Optimizing parametric deformable kernels: space-variant filtering and scaling-rotation invariance

We propose an efficient method for designing filters adjustable in phase, orientation, scale and bandwidth. In contrast with current design methods, (1) our filters are quadrature-pair (complex), which allows us to estimate the modulus and phase of their responses; and (2) we do not fix the function of the kernel, but determine it by imposing its bandwidth and minimizing the squared error associated with the representation using N generic parametric basis functions. We show that this technique improves the fidelity of the resulting filters (or, alternatively, reduces the number of required convolutions for a given error tolerance) with respect to using non-optimized filters. We apply it to space-variant filtering, scaling-rotation invariant pattern detection and scale-rotation estimation