How is the segmentation defined?

The MATLAB structure that FieldTrip uses to describe a segmentation represents different tissue-types in the anatomical MRI typically after obtained calling ft_volumesegment or ft_read_atlas. The segmentation is a special kind of a volumetric structure that contains additional fields describing for each voxel to which tissue type or brain area it belongs.

An example segmentation obtained after ft_volumesegment with the default segmentation options is shown here. The style of this representation is “probabilistic” (see below):

          dim: [256 256 256]        % the size of the 3D volume in voxels  
    transform: [4x4 double]         % affine transformation matrix 
     coordsys: 'ctf'                % description of the coordinate system
         unit: 'mm'                 % the units in which the coordinate system is expressed
         gray: [256x256x256 double] % probabilistic map of the gray matter
        white: [256x256x256 double] % probabilistic map of the white matter
          csf: [256x256x256 double] % probabilistic map of the cerebrospinal fluid

The tissue type of each voxel can be represented in the FieldTrip structure in two different ways, which are mutually exclusive. The representation can be either “probablistic” or “indexed”. The remainder of this page explains the difference between the two representations.

Probabilistic representation

Tissue probability maps

The default output of the ft_volumesegment function (see above) is a segmentation data-type structure with probabilistic tissue maps. The gray, white and csf fields contain probabilistic values for representing the gray, white matter and the cerebrospinal fluid. This means, for example, that at the field white everything that is not the white matter represented by 0, and voxels which belong to the white matter have a value between 0 and 1.

probability tissue map of gray matter probability tissue map of white matter probability tissue map of cerebro-spinal fluid
Figure 1. Probabilistic maps of the gray (left), white (middle) and cerebrospinal fluid (right). The colors represent probabilities ranging from 0 to 1.

Here is to code that creates this data-structure. It makes use of one of the MRIs from the tutorials.

% read in the anatomical data
mri  = ft_read_mri('Subject01.mri');

% use the ft_volumereslice function to be able to plot the MRI with the top of the head upwards
cfg              = [];   
cfg.dim          = [256 256 256];                 % original dimension
mri              = ft_volumereslice(cfg,mri);

% obtain the gray, white and csf tissue probability maps (tpm)
cfg              = [];
tpm              = ft_volumesegment(cfg,mri);

% plot the gray matter
cfg              = [];
cfg.funparameter = 'gray';
ft_sourceplot(cfg, tpm);

The output of this code can be seen in the introduction of this faq.

Here, we used the ft_volumereslice function prior to segmentation. It is not required to use this function , but we used it here to obtain a nicer orientation of the MRI images for visualization with ft_sourceplot.

The reason for this is explained in more detail here.

Binary representations of brain, skull and scalp

When the brain, skull and scalp tissues are requested as outputs from ft_volumesegment, the output also represents the probabilistic representation. However, in this case each fields contain a binary or boolean value, i.e. a probability of 0 (false) or 1 (true). Hence, the binary representation is a special case of the probabilistic representation.

binary brain-mask binary skull-mask binary scalp-mask
Figure 2. The brain (left), the skull (middle) and scalp (right). The colors represent only zeros and ones.

The brain, scalp and skull segmentations are used for creating volume conduction models of the head by triangulation the outside surface of the three tissues. This type of segmentation of the MRI is obtained by the following code:

% obtain the brain, skull and scalp tissues 
cfg              = [];
cfg.output       = {'brain','skull','scalp'};
bss              = ft_volumesegment(cfg, mri);     % the mri is the same as in the code before

cfg              = [];
cfg.funparameter = 'brain';
cfg.location     = 'center';
ft_sourceplot(cfg, bss);

This segmentation data structure looks similar to the structure above (in the introduction), but here, the fields representing the different tissue types contain binary matrices.

           dim: [256 256 256]          
      transform: [4x4 double]         
       coordsys: 'ctf'                 
           unit: 'mm'                  
          brain: [256x256x256 logical] % binary map representing the brain
          scalp: [256x256x256 logical] % binary map representing the scalp
          skull: [256x256x256 logical] % binary map representing the skull

Regardless of whether the probabilities are crisp (i.e. either exactly 0 or 1) or probabilistic (i.e. a floating point value ranging between 0 and 1), the representation of the volume is always in a field of the MATLAB structure with a field name that describes the tissue. A similar example would be

             dim: [256 256 256]          
        transform: [4x4 double]         
         coordsys: 'mni'                 
             unit: 'mm'                  
  brodmann_area_1: [256x256x256 logical] % binary map representing a Brodmann area
  brodmann_area_2: [256x256x256 logical] % binary map representing a Brodmann area
  brodmann_area_3: [256x256x256 logical] % binary map representing a Brodmann area
  brodmann_area_4: [256x256x256 logical] % binary map representing a Brodmann area
  ...

When only the scalp as output is required from the segmentation, the scalp-mask includes also the brain and skull tissues.

binary scalp-mask
Figure 3. The binary representation of the outside surface of the scalp. The colors represent only zeros and ones.

This representation differentiates the boarder of the outer skin, but not the inside skin surface. The advantage of such a representation is that it is created faster.

cfg=[];
cfg.output='scalp';
scalp=ft_volumesegment(cfg,mri);

cfg              = [];
cfg.funparameter = 'scalp';
cfg.location     = 'center';
ft_sourceplot(cfg, scalp);

Indexed representation

Another way of representing tissue types is done by indexing. When indexing, one field structure can represent multiple non-overlapping tissues or brain areas with integer numbers. Everything that doesn't belong to any tissue types is represented by 0 and the voxels which belong to different tissues are represented by different numbers (Figure 3). The index-numbers must start with 1 and should increased one-by-one for each subsequent tissue type.

An additional field in the structure contains the labels that describe the names of the tissues for each index number. The order of the names in the label field are according to the index numbering. This representation is memory wise more efficient in the case of many tissue types and therefore often used for representing a brain atlas.

An example of an indexed segmentation data-structure (the AFNI TTatlas+tlrc segmented brain atlas):

atlas            =   ft_read_atlas('TTatlas+tlrc.BRICK');

disp(atlas)
               dim: [161 191 141]        
         transform: [4x4 double]        
             coord: 'tal'               
              unit: 'mm'               
            brick0: [161x191x141 uint8]  % integer values from 1 to 50, (0 means unknown)
            brick1: [161x191x141 uint8]  % integer values from 1 to 69, (0 means unknown)
       brick0label: {50x1 cell}          % names (labels) of brain areas indexed in brick0 
       brick1label: {69x1 cell}          % names (labels) of brain areas indexed in brick1

In this structure, the brick0 and brick1 field contains two different indexed representations of brain areas. The corresponding labels of the index-numbers can be found in the briack0label and in the brick1label fields. Note that the nomenclature “brick0” and “brick1” is AFNI specific and does not mean anything in special.

An indexed representation can also be plotted to inspect the different tissues in an image (see below).
atlas
Figure 4. Plot of the integer values that are represented in the indexed “brick0” representation of the AFNI atlas. The figure was made with “colormap lines”.

Conversion between probabilistic and indexed representations

The following code demonstrates how to create an indexed representation from the earlier obtained probabilistic/boolean brain, skull and scalp tissues.

 
% convert to indexed representation
bss_i                = bss;
bss_i.seg            = double(bss.scalp);         % scalp is logical but seg will contain: 0,1,2,3
bss_i.seg(bss.skull) = 2;                         % skull is represented by index 2 
bss_i.seg(bss.brain) = 3;                         % brain is represented by index 3
bss_i.seglabel       = {'scalp','skull','brain'}; % label-order corresponds to index from 1 to 3 

cfg                  = [];
cfg.funparameter     = 'seg';
cfg.location         = 'center';
ft_sourceplot(cfg,bss_i);

% change the colormap 
map = [0 0 0; 1 0 0; 0 1 0; 0 0 1];

colormap(map);

indexed representation of brain, skull and scalp

Figure 5. The brain (blue), skull (green) and scalp (red) after segmentation with indexing. The colors represent integers from zero to three.

It is always possible to convert a segmentation with an indexed representation to a probabilistic binary representation. The converse, i.e. a conversion from probabilistic to indexed representations, is not always easily possible.

An indexed segmentation can represent only non-overlapping tissues/brain areas, the only information that is represented is if a voxel belongs to one particular tissue/brain area. Therefore, it is possible to directly convert a binary probabilistic representation of a segmentation with non-overlapping tissue-types into an indexed representation.

When a non-binary probabilistic segmentation is used and when the binary representations of the different tissue types partially overlap, the conversion to an indexed representation would involve a disambiguation of each voxel to which tissue/brain area it belongs to and the more fine-grade information of the probability values would disappear.

Figure 6. Schematic figure of conversion between different representation of the segmentation. Binary probabilistic representation of non-overlapping tissue-types can be directly converted to an indexed representation (A). When an overlapping or/and non-binary probabilistic representation is converted to indexed, the representations are not equivalent (B)

faq/how_is_the_segmentation_defined.txt · Last modified: 2012/10/25 15:47 by lilla

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