Morphological wavelets and the complexity of dyadic trees

In this paper we reveal a connection between the coefficients of the morphological wavelet transform and complexity measures of dyadic tree representations of level sets. This leads to better understanding of the edge preserving property that has been discovered in both areas. As an immediate application, we examine a depth-adaptive soft thresholding scheme on morphological wavelet coefficients in which the threshold decays geometrically as the resolution increases. A greater decay rate gives greater preference towards unbalanced trees and this can control edge enhancement in denoised signals.