A method is presented for the interpolation of optimally 'smooth' background correction matrices within arbitrarily shaped boundaries. Practical means of implementing this technique are discussed, along with series expansions for the special cases of square and round boundaries. This class of interpolation methods has the advantages over previous techniques of providing a unique mathematical solution, connecting exactly to count rates on the boundary, and containing no singularities. Clinical scintigraphic images and mathematically generated surfaces are used to test the different cases of the method, and it is shown that confining the boundary to a circle produces the most rapid convergence with the minimum deviation from ideal surfaces. Under common clinical conditions, these techniques lend themselves well to automated, non-interventional computer processing.

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