Parametric Visualization

Parametric visualization addresses an emerging trend arising from the analysis of images to characterize functional information present in the images. Traditionally, parameters that describe certain functional information are computed and stored as numeric images that can be displayed like any other image. However, it may require large amount of storage space and processing time to handle such numeric images because they are usually represented as floating-point numbers and vector quantities. To simplify the representation of such information, parametric fields are used to provide an underlying (usually smooth) model that can be evaluated at any image location using its analytical formulation [43].

One of the major advantages of a parametric field is that it can efficiently make use of graphics architectures to provide the visualization of the data, eliminating the precomputation time and the need for high-resolution storage for visualization. Furthermore, successive derivative parametric images, such as velocity or acceleration maps from the motion fields, can be displayed in real time.

The example presented here is a 4D B-spline based motion field representation of cardiac-tagged MR images (Fig. 22). A motion field with 7x7x7x15 control points has been shown to adequately describe the full motion of the heart during cardiac cycle. Using this field, material points can be tracked over time and local mechanical properties (e.g., strain) can be computed. The visualization method presented here utilizes the similarity between the B-spline representation of the motion fields and the graphics hardware support for nonuniform rational B-spline (NURBS) display with texture mapping to achieve high-performance visualization of these parametric fields.

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