It follows from this definition that interpolation, in some form or another, is needed each time the data to process is known only by discrete samples, which is almost universally the case in the computer era. This ubiquitous applicability is also the rule in biomedical applications. In this chapter, we restrict the discussion to the case where the discrete data are regularly sampled on a Cartesian grid. We also restrict the discussion to exact interpolation, where the continuous model is required to take the same values as the sampled data at the grid locations. Finally, we restrict ourselves to linear methods, such that the sum of two interpolated functions is equal to the interpolation of the sum of the two functions. For this reason, we will only mention Kriging [2,3] and shape-based interpolation [4,5] as examples of non-linear interpolation, and quasi-interpolation [6] as an example of inexact interpolation, without discussing them further. In spite of these restrictions, the range of applicability of the interpolation methods discussed here remains large, especially in biomedical imagery, where it is very common to deal with regularly sampled data.

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