To render images from a three-dimensional array of sample values, it is necessary to interpolate between the samples. This paper is concerned with interpolation methods that are equivalent to convolving the samples with a reconstruction filter; this covers all commonly used schemes, including trilinear and cubic interpolation.We first outline the formal basis of interpolation in three-dimensional signal processing theory. We then propose numerical metrics that can be used to measure filter characteristics that are relevant to the appearance of images generated using that filter. We apply those metrics to several previously used filters and relate the results to isosurface images of the intrpolations. We show that the choice of interpolation scheme can have a dramatic effect on image quality, and we discuss the cost/benefit tradeoff inherent in choosing a filter.
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