On the duality of scalar and density flows

An image is captured as a coherent set of local integrations of a source field under an aperture function. This formulation is explicit in, for example, well-known scale-space theory. The source may be subjected to a flow changing the image over time. Depending on the physical model, the source may change as a density (preserving local mass) or as a scalar (preserving local intensity value). In this paper, we derive the dual transformation of the apertures. The apertures must transform in the dual way to create invariance. This has implications for any algorithm estimating flow from image sequences as it is based on the computational invariants.