Interpolation revisited [medical images application]
Based on the theory of approximation, this paper presents a unified analysis of interpolation and resampling techniques. An important issue is the choice of adequate basis functions. The authors show that, contrary to the common belief, those that perform best are not interpolating. By opposition to traditional interpolation, the authors call their use generalized interpolation; they involve a prefiltering step when correctly applied. The authors explain why the approximation order inherent in any basis function is important to limit interpolation artifacts. The decomposition theorem states that any basis function endowed with approximation order ran be expressed as the convolution of a B spline of the same order with another function that has none. This motivates the use of splines and spline-based functions as a tunable way to keep artifacts in check without any significant cost penalty. The authors discuss implementation and performance issues, and they provide experimental evidence to support their claims.