Image Processing II: B-spline Properties and Gradient Operators

This lecture covers the properties of B-splines, including symmetry, nonnegativity, compact support, and explicit differentiation formulas. It also discusses efficient B-spline interpolation, transfer functions, and poles of direct B-spline filters. The lecture further explores the limiting behavior of splines, spline interpolators, and the spline-based gradient operator. Additionally, it delves into the variational properties of splines, their unification of multiple perspectives, and the spline-based gradient operator for computing the gradient of a function. The lecture concludes with a discussion on differentiation filters, cubic-spline image differentials, and the advantages of using B-splines in image processing.