BIOMEDICAL IMAGING GROUP (BIG)
Laboratoire d'imagerie biomédicale (LIB)

Ten Good Reasons for Using Splines for Signal/Image Processing

M. Unser

Invited talk, Journée "Approximation et Modélisation Géométrique" (SMAI-AFA'08), Paris, French Republic, March 14, 2008.

We argue that cardinal splines constitute an ideal framework for performing signal/image processing—the underlying philosophy being “thing analog, act digital”. We show that multidimensional spline interpolation or approximation can be performed most efficiently using recursive digital filtering techniques. We highlight a number of “optimal” aspects of splines (in particular, polynomial ones) and discuss fundamental relations with: (1) Shannon's sampling theory, (2) linear system theory, (3) wavelet theory, (4) regularization theory, (5) estimation theory, and (6) stochastic processes (in particular, fractals). The practicality of the spline framework is illustrated with concrete image processing examples; these include derivative-based feature extraction, high-quality rotation and scaling, and (rigid body or elastic) image registration.

Slides of the presentation (PDF, 12.9 Mb) 

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