Pseudo-Linear Scale-Space Theory Towards the Integration of Linear and Morphological Scale-Space Paradigms

It has been observed that linear, Gaussian scale-space, and nonlinear, morphological erosion and dilation scale-spaces generated by a quadratic structuring function have a lot in common. Indeed, far-reaching analogies have been reported, which seems to suggest the existence of an underlying isomorphism. However, an actual mapping appears to be missing. In the present work a one-parameter isomorphism is constructed in closed-form, which encompasses linear and both types of morphological scale-spaces as (non-uniform) limiting cases. Apart from establishing such a formal connection, the unfolding of the family provides a means to transfer known results from one domain to the other. Moreover, for any fixed and non-degenerate parameter value one obtains a novel type of “pseudo-linear” multiscale representation that is, in a precise way, “in-between” the familiar ones, and may be of interest in its own right.