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Fast Surface Segmentation Guided by User Input Using Implicit Extension of Minimal Paths

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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 or more known curves (the constraining curves), given by an expert. The aim of our method is to find the desired surface by exploiting the information given in the supplied curves as much as possible. We use a cost potential which penalizes image regions of low interest (for example areas of low gradient). 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. These paths globally minimize an energy which is defined from the cost potential. Our approach, although conceptually different, can be seen as an implicit extension to 3D of the minimal path framework already known for 2D image segmentation. As for this previous approach, and unlike other variational methods, our method is not prone to local minima traps of the energy. We present a fast implementation which has been successfully applied to 3D medical and synthetic images.

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Authors and Affiliations

  1. MEDISYS-Philips France, 51, rue Carnot, 92156, Suresnes, France

    Roberto Ardon

  2. CEREMADE, UMR CNRS 7534, Université Paris Dauphine, Place du Marchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Roberto Ardon & Laurent D. Cohen

  3. Georgia Institute of Technology, Atlanta, GA, USA

    Anthony Yezzi

Authors
  1. Roberto Ardon
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  2. Laurent D. Cohen
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  3. Anthony Yezzi
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Correspondence to Roberto Ardon.

Additional information

Roberto Ardon graduated from the Ecole Centrale Paris in 2001 with a major in applied mathematics, obtained his master degree in image processing from the Ecole Normale Supérieure de Cachan in the same year and his Ph.D. degree in applied mathematics from the University Paris-Dauphine in 2005. Currently he is a research scientist in Philips Medical Systems Research Paris. His research interests include calculus of variations mainlly focused on medical image processing.

Laurent D. Cohen was at Ecole Normale Superieure Ulm in Paris from 1981 to 1985. He received Master's and Ph.D. degrees in Applied Mathematics from Paris 6 in 1983 and 1986. From 1985 to 1987, he was member at the Computer Graphics and Image Processing group at Schlumberger Palo Alto Research, California and Schlumberger Montrouge Research, and remained consultant there for a few years afterwards. He began working with INRIA, France in 1988, mainly with the medical image understanding group Epidaure. Since 1990, he is Research Scholar (Charge then Directeur de Recherche) with CNRS in the Applied Mathematics and Image Processing group at CEREMADE, University Paris-Dauphine. His research interests and teaching at the university are applications of variational methods and Partial Differential Equations to Image Processing and Computer Vision, like deformable models, minimal paths, surface reconstruction, Image registration, Image segmentation and restoration. He obtained CS 2002 Prize for Image and Signal Processing. He has been member in program committees for boards for about 20 international conferences.

Anthony Yezzi obtained his Ph.D. in 1997 through the Department of Electrical Engineering at the University of Minnesota. After completing a postdoctoral research position in the Laboratory for Information and Decision Systems (LIDS) at Massacusetts Institute of Technology, he joined the faculty of the School of Electrical and Computer Engineering at Georgia Institute of Technology in 1999 where he currently holds the position of Associate Professor. Prof. Yezzi has also consulted for a number of medical imaging companies including GE, Picker, and VTI, and has been an IEEE member since 1999. His research lies primarily within the fields of image processing and computer vision. He has worked on a variety of problems including image denoising, edge-detection, segmentation and grouping, shape analysis, multi-frame stereo reconstruction, tracking, and registration. Some central themes of his research include curve and surface evolution theory, differential geometry, and partial differential equations.

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Ardon, R., Cohen, L.D. & Yezzi, A. Fast Surface Segmentation Guided by User Input Using Implicit Extension of Minimal Paths. J Math Imaging Vis 25, 289–305 (2006). https://doi.org/10.1007/s10851-006-9641-9

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  • DOI: https://doi.org/10.1007/s10851-006-9641-9

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