Search results for "Hausdorff"
showing 10 items of 162 documents
A 3D deep learning approach based on Shape Prior for automatic segmentation of myocardial diseases
2020
Accurate three-dimensional (3D) cardiac segmentation from late gadolinium enhancement (LGE)-MRI plays a critical role in designing a structure of reference for diagnosing many cardiac pathologies such as ischemia, myocarditis and myocardial infarction. This segmentation is however still a non-trivial task, due to the motion artifacts during acquisition, and heterogeneous intensity distributions. In this study, we develop a fully 3D automated model based on deep neural networks (DNN) for LGE-MRI myocardial pathologies (scar and No-reflow tissues) segmentation in a new expert annotated dataset. Considering that damaged tissue constitutes a small area of the whole LGE-MRI, we concentrated on m…
Structure of equilibrium states on self-affine sets and strict monotonicity of affinity dimension
2017
A fundamental problem in the dimension theory of self-affine sets is the construction of high- dimensional measures which yield sharp lower bounds for the Hausdorff dimension of the set. A natural strategy for the construction of such high-dimensional measures is to investigate measures of maximal Lyapunov dimension; these measures can be alternatively interpreted as equilibrium states of the singular value function introduced by Falconer. Whilst the existence of these equilibrium states has been well-known for some years their structure has remained elusive, particularly in dimensions higher than two. In this article we give a complete description of the equilibrium states of the singular …
A spline-based non-linear diffeomorphism for multimodal prostate registration.
2012
This paper presents a novel method for non-rigid registration of transrectal ultrasound and magnetic resonance prostate images based on a non-linear regularized framework of point correspondences obtained from a statistical measure of shape-contexts. The segmented prostate shapes are represented by shape-contexts and the Bhattacharyya distance between the shape representations is used to find the point correspondences between the 2D fixed and moving images. The registration method involves parametric estimation of the non-linear diffeomorphism between the multimodal images and has its basis in solving a set of non-linear equations of thin-plate splines. The solution is obtained as the least…
Automatic segmentation of the spine by means of a probabilistic atlas with a special focus on ribs suppression. Preliminary results
2015
Spine is a structure commonly involved in several prevalent diseases. In clinical diagnosis, therapy, and surgical intervention, the identification and segmentation of the vertebral bodies are crucial steps. However, automatic and detailed segmentation of vertebrae is a challenging task, especially due to the proximity of the vertebrae to the corresponding ribs and other structures such as blood vessels. In this study, to overcome these problems, a probabilistic atlas of the spine, including cervical, thoracic and lumbar vertebrae has been built to introduce anatomical knowledge in the segmentation process, aiming to deal with overlapping gray levels and the proximity to other structures. F…
Statistical Shape and Probability Prior Model for Automatic Prostate Segmentation
2011
International audience; Accurate prostate segmentation in Trans Rectal Ultra Sound (TRUS) images is an important step in different clinical applications. However, the development of computer aided automatic prostate segmentation in TRUS images is a challenging task due to low contrast, heterogeneous intensity distribution inside the prostate region, imaging artifacts like shadow, and speckle. Significant variations in prostate shape, size and contrast between the datasets pose further challenges to achieve an accurate segmentation. In this paper we propose to use graph cuts in a Bayesian framework for automatic initialization and propagate multiple mean parametric models derived from princi…
Estimation of the elastic parameters of human liver biomechanical models by means of medical images and evolutionary computation.
2013
This paper presents a method to computationally estimate the elastic parameters of two biomechanical models proposed for the human liver. The method is aimed at avoiding the invasive measurement of its mechanical response. The chosen models are a second order Mooney–Rivlin model and an Ogden model. A novel error function, the geometric similarity function (GSF), is formulated using similarity coefficients widely applied in the field of medical imaging (Jaccard coefficient and Hausdorff coefficient). This function is used to compare two 3D images. One of them corresponds to a reference deformation carried out over a finite element (FE) mesh of a human liver from a computer tomography image, …
A new definition of well-behaved discrimination functions
2009
Abstract A discrimination function shows the probability or degree with which stimuli are discriminated from each other when presented in pairs. In a previous publication [Kujala, J.V., & Dzhafarov, E.N. (2008). On minima of discrimination functions. Journal of Mathematical Psychology , 52 , 116–127] we introduced a condition under which the conformity of a discrimination function with the law of Regular Minimality (which says, essentially, that “being least discriminable from” is a symmetric relation) implies the constancy of the function’s minima (i.e., the same level of discriminability of every stimulus from the stimulus least discriminable from it). This condition, referred to as “well…
An upper gradient approach to weakly differentiable cochains
2012
Abstract The aim of the present paper is to define a notion of weakly differentiable cochain in the generality of metric measure spaces and to study basic properties of such cochains. Our cochains are (sub)additive functionals on a subspace of chains, and a suitable notion of chains in metric spaces is given by Ambrosio–Kirchheimʼs theory of metric currents. The notion of weak differentiability we introduce is in analogy with Heinonen–Koskelaʼs concept of upper gradients of functions. In one of the main results of our paper, we prove continuity estimates for cochains with p-integrable upper gradient in n-dimensional Lie groups endowed with a left-invariant Finsler metric. Our result general…
Area of intrinsic graphs and coarea formula in Carnot Groups
2020
AbstractWe consider submanifolds of sub-Riemannian Carnot groups with intrinsic $$C^1$$ C 1 regularity ($$C^1_H$$ C H 1 ). Our first main result is an area formula for $$C^1_H$$ C H 1 intrinsic graphs; as an application, we deduce density properties for Hausdorff measures on rectifiable sets. Our second main result is a coarea formula for slicing $$C^1_H$$ C H 1 submanifolds into level sets of a $$C^1_H$$ C H 1 function.
Convergence for varying measures in the topological case
2023
In this paper convergence theorems for sequences of scalar, vector and multivalued Pettis integrable functions on a topological measure space are proved for varying measures vaguely convergent.