3D cerebral MR image segmentation using multiple-classifier system

Abstract

The three soft brain tissues white matter (WM), gray matter (GM), and cerebral spinal fluid (CSF) identified in a magnetic resonance (MR) image via image segmentation techniques can aid in structural and functional brain analysis, brain’s anatomical structures measurement and visualization, neurodegenerative disorders diagnosis, and surgical planning and image-guided interventions, but only if obtained segmentation results are correct. This paper presents a multiple-classifier-based system for automatic brain tissue segmentation from cerebral MR images. The developed system categorizes each voxel of a given MR image as GM, WM, and CSF. The algorithm consists of preprocessing, feature extraction, and supervised classification steps. In the first step, intensity non-uniformity in a given MR image is corrected and then non-brain tissues such as skull, eyeballs, and skin are removed from the image. For each voxel, statistical features and non-statistical features were computed and used a feature vector representing the voxel. Three multilayer perceptron (MLP) neural networks trained using three different datasets were used as the base classifiers of the multiple-classifier system. The output of the base classifiers was fused using majority voting scheme. Evaluation of the proposed system was performed using Brainweb simulated MR images with different noise and intensity non-uniformity and internet brain segmentation repository (IBSR) real MR images. The quantitative assessment of the proposed method using Dice, Jaccard, and conformity coefficient metrics demonstrates improvement (around 5 % for CSF) in terms of accuracy as compared to single MLP classifier and the existing methods and tools such FSL-FAST and SPM. As accurately segmenting a MR image is of paramount importance for successfully promoting the clinical application of MR image segmentation techniques, the improvement obtained by using multiple-classifier-based system is encouraging.

Appendices

Appendix 1: Statistical features

The statistical features consisting of mean, median, standard deviations, entropy, contrast, energy, correlation, and intensity of each voxel [4, 32] mentioned in Sect. 2.2 are detailed as follows:

• 1. Mean (μ) and standard deviation (σ) of voxel intensity features which in fact present the mean intensity and variation in intensity level of the voxels lied around a given voxel are calculated as:

  $$ \mu = \frac{1}{x + y + z}\sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {I(x,y,z)} } } $$

  (4)
  $$ \sigma = \sqrt {\frac{1}{x + y + z}\sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {(I(x,y,z) - \mu } } } )^{2} } $$

  (5)

• 2. Median is the numerical value separating the higher half of intensity from the lower half. The median can be found by arranging all the intensities from lowest value to highest value and picking the middle on.

• 3. Energy is the performance index for image uniformity that is a good quality to manifest the disorder and entropy in the image. If it grows to increase, it means that the intensity will be changed slightly.

  $$ {\text{Energy}} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {I(x,y,z)^{2} } } } $$

  (6)

• 4. Entropy is a measure of variability and for a fixed image is zero.

$$ {\text{Entropy}} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} { - I(x,y,z)\log (I(x,y,z))} } } $$

(7)

• 5. Contrast expresses the rate of local changes in the image. The high value of the contrast expresses the high local changes in the region of the interest. Contrast is the difference between the highest and the lowest values of a interconnected set of voxels.

$$ {\text{Contrast}} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {((x - y)(x - z)(y - z))^{2} I(x,y,z)} } } $$

(8)

• 6. Correlation is another parameter used to measure randomness in a given image. This parameter can also be used to estimate the similarity between a given voxel and other voxels of the image. Correlation is zero in random images.

$$ {\text{Correlation}} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {(x - \mu_{x} )(} } } y - \mu_{y} )(z - \mu_{z} )\frac{I(x,y,z)}{{\sigma_{x} \sigma_{y} \sigma_{z} }} $$

(9)

$$ \mu_{x} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {xI(x,y,z)} } } ,\,\mu_{y} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {yI(x,y,z)} } } ,\,\mu_{z} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {zI(x,y,z)} } } $$

(10)

$$ \sigma_{x} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {(x - \mu_{x} )^{2} I(x,y,z)} } } ,\,\sigma_{y} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {(y - \mu_{y} )^{2} I(x,y,z)} } } ,\,\sigma_{z} = \sum\limits_{x} {\sum\limits_{y} {\sum\limits_{z} {(z - \mu_{z} )^{2} I(x,y,z)} } } $$

Appendix 2: Geometric moments features

For non-statistical feature, the geometric moments are calculated and employed [18, 22, 24]. In general, the geometric moment of order (p + q + r) of image I(x, y, z) is given by:

$$ m_{pqr} = \sum\limits_{x = 0}^{M - 1} {\sum\limits_{y = 0}^{N - 1} {\sum\limits_{z = 0}^{L - 1} {x^{p} y^{q} z^{r} I(x,y,z)} } } ,\quad p,q,r = 1,2, \ldots $$

(11)

where M, N, and L are image dimensions.

By using equation (12), geometrical central moments of order equal to (p + q + r) can be computed.

$$ \mu_{pqr} = \sum\limits_{x = 0}^{M - 1} {\sum\limits_{y = 0}^{N - 1} {\sum\limits_{z = 0}^{L - 1} {(x - \bar{x})^{p} (y - \bar{y})^{q} (z - \bar{z})^{r} I(x,y,z)} } ,\quad p,q,r = 1,2, \ldots } $$

(12)

where $\bar{x}$, $\bar{y}$, and $\bar{z}$ are gravity center of image and are calculated as follows:

$$ \bar{x} = \frac{{m_{100} }}{{m_{000} }}; \quad \bar{y} = \frac{{m_{010} }}{{m_{000} }};\,\,\,\,\bar{z} = \frac{{m_{001} }}{{m_{000} }} $$

(13)

$$ m_{pqr} = \sum\limits_{x = 0}^{M - 1} {\sum\limits_{y = 0}^{N - 1} {\sum\limits_{z = 0}^{L - 1} {(x)^{p} (y)^{q} (z)^{r} I(x,y,z)} } } $$

(14)