Quadtrees and the Hausdorff dimension of pictures. (English) Zbl 0679.68169

Staiger, Ludwig

Geometrical problems of image processing, Proc. 4th Workshop, Geobild, Georgenthal/GDR 1989, Math. Res. 51, 173-178 (1989).

[For the entire collection see Zbl 0669.00014.]
Let Q be a set consisting of 4 elements and let \(X^{\omega}\) be the set of all sequences of elements of Q. The author reduced the calculation of the Hausdorff dimension \(\alpha_ P\) of a picture \(P\subset [0,1]\times [0,1]\subset E^ 2\) to the estimation of the Hausdorff dimension of a closed subset of \(X^{\omega}\) and then to the estimation of the maximum eigenvalue of a non-negative matrix A having integer entries. He discusses also whether the corresponding \(\alpha_ P\)-dimensional measure is finite or infinite.

Reviewer: M.Jůza

MSC:

68T10	Pattern recognition, speech recognition
28A75	Length, area, volume, other geometric measure theory
68P05	Data structures

Keywords:

quadtrees; Hausdorff dimension of pictures

Citations:

Zbl 0669.00014