Local Filters of B-spline Wavelets

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the locality of their decomposition and reconstruction filters. However, Haar wavelets are not satisfactory for some applications due to their non-continuous behaviour. Having a particular level of smoothness is important for many applications. B-spline wavelets are capable of being applied to signals and functions of any smoothness. However, the conventional B-spline wavelets results ”non-local” decomposition filters and consequently, they are not efficient as are the Haar wavelets. We present our recently developed local filters of Bspline wavelets. Here, we focus on quadratic case that guarantees once-differentiable smoothness. Practical issues for the efficient implementation are discussed. We show that how the resulting filters can be applied to curves, images and surfaces.