Local Filters of B-spline Wavelets

Haar wavelets have been widely used in Biometrics. One advantage of Haar wavelets is the simplicity and the local- ity of their decomposition and reconstruction filters. How- ever, Haar wavelets are not satisfactory for some applica- tions due to their non-continuous behaviour. Having a par- ticular level of smoothness is important for many applica- tions. B-spline wavelets are capable of being applied to sig- nals and functions of any smoothness. However, the con- ventional B-spline wavelets results "non-local" decomposi- tion filters and consequently, they are not efficient as are the Haar wavelets. We present our recently developed local filters of B- spline wavelets. Here, we focus on quadratic case that guar- antees 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.