Image Segmentation free book chapter
This chapter describes a method of segmenting MR images into di erent tissue classes, using a modi ed Gaussian Mixture Model. By knowing the prior spatial probability of each voxel being grey matter, white matter or cerebro-spinal uid, it is possible to obtain a more robust classi cation. In addition, a step for correcting intensity non-uniformity is also included, which makes the method more applicable to images corrupted by smooth intensity variations. 5.1 Introduction Healthy brain tissue can generally be classi ed into three broad tissue types on the basis of an MR image. These are grey matter (GM), white matter (WM) and cerebro-spinal uid (CSF). This classification can be performed manually on a good quality T1 image, by simply selecting suitable
image intensity ranges which encompass most of the voxel intensities of a particular tissue type. However, this manual selection of thresholds is highly subjective. Some groups have used clustering algorithms to partition MR images into di erent tissue types, either using images acquired from a single MR sequence, or by combining information from two or more registered images acquired using di erent scanning sequences or echo times (eg. proton-density and T2-weighted). The approach described here is a version of the `mixture model’ clustering algorithm , which has been extended to include spatial maps of prior belonging probabilities, and also a correction for image intensity non-uniformity that arises for many reasons in MR imaging. Because the tissue classi cation is based on voxel intensities, partitions derived without the correction can be confounded by these smooth intensity variations. The model assumes that the MR image (or images) consists of a number of distinct tissue types (clusters) from which every voxel has been drawn. The intensities of voxels belonging to each of these clusters conform to a normal distribution, which can be described by a mean, a variance and the number of voxels belonging to the distribution. For multi-spectral data (e.g. simultaneous segmentation of registered T2 and PD images), multivariate normal distributions can be used. In addition, the model has approximate knowledge of the spatial distributions of these clusters, in the form of prior probability images. Before using the current method for classifying an image, the image has to be in register with the prior probability images. The registration is normally achieved by least squares matching with template images in the same stereotaxic space as the prior probability images. This can be done using nonlinear warping, but the examples provided in this chapter were done using ane registration .
One of the greatest problems faced by tissue classi cation techniques is non-uniformity of the images intensity. Many groups have developed methods for correcting intensity non-uniformities, and the scheme developed here shares common features. There are two basic models describing image noise properties: multiplicative noise and additive noise. The multiplicative model de- scribes images that have noise added before being modulated by the non-uniformity eld (i.e., the standard deviation of the noise is multiplied by the modulating eld), whereas the additive version models noise that is added after the modulation (standard deviation is constant). The current method uses a multiplicative noise model, which assumes that the errors originate from tissue variability rather than addit