SSVM07 Spatio-Temporal Scale-Spaces

This document discusses spatio-temporal scale-spaces and their properties. It proposes a definition of a time causal Galilean scale-space based on evolution equations on space and memory rather than space and time. The key points are: 1) A time causal Galilean scale-space is defined as a covariant point measurement space in space-time that is a Lie wedge in memory. 2) This scale-space is generated by an evolution equation involving spatial derivatives, temporal derivatives in memory, and a velocity term. 3) The unique equation in this family with local generators is the heat equation on the half-space of memory, which provides a causal solution.