## Initial Brain Mask

The process that generates the initial brain mask has three steps. First, it smooths the brain image using 2D nonlinear anisotropic diffusion and attenuates narrow nonbrain regions. Then, it sets an automated threshold to the diffused MR volume and produces a binary mask. Third, it removes misclassified nonbrain regions such as the eyes from the binary mask based on morphology and spatial information obtained from the head mask.

### Nonlinear Anisotropic Diffusion

Nonlinear anisotropic diffusion filters introduced by Perona and Malik [26] are tunable iterative filters that can be used to enhance MR images [15]. Nonlinear anisotropic diffusion filters can be used also to enhance and detect object edges [24,26,2].

The anisotropic diffusion filter is a diffusion process that facilitates intraregion smoothing and inhibits interregion smoothing:

Segmentation of the original image in Fig. 4a with this automatic threshold r produces the head mask in Fig. 4b, where some misclassified pixels within the head region and speckle outside the head region are apparent. Morphological operations with a small structuring element such as a 5 x 5 kernel can effectively remove such noise components [22], as shown in Fig. 4c.

FIGURE 3 A truncated histogram of a PD-weighted MR volume. The background noise at the low end of the histogram is characterized by a Rayleigh distribution. Reprinted from M. S. Atkins and B. Mackiewich. Fully automatic segmentation of the brain in MRI. IEEE Transactions on Medical Imaging, 17(1):98-107, February, 1998. © 1998 IEEE.

Consider I(x, t) to be the MR image where x represents the image coordinates (i.e., x, y), t is the iteration step, and c(x, t), the diffusion function, is a monotonically decreasing function of the image gradient magnitude. Edges can be selectively smoothed or enhanced according to the diffusion function. An effective diffusion function is [26]

FIGURE 3 A truncated histogram of a PD-weighted MR volume. The background noise at the low end of the histogram is characterized by a Rayleigh distribution. Reprinted from M. S. Atkins and B. Mackiewich. Fully automatic segmentation of the brain in MRI. IEEE Transactions on Medical Imaging, 17(1):98-107, February, 1998. © 1998 IEEE.

where K is the diffusion or flow constant that dictates the behavior of the filter. Good choices of parameters that produce an appropriately blurred image for thresholding are K = 128 with 25 iterations and a time step value of just under 0.2. Filtering can be fairly sensitive to these three parameters [22]; however, for all the PD-, T2-, and T1-weighted data sets displayed axially or coronally, the preceding parameter settings provide a good initial brain segmentation. The discrete diffusion updates each pixel by an amount equal to the flow contributed by its four nearest neighbors. If the flow contribution of the diagonal neighbors is scaled according to their relative distance from the pixel of interest, then eight nearest neighbors can also be used [15] for diffusion. With this approach anisotropic data also can be addressed.

Once nonlinear anisotropic diffusion attenuates the intensity of the skull and other nonbrain regions, a simple low threshold can be used to segment the brain and the eyes as shown in Fig. 5. Simple thresholding would not be effective without prior filtering with the diffusion technique.

FIGURE 5 Intracranial boundary detection using 2D nonlinear anisotropic diffusion filtering. (a) Original T2-weighted image. (b) 2D diffused image. Diffusion reduces nonbrain tissues, enabling a simple threshold to segment the brain. Reprinted from M. S. Atkins and B. Mackiewich. Fully automatic segmentation of the brain in MRI. IEEE Transactions on Medical Imaging, 17(1):98-107, February, 1998. © 1998 IEEE.

FIGURE 5 Intracranial boundary detection using 2D nonlinear anisotropic diffusion filtering. (a) Original T2-weighted image. (b) 2D diffused image. Diffusion reduces nonbrain tissues, enabling a simple threshold to segment the brain. Reprinted from M. S. Atkins and B. Mackiewich. Fully automatic segmentation of the brain in MRI. IEEE Transactions on Medical Imaging, 17(1):98-107, February, 1998. © 1998 IEEE.

### Automated Threshold

After diffusion filtering, brain voxel distribution becomes close to normal for T2-weighted and even PD images. Consequently, the threshold can be determined by fitting a Gaussian curve to the histogram of the diffused volume data. For PD- and T2-weighted slices, a good threshold is set at two standard deviations below the mean [7]. For Tl-weighted axially displayed images, the minimum value in the brain histogram plot is selected as the threshold. This value typically corresponds to about 0.5 standard deviations below the mean of the fitted Gaussian. The voxel intensity histogram of a diffused T2-weighted volume, the best fit Gaussian curve, and the selected threshold are illustrated in Fig. 6. A binary mask produced by the threshold is shown in Fig. 7.

### Refinement of Mask

Misclassified regions, such as the eyes, that occur after automatic thresholding (Fig. 7b) are removed using morphological filtering and spatial information provided by the head mask. In each region of the binary mask, first holes are filled and then binary erosion separates weakly connected regions. The erosion operation uses a 10 x 10 binary matrix of l's whose four corners have six symmetrically located 0's providing a hexagonal symmetric element with four pixels on each edge. The width of this element is sufficient to separate the brain from the eyes in all axial slices we studied whose fields of view were between 200 and 260 mm. After the erosion operation, the algorithm discards regions whose centroids are outside a bounding box defined by the head mask illustrated in Fig. 8. Dimensions of the bounding box in Fig. 8 yield good results for data sets with the eyes up, for several fields of view. Different parameters are needed for images with the eyes down, and for coronally and sagittally displayed images. Two bounding boxes will be required for sagitally displayed images where there is no symmetry. The remaining regions are returned close to their original size with binary dilation using the same 10 x 10 kernel.

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FIGURE 6 A histogram of the diffused T2-weighted MR scan with the best fit Gaussian curve and threshold levels overlaid. Reprinted from M. S. Atkins and B. Mackiewich. Fully automatic segmentation of the brain in MRI. IEEE Transactions on Medical Imaging, 17(1):98-107, February, 1998. © 1998 IEEE.

Since thresholding eliminates the darkest pixels at the brain edge, this dilation step ensures that the mask is closer to the required edge. The steps of mask refinement are illustrated in Fig. 9.

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