Fast Detection and Refined Scale Estimation Using Complex Isotropic Wavelets

The dyadic scaling in the discrete wavelet transform can lead to a loss of precision, in comparison to the computationally unrealistic continuous wavelet transform. To overcome this obstacle, we propose a novel method to locally scale wavelets between dyadic scales in an efficient way. We compute complex wavelet coefficients for a tight frame with a dyadic scale progression. Our isotropic complex wavelets are designed such that the deviation from the nominal scale is encoded in the phase of the coefficients. Moreover, the magnitude of the coefficients is used for feature detection. Numerical experiments are presented to justify our method, and we present results for feature extraction from real data.