Search results for "Hausdorff"

Nonsymmetric conical upper density and $k$-porosity

2017

We study how the Hausdorff measure is distributed in nonsymmetric narrow cones in R n \mathbb {R}^n . As an application, we find an upper bound close to n − k n-k for the Hausdorff dimension of sets with large k k -porosity. With k k -porous sets we mean sets which have holes in k k different directions on every small scale.

Dimension of self-affine sets for fixed translation vectors

2016

An affine iterated function system is a finite collection of affine invertible contractions and the invariant set associated to the mappings is called self-affine. In 1988, Falconer proved that, for given matrices, the Hausdorff dimension of the self-affine set is the affinity dimension for Lebesgue almost every translation vectors. Similar statement was proven by Jordan, Pollicott, and Simon in 2007 for the dimension of self-affine measures. In this article, we have an orthogonal approach. We introduce a class of self-affine systems in which, given translation vectors, we get the same results for Lebesgue almost all matrices. The proofs rely on Ledrappier-Young theory that was recently ver…

Which measures are projections of purely unrectifiable one-dimensional Hausdorff measures

2008

We give a necessary and sufficient condition for a measure p, on the real line to be an orthogonal projection of XAl for some purely 1-unrectifiable planar set A.

Homogeneous Suslinian Continua

2011

AbstractA continuumis said to be Suslinian if it does not contain uncountably many mutually exclusive non-degenerate subcontinua. Fitzpatrick and Lelek have shown that a metric Suslinian continuum X has the property that the set of points at which X is connected im kleinen is dense in X. We extend their result to Hausdorff Suslinian continua and obtain a number of corollaries. In particular, we prove that a homogeneous, non-degenerate, Suslinian continuum is a simple closed curve and that each separable, non-degenerate, homogenous, Suslinian continuum is metrizable.

MR2896126 Selmanogullari, T.; Savas, E.; Rhoades, B. E. On $q$-Hausdorff matrices. Taiwanese J. Math. 15 (2011), no. 6, 2429--2437

2011

The Henstock-Kurzweil-Stieltjes type integral for real functions on a fractal subset of the real line

2011

The aim of this paper is to introduce an Henstock-Kurzweil type integration process for real functions on a fractal subset E of the real line.

An enhanced random walk algorithm for delineation of head and neck cancers in PET studies

2017

An algorithm for delineating complex head and neck cancers in positron emission tomography (PET) images is presented in this article. An enhanced random walk (RW) algorithm with automatic seed detection is proposed and used to make the segmentation process feasible in the event of inhomogeneous lesions with bifurcations. In addition, an adaptive probability threshold and a k-means based clustering technique have been integrated in the proposed enhanced RW algorithm. The new threshold is capable of following the intensity changes between adjacent slices along the whole cancer volume, leading to an operator-independent algorithm. Validation experiments were first conducted on phantom studies:…

A Coupled Schema of Probabilistic Atlas and Statistical Shape and Appearance Model for 3D Prostate Segmentation in MR Images

2012

International audience; A hybrid framework of probabilistic atlas and statistical shape and appearance model (SSAM) is proposed to achieve 3D prostate segmentation. An initial 3D segmentation of the prostate is obtained by registering the probabilistic atlas to the test dataset with deformable Demons registration. The initial results obtained are used to initialize multiple SSAMs corresponding to the apex, central and base regions of the prostate gland to incorporate local variabilities. Multiple mean parametric models of shape and appearance are derived from principal component analysis of prior shape and intensity information of the prostate from the training data. The parameters are then…

A new weighted normal-based filter for 3D mesh denoising

2018

In this paper, we propose a normal based filtering method for 3D mesh denoising. For this purpose, we compute the new triangle normal vectors by using a weighted sum of the average (smoothness) and the myriad (sharpness) filters in each neighborhood. These weights, that reflect the degree of the surface sharpness, are calculated according to the statistical distribution of the angles between the normal vectors of the triangles. The histogram of the angles between surface normal vectors is accurately fitted by the well known Cauchy distribution. Here, we justify the use of the myriad filter whose estimated value represents the optimum of the location parameter of the investigated distributio…

Applications de type Lasota–Yorke à trou : mesure de probabilité conditionellement invariante et mesure de probabilité invariante sur l'ensemble des …

2003

Abstract Let T :I→I be a Lasota–Yorke map on the interval I, let Y be a nontrivial sub-interval of I and g 0 :I→ R + , be a strictly positive potential which belongs to BV and admits a conformal measure m. We give constructive conditions on Y ensuring the existence of absolutely continuous (w.r.t. m) conditionally invariant probability measures to nonabsorption in Y. These conditions imply also existence of an invariant probability measure on the set X∞ of points which never fall into Y. Our conditions allow rather “large” holes.