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A Survey of Mathematical Structures for Extending 2D Neurogeometry to 3D Image Processing

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Book cover Medical Computer Vision: Algorithms for Big Data (MCV 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9601))

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Abstract

In the Big Data landscape, learning algorithms are often “black-boxes” and as such, hard to interpret. We need new constructive models, to eventually feed the Big Data framework. The emerging field of Neurogeometry provides inspiration for models in medical computer vision. Neurogeometry models the neuronal architecture of the visual cortex through Differential Geometry. First, Neurogeometry can explain visual phenomena like human perceptual completion. And second, it provides efficient algorithms for computer vision. Examples of applications are image completion (in-painting) and crossing-preserving smoothing. In medical computer vision, Neurogeometry is less known. One reason is that one often deals with 3D images, whereas Neurogeometry is essentially 2D (our retina is 2D). Moreover, the generalization to 3D is not mathematically straight-forward. This article presents the theoretical framework of a 3D-Neurogeometry inspired by the 2D case. The aim is to provide a “theoretical toolbox” and inspiration for new models in 3D medical computer vision.

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Authors and Affiliations

  1. INRIA Asclepios, 2004 Route des Lucioles BP93, 06902, Sophia Antipolis, France

    Nina Miolane & Xavier Pennec

  2. Department of Statistics, Stanford University, Sequoia Hall, 390 Serra Mall, Stanford, CA, 94305-4065, USA

    Nina Miolane

Authors
  1. Nina Miolane
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  2. Xavier Pennec
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Corresponding author

Correspondence to Nina Miolane .

Editor information

Editors and Affiliations

  1. TU München, Computer Science , München, Germany

    Bjoern Menze

  2. Medical University of Vienna , Wien, Austria

    Georg Langs

  3. Southwestern Medical Center, University of Texas Southwestern Medical Center, Dallas, Texas, USA

    Albert Montillo

  4. Siemens AG , Erlangen, Germany

    Michael Kelm

  5. University of Applied Sciences HES- , Sierre, Switzerland

    Henning Müller

  6. University of North Carolina , CHARLOTTE, USA

    Shaoting Zhang

  7. Sydney, Australia

    Weidong Cai

  8. Computer Science, State University of New Jersey Rutgers Computer Science, Piscataway, New Jersey, USA

    Dimitris Metaxas

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Miolane, N., Pennec, X. (2016). A Survey of Mathematical Structures for Extending 2D Neurogeometry to 3D Image Processing. In: Menze, B., et al. Medical Computer Vision: Algorithms for Big Data. MCV 2015. Lecture Notes in Computer Science(), vol 9601. Springer, Cham. https://doi.org/10.1007/978-3-319-42016-5_15

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  • DOI: https://doi.org/10.1007/978-3-319-42016-5_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-42015-8

  • Online ISBN: 978-3-319-42016-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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