Abstract

In the three-dimensional (3-D) image display, we often need, fixed of all, to obtain data on the 3-D rectangular grid points from the acquisited raw data, usually through some kind of interpolation, since a cut view on an arbitrary plane is needed in many cases and a plane in the 3-D space is most simply expressed in terms of the rectangular coordinates. If we use a constant sampling rate in the data acquisition, then the sampled data points are located on either concentric cylindrical surfaces or concentrical spherical surfaces, depending on the scanning method used. Therefore, first of all, the coordinate transformation from the cylindrical or spherical system to the rectangular system must be performed, which is rather time-consuming and prone to interpolation error. This coordinate transformation can be completely eliminated if we use a variable sampling frequency from the beginning. Then, pixel values on all 3-D rectangular grid points can be calculated by a few times linear interpolation.

Full Text
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