Current medical imaging systems provide excellent spatial resolution, high tissue contrast, and up to 65535 intensity levels. Thus, image processing techniques which aim to exploit the information contained in the images are necessary for using these images in computer-aided diagnosis (CAD) systems. Image segmentation may be defined as the process of parcelling the image to delimit different neuroanatomical tissues present on the brain. In this paper we propose a segmentation technique using 3D statistical features extracted from the volume image. In addition, the presented method is based on unsupervised vector quantization and fuzzy clustering techniques and does not use any a priori information. The resulting fuzzy segmentation method addresses the problem of partial volume effect (PVE) and has been assessed using real brain images from the Internet Brain Image Repository (IBSR).
Recent advances in the medical imaging systems make it possible to acquire high resolution images with high tissue contrast. Moreover, these systems provide images up to 16-bit depth, corresponding to 65535 intensity levels. On the other hand, the human vision system is not able to recognize more than several tens of gray levels. Thus, image processing techniques are necessary to exploit the information contained in medical images, to be successfully used in CAD systems. In addition, computer-aided tools can analyze the volume image in a reasonable amount of time. These are valuable tools for diagnosing some neurological disorders such as schizophrenia, multiple sclerosis, the Alzheimer’s [
This section consists of six subsections which explain in detail the segmentation method presented in this paper and summarized in the block diagram shown in Figure
Block diagram of the segmentation method.
The performance of our proposal has been evaluated in comparison with other methods, using the Internet Brain Segmentation Repository (IBSR) from the Massachusetts General Hospital [
Although the images are already registered in the database, they contain nonbrain structures such as scalp and skull. These structures have to be removed before dealing with segmentation. In our case, nonbrain structures were removed using the BET 2.0 tool [
Unlike other MRI segmentation approaches which use 2D statistical descriptors [
2D gray level cooccurrence matrix (GLCM) computation. Main directions (0°, 45°, 90°, and 135°) are used and average value is associated with central voxel.
In the case of 3D-GLCM, cubes of size
(a) 3D overlapped windows extraction process. Note that overlapping is shown as color mixture. (b)
While four independent directions exist in 2D for GLCM calculation, 13 independent directions are found in 3D, and GLCM computation can be generalized as
3D GLCM calculation in direction
This way, 3D GLCM is computed through an offset
Regarding implementation details, cubes are vectorized as shown in Figure
Once 3D GLCM has been defined, Haralick’s textural features can be computed as in 2D, but using the 3D GLCM as previously defined in (
In addition to 3D Haralick features, we extract local histogram-based features from each 3D window. These features include maximum probability local intensity, mean, variance, skewness, entropy, energy and kurtosis [
Moreover, intensity probability in terms of the entire image is also included in the feature set. Thus, the entire feature set extracted from the image is summarized in Table
Features computed from each window (cube) are extracted from the image and associated with the central voxel which is described by 23 features (i.e., feature space is composed by
The self-organizing map [ Input space modelling: the prototypes computed during the SOM training, Topological order: units on the output map are arranged into a 2D or 3D lattice, and their position depends on the specific features of the input space. Density distribution: SOM reveals statistical variations on the distribution of the input data. This way, a higher density on the output space corresponds to a higher density on the input space. Feature selection: prototypes computed from the input data space represent the data manifold. Thus, the algorithm reduces the input space to a set of prototype vectors.
The process mentioned previously is performed in a competitive way, where only one neuron wins (i.e., its prototype vector is the most similar to the input data instance) with each input data instance. Nevertheless, prototypes of neurons belonging to the neighbourhood of the wining unit (called best matching unit (BMU)) are also updated. Let the SOM units be linearly indexed. The BMU
SOM can be seen as a clustering method as it quantizes the feature space by a number of prototypes, and each prototype can be considered as the most representative vector of a class. On the other hand, the prototypes are projected onto a two- or three-dimensional space while topology (i.e., distribution of SOM units in the projection space) is preserved. In that sense, SOM assumes that each map unit acts as a single cluster. In this work, input space is composed by feature vectors whose coordinates represent a different feature as presented in Section
Fuzzy clustering is carried out by optimizing the objective function (
Once the SOM is trained and clustered, each voxel (described by its corresponding feature vector) is mapped to a cluster, so that it belongs to a specific tissue with a probability. Figure
SOM units membership probability for WM (a), GM (b), and CSF (c) clusters according to FCM clustering for IBSR volume 7.
3D projection of the SOM prototypes for IBSR volume 7. Units have been colored according to the
Thus, voxels whose BMU fulfills the
In order to identify the tissue corresponding to each cluster, we use the fact that GM voxels usually present lower intensity values than CSF, and WM voxels present the higher intensity values due to the MRI acquisition process. This way, the cluster with the lower mean intensity value is associated with GM voxels and the cluster with the higher mean intensity values is associated with WM voxels.
As shown in Section
Figure
Fitness function in the optimization process. Convergence is achieved in 50 generations.
Thus, these features have been used to process the images on the IBSR database and to provide the segmentation outcomes based on the Jaccard index as shown in Section
The number of SOM units usually determines the performance of the clustering. Figure
Mean quantization error as a function of the number of SOM units.
The quantization error in this figure represents a measure of the reconstruction error, which tends to stabilize from 64 units. Thus, we choose 10 × 10 units map as a trade-off between quantization error and performance. Moreover, 3D SOM layer with hexagonal lattice was used as it yields better segmentation results.
Unsupervised segmentation using SOM requires to cluster the SOM units after training. This can be addressed using a standard clustering algorithm or a specific algorithm developed to cluster the SOM layer, as shown in Section
(1) Remove the background (i.e. null intensity voxels). (2) Extract overlapping cubes from 3D MRI. (3) Compute features from the cubes. (4) Normalize the samples for zero mean and unity variance. (5) Train the SOM. (6) Cluster the SOM prototypes using the FCM algorithm. (7) Compute the mean intensity of the receptive field of each cluster. (8) Assign a tissue to each cluster depending on its intensity profile. (9) Build the segmented image using the receptive fields of each cluster.
Cluster assignment of SOM units can be addressed in two ways. Since FCM computes membership probability, the units can be assigned to the cluster providing the maximum probability. This method uses the
Numerous experiments were carried out to assess the performance of the proposed algorithm using the IBRS2 database, as it provides real brain MRIs. Figure
Segmentation results for the IBSR volume 7. Some slices of the axial and coronal planes are shown in (a) and (b), respectively. Segmentation performed by experts is shown in (c) and (d) for the axial and coronal planes, respectively.
Thus, in Figure
In order to show segmentation outcomes, Figure
Axial slice from volume no. 7 (a). Segmentation results show CSF (b), WM (c), and GM (d).
In addition, PVE correction is applied as explained in Section
Axial slice from volume no. 7 (a). Segmentation results show CSF (b), WM (c), and GM (d) with PVE correction,
Coronal slice from volume no. 7 (a). Segmentation results show CSF (b), WM (c), and GM (d).
Coronal slice from volume no. 7 (a). Segmentation results show CSF (b), WM (c), and GM (d) with PVE correction,
Jaccard index calculated throughout the images in the IBSR2 database.
In this paper, we present MRI segmentation methods using 3D statistical features (Tables
3D directions in spherical coordinates and offset coding. Offset (
Direction |
Offset vector | Direction |
Offset vector |
---|---|---|---|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
Feature set extracted from 3D image.
Index | Feature | Index | Feature |
---|---|---|---|
3D Haralick (Textural) | |||
| |||
1 | Energy | 7 | Sum average |
2 | Entropy | 8 | Dissimilarity |
3 | Correlation | 9 | Cluster shade |
4 | Contrast | 10 | Cluster tendency |
5 | Homogeneity | 11 | Maximum probability |
6 | Variance | 12 | Difference variance |
| |||
Local histogram | |||
| |||
13 | Central voxel Intensity | ||
14 | Intensity mean | ||
15 | Intensity variance | ||
| |||
Local histogram | |||
| |||
16 | Mean intensity | 20 | Skewness |
17 | Intensity variance | 21 | Kurtosis |
18 | Energy | 22 | Maximum probability intensity |
19 | Entropy | ||
| |||
Image histogram | |||
| |||
23 | Intensity probability |
Optimized feature set.
Index | Feature type | Feature |
---|---|---|
1 | 3D-GLCM/Haralick-textural | Energy |
4 | 3D-GLCM/Haralick-textural | Contrast |
6 | 3D-GLCM/Haralick-textural | Homogeneity |
9 | 3D-GLCM/Haralick-textural | Cluster shade |
12 | 3D-GLCM/Haralick-textural | Inverse variance |
13 | 1st order | Voxel intensity |
14 | 1st order | Voxel mean intensity |
15 | 1st order | Voxel intensity variance |
18 | Local histogram | Energy |
20 | Local histogram | Skewness |
21 | Local histogram | Kurtosis |
Mean and standard deviation of the Jaccard index for the segmentation methods in Figure
Algorithm | Ref. | WM index | GM index |
---|---|---|---|
SOM-FCM + PVE ( |
— |
|
|
SOM-FCM | — |
|
|
NL-FCM | [ |
|
|
R-FCM | [ |
|
|
FCM | [ |
|
|
Energy:
Entropy:
Correlation:
Contrast:
Inverse difference moment (ASM, homogeneity):
Variance:
Sum average:
Dissimilarity:
Cluster shade:
Cluster prominence:
Maximum probability:
Difference variance:
This work was partly supported by the MICINN under the TEC2012-34306 project and the Consejería de Innovación, Ciencia y Empresa (Junta de Andalucía, Spain) under the Excellence Projects P09-TIC-4530 and P11-TIC-7103.