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and software for manipulation of image data.

The major difficulty in interpreting cross-sectional gray-scale images is that anatomic structures look very different from their three-dimensional appearance. This discrepancy requires the physician to perform a significant mental translation of the data, a task that requires highly specialized training. Although radiologists undergo such training, the visual interpretation of the data sets becomes observer dependent, and others may have more difficulty in visualizing the data. In view of the relatively large size of a typical three-dimensional data set (e.g., 80 x 256 x 256) and the fact that a single imaging examination may include the acquisition of several such data sets, the radiologist can work more efficiently if the information from many slices is concentrated into one rendering. A composite image also facilitates communication with other clinicians and leads to the possibility of generating quantitative rather than qualitative information from the images.

These observations make it clear that for medical image analysis, the fundamental mathematical need is the derivation of procedures for extracting the clinically important features from one or more large data sets—for example, quantitative information on tumor volume for each of several studies over a time period, to help gauge the efficacy of different treatments, or a parametric map created to represent rate constants from a time series of tracer movements in the brain or heart. The procedures associated with this type of contemporary image analysis can be separated into several different classes:

·      Image segmentation,

·      Computational anatomy,

·      Registration of multimodality images,

·      Synthesis of parametric images,

·      Data visualization, and

·      Treatment planning.

The following discussion presents some of the key mathematical methods being considered for addressing these requirements. See also the related discussions earlier in this report in sections 3.5, 4.3, and 7.2.3.

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