The sigma-Hull - The Hull Where Fractals Live Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits
Abstract
Global IFS seem to be suited best for compressed encoding of natural objects which are in most cases self affine even if not always exactly. Since affine transformations, the IFS-Codes, resp. the union of all their orbits generate an object (an IFS-Attractor), the detection of a non minimal set of these orbits solves the inverse IFS-Problem by calculating a superset of IFS-Codes, which has to be minimized. Here a method is presusted how these orbits (in particular those on the object boundary) can be calculated. Therefore a generalized convex hull; the sigma-Hull; is defined. This fractal hull is bounded by log spirals, that curves formed by the orbits. It is shown that log spirals can be represented by a continous function of powers of affine maps and that by using this "spiral equivalent" the generating transformations of the orbits by which an IFS-object is bound, can be calculated in the x/y-plane. Further more this representation can be used for the classification of the detected orbits, necessary to calculate the IFS-Codes of a minimal IFS from their generating transformations, subsequently.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 2000
- Accession Number
- ADP010911
Entities
People
- Erwin Hocevar
Organizations
- TU Wien