Towards a Morphological Scale-Space Theory

In this paper it is shown that erosions and dilations using increasingly larger quadratic structuring functions can be used to construct a morphological scale-space which is incrementally computable (the image at scale ρ can be calculated from the image at scale μ for μ ≤ ρ and the (weak) solution of a differential equation. Furthermore it is argued that the morphological scale-space preserves causality in the resolution domain, in the sense that no spatial details are introduced by moving towards larger scales. This is illustrated with an example showing the singularity trace through scale-space.