Pseudo-linear scale-space theory

It has been observed that linear, Gaussian scale-space, and nonlinear, morp hological erosion and dilation scale-spaces generated by a quadratic struct uring function have a lot in common. Indeed, far-reaching analogies have be en reported, which seems to suggest the existence of an underlying isomorph ism. However, an actual mapping appears to be missing. In the present work a one-parameter isomorphism is constructed in closed-fo rm, which encompasses linear and both types of morphological scale-spaces a s (non-uniform) limiting cases. The unfolding of the one-parameter family p rovides a means to transfer known results from one domain to the other. Mor eover, for any fixed and non-degenerate parameter value one obtains a novel type of "pseudo-linear" multiscale representation that is, in a precise wa y, "in-between" the familiar ones. This is of interest in its own right, as it enables one to balance pros and cons of linear versus morphological sca le-space representations in any particular situation.