Multiscale Analysis of Geometric Planar Deformations: Application to Wild Animal Electronic Tracking and Satellite Ocean Observation Data

The development of animal tracking technologies (including GPS and ARGOS satellite systems) and the increasing resolution of remote-sensing observations call for tools extracting and describing the geometric patterns along a track or within an image over a wide range of spatial scales. Whereas shape analysis has largely been addressed over the last decades, the multiscale analysis of the geometry of opened planar curves has received little attention. We here show that classical multiscale techniques cannot properly address this issue and propose an original wavelet-based scheme. To highlight the generic nature of our multiscale wavelet technique, we report applications to two different observation data sets, namely, wild animal movement paths recorded by electronic tags and satellite observations of sea-surface geophysical fields.