Results 11 to 20 of about 2,931,499 (197)
Dimension and measure theory of self-similar structures with no separation condition [PDF]
, 2015 We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any separation condition.
Farkas, Ábel
core +2 more sources
European Radiology Experimental, 2021 Average Hausdorff distance is a widely used performance measure to calculate the distance between two point sets. In medical image segmentation, it is used to compare ground truth images with segmentations allowing their ranking.
Orhun Utku Aydin +7 more
doaj +1 more source
Directed graph iterated function systems [PDF]
, 2011 This thesis concerns an active research area within fractal geometry. In the first part, in Chapters 2 and 3, for directed graph iterated function systems (IFSs) defined on ℝ, we prove that a class of 2-vertex directed graph IFSs have attractors that ...
Boore, Graeme C.
core +2 more sources
ON THE MUTUAL MULTIFRACTAL ANALYSIS FOR SOME NON-REGULAR MORAN MEASURES
Проблемы анализа, 2023 In this paper, we study the mutual multifractal Hausdorff dimension and the packing dimension of level sets 𝐾(𝛼, 𝛽) for some non-regular Moran measures satisfying the so-called Strong Separation Condition.We obtain sufficient conditions for the valid ...
B. Selmi, N. Yu. Svetova
doaj +1 more source
Hausdorff-Distance Enhanced Matching of Scale Invariant Feature Transform Descriptors in Context of Image Querying [PDF]
, 2012 Reliable and effective matching of visual descriptors is a key step for many vision applications, e.g. image retrieval. In this paper, we propose to integrate the Hausdorff distance matching together with our pairing algorithm, in order to obtain a ...
D. Wilson +3 more
core +1 more source
The geometry of self-affine fractals [PDF]
, 2008 In this thesis we study the dimension theory of self-affine sets. We begin by introducing a number of notions from fractal geometry, in particular, dimensions, measure properties and iterated functions systems.
Miao, Jun Jie
core +2 more sources
On Focal Borel Probability Measures
Mathematics, 2022 The novel concept of focality is introduced for Borel probability measures on compact Hausdorff topological spaces. We characterize focal Borel probability measures as those Borel probability measures that are strictly positive on every nonempty open ...
Francisco Javier García-Pacheco +2 more
doaj +1 more source
An evaluation of performance measures for arterial brain vessel segmentation
BMC Medical Imaging, 2021 Background Arterial brain vessel segmentation allows utilising clinically relevant information contained within the cerebral vascular tree. Currently, however, no standardised performance measure is available to evaluate the quality of cerebral vessel ...
Orhun Utku Aydin +7 more
doaj +1 more source
Codimension formulae for the intersection of fractal subsets of Cantor spaces [PDF]
, 2015 We examine the dimensions of the intersection of a subset E of an m-ary Cantor space Cm with the image of a subset F under a random isometry with respect to a natural metric.
Falconer, Kenneth John, Donoven, Casey
core +1 more source
Hölder differentiability of self-conformal devil's staircases [PDF]
, 2014 In this paper we consider the probability distribution function of a Gibbs measure supported on a self-conformal set given by an iterated function system (devil's staircase) applied to a compact subset of ℝ. We use thermodynamic multifractal formalism to
Troscheit, S., Sascha Troscheit
core +1 more source