A Weighted Sum of Multi-scale Gaussians Generates New Near-ideal Interpolation Functions

Interpolation is a very important technique in medical image processing. Of the different generations of interpolation kernels, the one using combinations of Gaussians and its partial derivatives, is locally compact, has excellent Fourier properties and is easy to handle analytically. But the de-constancy behaviour i.e. the sum of the samples of these Gaussian kernels is not necessarily one and also the zero-crossings do not fit exactly. These deviations from the ideal behaviour contribute to artifacts during interpolation. We propose in this article a novel approach for the generation of kernels from the combinations of Gaussians at different scales. We will show that these kernels are locally compact, have excellent Fourier properties and the zero-crossings fit exactly. The DC-constancy behaviour is better than those reported. It has been shown that the proposed kernels are likely to be very useful in medical images