A wavelet based algorithm for pattern analysis

Patterns with a local roll structure arise in many diverse physical systems which have little in common at the microscopic level. In this paper we construct an algorithm based on the wavelet transform that can be used as a diagnostic tool to extract from such patterns macroscopic information like the local director field, the local amplitude away from defects, and slowly varying fields, such as mean drift, which may be soft modes of pattern. It allows a precise detection of phase grain boundaries and point defects. Several tests are conducted on numerically generated signals to demonstrate the applicability and precision of the algorithm. Finally, the algorithm is applied to actual experimental convection patterns, allowing us to draw several conclusions about the nature of the wave director field in such patterns.