Harmonic measures, Hausdorff measures and positive eigenfunctions

On Hausdorff Distance Measures

A number of Hausdorff-based algorithms have been proposed for finding objects in images. We evaluate different measures and argue that the Hausdorff Average distance measure outperforms other variants for model detection. This method has improved robustness properties with respect to noise. We discuss the algorithms with respect to typical classes of noise, and we illustrate their relative perf...

On Hausdorff Measures and Sbr Measures for Parabolic Rational Maps

Quasiconformal Distortion of Hausdorff Measures

In this paper we prove that if φ : C → C is a K-quasiconformal map, 0 < t < 2, and E ⊂ C is a compact set contained in a ball B, then H(E) diam(B) ≤ C(K) ( H ′ (φ(E)) diam(φ(B))t′ ) t tK

Measure Theory on Hausdorff Measures

Let y = h(x) be defined for 0 < x < oo and assume values in 0 ^ y ^ + co. Let S be any linear set of points and p an arbitrary positive number. Cover S by a countable number of open intervals h , I2, • • • of lengths xx, x2 , • • • each of which is less than p, and denote by mp(S; h) the lower bound of h(xi) + h(x2) + • • • for all such coverings of S. Then m(S; h) = limp|0mp(/S; h) is called t...

An Introduction to Fractals and Hausdorff Measures

It is possible for one to define fractals as those sets which have non-integral Hausdorff Dimension. This paper defines Hausdorff Dimension and rigorously introduces the necessary theory to prove that one such set is indeed a fractal. The first chapter includes a proof of Banach’s Fixed Point Theorem. The Hausdorff Metric is defined and it is mentioned how one produces ‘generators’ for creating...