A Generic Framework for Image Geometry
Jan J. Koenderink · Birkhäuser Boston eBooks · 2002
In image processing it is common practice to find Euclidean differential invariants of the “image surface” in “image space” (that is the picture plane times intensity space). Many well-known algorithms are based on this usage. Yet this makes no sense since these invariants are with respect to Euclidean isometries, e.g., rotations. But clearly you can’t rotate the image surface to see its other side, or the intensity to a spatial direction. Thus the angle measure cannot be periodic in planes other than the picture plane. One needs to set up the proper transformation group to arrive at a set of invariants that makes sense. This yields a novel, generic geometrical framework for image processing. Most of the well-known global image transformations are movements, similarities or conformal transformations in this geometry. The differential geometry yields novel definitions for many features such as ruts and ridges. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.