the probability function of the vector of the complete data.
This is solved iterating the following EM steps:
estimation of Q(θ∣θ^{(k)}) = ∑_{ T }lnf(D, T∣θ)f(T∣D, θ^{ k }).
4.2 Our Strategy
Initialisation Strategy
A blind use of the above procedure for determining a single template mask can lead to errors. This is because each one of the original template masks M _{ i }is representative of a class of hippocampus, therefore using all of them on each input H _{0}is not correct. We solve this problem taking into account the different degree of deformation of each M _{ i }on H _{0}to weight the contribution of each template mask M _{ i }.

To the HB template with lower average modulus (minHB) will be assigned the following values: \({p}_{\mathit{best}}^{0} = {q}_{\mathit{best}}^{0} = 0.99\).

To the HB template with higher average modulus (maxHB) will be assigned the following values: \({p}_{\mathit{worst}}^{0} = {q}_{\mathit{worst}}^{0} = 0.01\).
 To the remaining HB template will be assigned the values according to the following formula : ∀i≠best, i≠worst, i= 1, …, classifiers$${p}_{i}^{0} = {q}_{ i}^{0} = 0.99  \frac{{\mathit{HB}}_{i} \mathit{minHB}} {\mathit{maxHB} \mathit{minHB}}.$$(10)
pand qcalculated according to our strategy
Mean norm  p  q  

HB Template 1  1.70052  0.99  0.99  
HB Template 2  1.83688  0.72  0.72  
HB Template 3  2.03555  0.33  0.33  
HB Template 4  2.21146  0.01  0.01  
HB Template 5  1.97187  0.45  0.45  
HB Template 6  2.14845  0.11  0.11  
HB Template 7  2.15173  0.10  0.10  
HB Template 8  2.04179  0.32  0.32 
Summary of the algorithm
Convergence Check
Model Parameters
The selection of different a priori probabilities f(T _{ i }= 1), that can vary spatially or globally, can move the local maxima to which the algorithm converges. A probability f(T _{ i }= 1) that changes spatially is a good choice for those structures for which a probabilistic atlas is available.
5 Experimental Assessment
In this section we first discuss how the number of Gaussians for the CGMM segmentation module has been experimentally determined, and the we show a result of the hippocampal mask template generation module.
First of all we can note that the use of three (Fig. 4b) or four (Fig. 4c) Gaussians leads to a bad matching. A much better result is obtained when using five Gaussians (Fig. 4d). In particular, moving from left to right on the x axis, we can assign the first Gaussian to the CSF, the second and the third to the GM. More difficult is to decide if the fourth Gaussian should be assigned to the GM or to the WM. In fact, if it is assigned to the GM we risk to oversample the GM; on the other hand if it is assigned to the WM, then the GM might be under estimated, leading to errors in the hippocampus segmentation, as the hippocampus is part of the grey matter. The extraction process makes use of the GM segmentation for refining the results from the STAPLE module, that often expands on areas that have not been classified as grey matter. Therefore, it is much better to assign more Gaussians to the grey matter.
In Fig. 4f the outcome of modelling the histogram using seven Gaussians. The results is better than when using only five Gaussians, however there is the problem if the second Gaussian from the left is assigned to the CSF or to the GM should be assigned to the CSF or to the GM: either ways we end up with a downsampling or a oversampling of the GM respect to the CSF.
Parameters of the CGMM segmentation used for our experiments
Tissue  Number of clusters  Number of Gaussians  

GM  3  3  
WM  2  2  
CSF  1  1 
We used the hippocampus template determined with the method described above to actually refine a segmentation of the grey matter obtained with the constrained mixture of Gaussians method described earlier in this chapter.
6 Conclusions
In this work it is presented a novel method for the segmentation of the hippocampus in MR images based on the use of template masks. Our method is implemented in a pipeline that aims to perform an automated analysis of the hippocampus starting from his segmentation to perform a morphological analysis that can be very useful for the early diagnosis of neurodegenerative diseases, such as the Alzheimer’s disease. The main idea behind the pipeline is the use of the side effect of the STAPLE algorithm to produce a single, meaningful template which can refine a rough segmentation produced by a segmentation algorithm based on the CGMM framework. The next steps of our work aim to get a ground truth of segmented hippocampi to proceed to the validation of the whole pipeline and, consequently, aim to the implementation of a strategy to produce some parameters, arising from the morphological analysis of the hippocampus, such as clinical scores.
Notes
Acknowledgements
This work was partially funded by INFN within the MAGIC5 research project.
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