# Supervoxels-Based Histon as a New Alzheimer's Disease Imaging Biomarker
## 3 Materials and Methods
### Features Extraction: Supervoxel-Based Histons for Structural MRI Alzheimer Detection  
As can be seen in [52], in the process of unified segmentation, there is a relationship between neuronal degeneration and the presence of voxels with a relatively low probability of it being part of a specific type of tissue. Since [PERSON]'s disease tends to manifest itself as atrophy in specific areas of the brain, in these cases, the process of tissue segmentation will tend to show \"ambiguous\" areas difficult to classify as one or the other type of tissue, in addition to the decrease in the total volume of white matter and grey matter associated with ageing. In this work, we propose the possibility of exploiting both the decrease in the total volume of GM and WM and the relationship between GM, WM and CSF through the use of histones as a textural volumetric characteristic. In [53], we propose the use of super pixel segmentation (using SLIC) as a way of mitigating some of the limitations of the original histon generation method [44] (histons calculated from a color sphere based on a predefined neighbourhood and colour distance), as a method oriented to the segmentation of multispectral images. In this case, we have extended the original method to MRI volumes. Thus, we have used an aggregation of the probability volumes for GM, WM and CSF to carry out a segmentation using supervoxels. In this respect, for segmentation purposes, the different probability volumes (which are represented as 8-bit intensity maps) can be equated to the spectral bands of a colour volume (see Figure 3). Using a supervoxel segmentation (over-segmentation), we get a way of characterizing the local similarities within the aggregate volume, obtaining a natural set of neighbourhoods for the generation of histones. Similarly to what can be seen in [53], the use of supervoxels as a neighbourhood implies the adherence of the neighbourhoods set to the boundaries and features present in the image, so, when a histon is calculated, there is a direct spatial relationship between the voxel tested for its belonging and the color sphere. Furthermore, we can quantify the overall local homogeneity of a volume using the average intensity standard deviation of the supervoxel-defined space since segmentation using supervoxels already produces locally homogeneous areas. We will associate intensity with the probability of it being GM, WM and CSF in each of the probability volumes. Thus, when calculating a histon, a voxel will be considered to be inside the color sphere if the distance between the mean intensity of its corresponding supervoxel and the intensity of that voxel is less than the mean local deviation of the probability volume in the space defined by the supervoxels, in each of the probability volumes. Let us denote the set of resulting supervoxels in an image segmentation as \(Cs=\{Cs_{1},Cs_{2},\cdots,Cs_{Ns}\}\), where \(Ns\) is the total number of supervoxels; \(I(x_{Cs_{j}},y_{Cs_{j}},z_{Cs_{j}},v_{i})\) represents the centroid of the supervoxel \(Cs_{j}\) in the probability volume \(v_{i}\in V_{p}\), where \(V_{p}\) is the set of probability volumes \(V_{p}=\{WM,GM,CLF\}\); and \(Np_{j}\) is the number of voxels in that supervoxel. Then, the similarity function \(S_{2}\left(x,y,z\right)\) is defined as:  
\[S_{2}\left(x,y,z\right)= \begin{cases}1,&\text{if }\forall s_{i}\in V_{p}\ \ d_{ ts_{i}}\left(x,y,z\right)<E_{v_{i}},\\ 0,&\text{otherwise},\end{cases}  \tag{5}\]  
\[d_{ts_{i}}\left(x,y,z\right)=\left|I(x,y,z,v_{i})-I(x_{Cs_{j}},y_{Cs_{j}},v_{ i})\right|\ \ \ I(x,y,z,v_{i})\in Cs_{j}, \tag{6}\]  
\[E_{v_{i}}=\frac{1}{Ns}\sum_{j=1}^{Ns}\frac{1}{Np_{j}}\sum_{l\in Cs_{j}}I(x,y, z,v_{i}). \tag{7}\]  
The use of supervoxels as a neighbourhood allows the probability distribution to be represented in a natural and accurate way as a supervoxel represents a real volume within the image, created by taking into account the features present in the image.