The algorithm described in this chapter for classifying scalar-and vector-valued volume data produces more accurate results than existing techniques in many cases, particularly at boundaries between materials. The improvements arise because (1) a continuous function is reconstructed from the samples, (2) histograms taken over voxel-sized regions are used to represent the contents of the voxels, (3) subvoxel partial-volume effects caused by the band-limiting nature of the acquisition process are incorporated into the model, and (4) a Bayesian classification approach is used. The technique correctly classifies many voxels containing multiple materials in the examples of both simulated and real data. It also enables the creation of more accurate geometric models and images. Because the technique correctly classifies voxels containing multiple materials, it works well on low-resolution data, where such voxels are more prevalent. The examples also illustrate that it works well on noisy data (SNR <15).

The construction of a continuous function is based on the sampling theorem, and although it does not introduce new information, it provides classification algorithms with a richer context for the information. It incorporates neighbor information into the classification process for a voxel in a natural and mathematically rigorous way and thereby greatly increases classification accuracy. In addition, because the operations that can be safely performed directly on sampled data are so limited, treating the data as a continuous function helps to avoid introducing artifacts.

Histograms are a natural choice for representing voxel contents for a number of reasons. First, they generalize single measurements to measurements over a region, allowing classification concepts that apply to single measurements to be generalized. Second, the histograms can be calculated easily. Third, the histograms capture information about neighboring voxels; this increases the information content over single measurements and improves classification results. Fourth, histograms are orientation independent; orientation independence reduces the number of parameters in the classification process, hence simplifying and accelerating it.

Partial-volume effects are a nemesis of classification algorithms, which traditionally have drawn from techniques that classify isolated measurements. These techniques do not take into account the related nature of spatially correlated measure ments. Many attempts have been made to model partial-volume effects, and this work continues that trend, with results that suggest that continued study is warranted.

The Bayesian approach described is a useful formalism for capturing the assumptions and information gleaned from the continuous representation of the sample values, the histograms calculated from them, and the partial-volume effects of imaging. Together, these allow a generalization of many sample-based classification techniques.

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