Study of Lipschitz regularity - Feature extraction on regular and irregular grids

In this paper we study the pointwise Lipschitz regularity, covering several aspects: theoretical and practical, methods for its estimation on regular and irregular grids. The relevance of this value of regularity lies in its invariance properties to several transformations, and its fast computation thanks to wavelets. We study the influence of scale on wavelets transforms and show invariance properties this value of regularity. We also put forward an original technique for its estimation on regular grids. We also address the issue of irregular grids, based on the behavior of smoothing kernels with respect to scale. The obtained results emphasize the usefulness of such features for the applications, and motivate further work on this topic. Keywords: Lipschitz regularity, wavelets, smoothing kernels, robust feature extraction, regular and irregular gridsJRC.G.2-Global security and crisis managemen