Search results for "Hausdorff distance"
showing 10 items of 37 documents
3d mesh denoising using normal based myriad filter
2011
We propose a new filtering scheme for denoising of 3D objects which are represented by a triangular mesh. This scheme consists on applying myriad filter to face normals and then updating the vertices positions in order to preserve the original shape of the object. The choice of the Myriad is justified by the assumption of Cauchy distributed angles between surface normals. This filter improves the performance of a normal-based method which is adapted to the underlying mesh structure. To evaluate these methods of filtering, we use three error metrics. The first is based on the vertices, the second is based on the normals and the third is based on Hausdorff distance. Experimental results demon…
Comments on the paper "COINCIDENCE THEOREMS FOR SOME MULTIVALUED MAPPINGS" by B. E. RHOADES, S. L. SINGH AND CHITRA KULSHRESTHA
2011
The aim of this note is to point out an error in the proof of Theorem 1 in the paper entitled “Coincidence theorems for some multivalued mappings” by B. E. Rhoades, S. L. Singh and Chitra Kulshrestha [Internat. J. Math. & Math. Sci., 7 (1984), 429-434], and to indicate a way to repair it.
The “λ-medial axis”
2005
Medial axis is known to be unstable for nonsmooth objects. For an open set O, we define the weak feature size, wfs, minimum distance between Oc and the critical points of the function distance to Oc. We introduce the "lambda-medial axis" Mλ of O, a subset of the medial axis of O which captures the homotopy type of O when λ < wfs. We show that, at least for some "regular" values of λ, Mλ remains stable under Hausdorff distance perturbations of Oc.
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…
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…
Menger curvature and rectifiability in metric spaces
2008
We show that for any metric space $X$ the condition \[ \int_X\int_X\int_X c(z_1,z_2,z_3)^2\, d\Hm z_1\, d\Hm z_2\, d\Hm z_3 < \infty, \] where $c(z_1,z_2,z_3)$ is the Menger curvature of the triple $(z_1,z_2,z_3)$, guarantees that $X$ is rectifiable.
Planar Sobolev homeomorphisms and Hausdorff dimension distortion
2011
We investigate how planar Sobolev-Orlicz homeomorphisms map sets of Hausdorff dimension less than two. With the correct gauge functions the generalized Hausdorff measures of the image sets are shown to be zero.
A Non-linear Diffeomorphic Framework for Prostate Multimodal Registration
2011
International audience; This paper presents a novel method for non-rigid registration of prostate multimodal images based on a nonlinear framework. The parametric estimation of the non-linear diffeomorphism between the 2D fixed and moving images has its basis in solving a set of non-linear equations of thin-plate splines. The regularized bending energy of the thin-plate splines along with the localization error of established correspondences is jointly minimized with the fixed and transformed image difference; where, the transformed image is represented by the set of non-linear equations defined over the moving image. The traditional thin-plate splines with established correspondences may p…