Deep Structure from a Geometric Point of View

The geometry of “empty” scale space is investigated. By virtue of the proposed geometric axioms the generating PDE, the linear isotropic heat equation, can be presented in covariant, or geometrical form. The postulate of a metric for scale space cannot be upheld, as it is incompatible with the generating equation. Two familiar instances of scale spaces consistent with the geometric axioms are considered by way of example, viz. classical, homogeneous scale space, and foveal scale space.

• Type: Conference
• Year: 2005
• Where: DSSCV
• Authors: Luc Florack
• Keywords: Computer Vision, DSSCV 2005, Geometric Axioms, Homogeneous Scale Space, Scale Space