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Title: A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images

Abstract

We introduce a novel implicit approach for single-object segmentation in 3D images. The boundary surface of this object is assumed to contain two known curves (the constraining curves), given by an expert. The aim of our method is to find the wanted surface by exploiting as much as possible the information given in the supplied curves and in the image. As for active surfaces, we use a cost potential that penalizes image regions of low interest (most likely areas of low gradient or too far from the surface to be extracted). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. We present a fast implementation that has been successfully applied to 3D medical and synthetic images.

Authors:
 [1];  [2];  [3]
  1. MEDISYS-Philips France, 51 rue Carnot, 92156 (France), E-mail: roberto.ardon@philips.com
  2. CEREMADE-Universite Paris Dauphine, Place du Marechal de Lattre de Tassigny, 75775 (France), E-mail: cohen@ceremade.dauphine.fr
  3. Georgia Institute of Technology (United States), E-mail: ayezzi@ece.gatech.edu
Publication Date:
OSTI Identifier:
21067412
Resource Type:
Journal Article
Resource Relation:
Journal Name: Applied Mathematics and Optimization; Journal Volume: 55; Journal Issue: 2; Other Information: DOI: 10.1007/s00245-006-0885-y; Copyright (c) 2007 Springer; www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; GRAPH THEORY; IMAGES; MATHEMATICAL SOLUTIONS; PARTIAL DIFFERENTIAL EQUATIONS; SURFACES; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Ardon, Roberto, Cohen, Laurent D., and Yezzi, Anthony. A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images. United States: N. p., 2007. Web. doi:10.1007/S00245-006-0885-Y.
Ardon, Roberto, Cohen, Laurent D., & Yezzi, Anthony. A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images. United States. doi:10.1007/S00245-006-0885-Y.
Ardon, Roberto, Cohen, Laurent D., and Yezzi, Anthony. Thu . "A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images". United States. doi:10.1007/S00245-006-0885-Y.
@article{osti_21067412,
title = {A New Implicit Method for Surface Segmentation by Minimal Paths in 3D Images},
author = {Ardon, Roberto and Cohen, Laurent D. and Yezzi, Anthony},
abstractNote = {We introduce a novel implicit approach for single-object segmentation in 3D images. The boundary surface of this object is assumed to contain two known curves (the constraining curves), given by an expert. The aim of our method is to find the wanted surface by exploiting as much as possible the information given in the supplied curves and in the image. As for active surfaces, we use a cost potential that penalizes image regions of low interest (most likely areas of low gradient or too far from the surface to be extracted). In order to avoid local minima, we introduce a new partial differential equation and use its solution for segmentation. We show that the zero level set of this solution contains the constraining curves as well as a set of paths joining them. We present a fast implementation that has been successfully applied to 3D medical and synthetic images.},
doi = {10.1007/S00245-006-0885-Y},
journal = {Applied Mathematics and Optimization},
number = 2,
volume = 55,
place = {United States},
year = {Thu Mar 15 00:00:00 EDT 2007},
month = {Thu Mar 15 00:00:00 EDT 2007}
}
  • No abstract prepared.
  • Although there are many algorithms available in the literature aimed at segmentation and model reconstruction of 3D angiographic images, many are focused on characterizing only a part of the vascular network. This study is motivated by the recent emerging prospects of whole-organ simulations in coronary hemodynamics, autoregulation and tissue oxygen delivery for which anatomically accurate vascular meshes of extended scale are highly desirable. The key requirements of a reconstruction technique for this purpose are automation of processing and sub-voxel accuracy. We have designed a vascular reconstruction algorithm which satisfies these two criteria. It combines automatic seeding and tracking of vesselsmore » with radius detection based on active contours. The method was first examined through a series of tests on synthetic data, for accuracy in reproduced topology and morphology of the network and was shown to exhibit errors of less than 0.5 voxel for centerline and radius detections, and 3 for initial seed directions. The algorithm was then applied on real-world data of full rat coronary structure acquired using a micro-CT scanner at 20 {mu}m voxel size. For this, a further validation of radius quantification was carried out against a partially rescanned portion of the network at 8 {mu}m voxel size, which estimated less than 10% radius error in vessels larger than 2 voxels in radius.« less
  • Purpose: Automatic prostate segmentation from MR images is an important task in various clinical applications such as prostate cancer staging and MR-guided radiotherapy planning. However, the large appearance and shape variations of the prostate in MR images make the segmentation problem difficult to solve. Traditional Active Shape/Appearance Model (ASM/AAM) has limited accuracy on this problem, since its basic assumption, i.e., both shape and appearance of the targeted organ follow Gaussian distributions, is invalid in prostate MR images. To this end, the authors propose a sparse dictionary learning method to model the image appearance in a nonparametric fashion and further integratemore » the appearance model into a deformable segmentation framework for prostate MR segmentation. Methods: To drive the deformable model for prostate segmentation, the authors propose nonparametric appearance and shape models. The nonparametric appearance model is based on a novel dictionary learning method, namely distributed discriminative dictionary (DDD) learning, which is able to capture fine distinctions in image appearance. To increase the differential power of traditional dictionary-based classification methods, the authors' DDD learning approach takes three strategies. First, two dictionaries for prostate and nonprostate tissues are built, respectively, using the discriminative features obtained from minimum redundancy maximum relevance feature selection. Second, linear discriminant analysis is employed as a linear classifier to boost the optimal separation between prostate and nonprostate tissues, based on the representation residuals from sparse representation. Third, to enhance the robustness of the authors' classification method, multiple local dictionaries are learned for local regions along the prostate boundary (each with small appearance variations), instead of learning one global classifier for the entire prostate. These discriminative dictionaries are located on different patches of the prostate surface and trained to adaptively capture the appearance in different prostate zones, thus achieving better local tissue differentiation. For each local region, multiple classifiers are trained based on the randomly selected samples and finally assembled by a specific fusion method. In addition to this nonparametric appearance model, a prostate shape model is learned from the shape statistics using a novel approach, sparse shape composition, which can model nonGaussian distributions of shape variation and regularize the 3D mesh deformation by constraining it within the observed shape subspace. Results: The proposed method has been evaluated on two datasets consisting of T2-weighted MR prostate images. For the first (internal) dataset, the classification effectiveness of the authors' improved dictionary learning has been validated by comparing it with three other variants of traditional dictionary learning methods. The experimental results show that the authors' method yields a Dice Ratio of 89.1% compared to the manual segmentation, which is more accurate than the three state-of-the-art MR prostate segmentation methods under comparison. For the second dataset, the MICCAI 2012 challenge dataset, the authors' proposed method yields a Dice Ratio of 87.4%, which also achieves better segmentation accuracy than other methods under comparison. Conclusions: A new magnetic resonance image prostate segmentation method is proposed based on the combination of deformable model and dictionary learning methods, which achieves more accurate segmentation performance on prostate T2 MR images.« less
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