Modern Geometry of Image Formation

Image formation is quantised by imposing an image induced connection and computing the associated torsion and curvature in terms of diierential or integral invariants. Imposing invariance of the image formation under the classical group of movements slot-machines reading out the torsion and the curvature are shown to locate endpoints and other type of interesting topological objects. Requiring instead invari-ance under the group of anamorphoses and the group of diieomorphisms of the image only ridges and ruts can be identiied through a non-local topological or integral geometric operation.