Loglets: Generalized quadrature and phase for local spatio-temporal structure estimation

Abstract

The question of which properties of a local structure estimator are important is discussed. Answers are provided via the introduction of a number of fundamental invariances. Mathematical formulations corresponding to the required invariances leads up to the introduction of a new class of filter sets termed loglets. Using loglets it is shown how the concepts of quadrature and phase can be defined in n-dimensions. A number of experiments support the claim that loglets are preferable to other designs. In particular it is demonstrated that the loglet approach outperforms a Gaussian derivative approach in resolution and robustness to variations in object illumination. It is also shown how a measure of the certainty of the estimate can be obtained using the consistency of the generalized phase with respect to orientation. © Springer-Verlag 2003.