This section shows the results of voxel-histogram classification applied to both simulated and collected MRI datasets. When results can be verified and conditions are controlled, as shown with the classification of simulated data, the algorithm comes very close to "ground truth," or perfect classification. The results based on collected data illustrate that the algorithm works well on real data, with a geometric model of a tooth showing boundaries between materials, a section of a human brain showing classification results mapped onto colors, and a volume-rendered image of a human hand showing complex geometric relationships between different tissues.

The partial volume Bayesian algorithm (PVB) described in this chapter is compared with four other algorithms. The first, DML (discrete maximum likelihood), assigns each voxel or sample to a single material using a maximum likelihood algorithm. The second, PPVC (probabilistic partial volume classifier), is described in [23]. The third is a Mixel classifier [14], and the fourth is eigenimage filtering (Eigen)[12].

PVB significantly reduces artifacts introduced by the other techniques at boundaries between materials. Figure 10 compares performance ofPVB, DML, and PPVC on simulated data. PVB produces many fewer misclassified voxels, particularly in regions where materials are mixed because of partial-volume effects. In Figs 10b and 10d the difference is particularly noticeable where an incorrect layer of dark background material has been introduced between the two lighter regions, and where jagged boundaries occur between each pair of materials. In both cases this is caused by partial-volume effects, where multiple materials are present in the same voxel.

Table 1 shows comparative RMS error results for the PPVC, Eigen, and PVB simulated data results, and also compares PPVC with the Mixel algorithm. Signal-to-noise ratio (SNR) for the data used in PPVC/Eigen/PVB comparison was 14.2. SNR for the data used in PPVC/Mixel comparison was 21.6. Despite lower SNR, PPVC/PVB RMS error improvement is approximately double that of the PPVC/Mixel improvement. RMS error is defined as n \jE(a(x) -p(x))2'

where a(x) is classified data and p(x) is ground truth. The sum is made only over voxels that contain multiple materials. n is the number of voxels summed.

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