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Integration of Topological Constraints in Medical Image Segmentation

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Handbook of Biomedical Imaging

Abstract

Topology is a strong global constraint that can be useful in generating geometrically accurate segmentations of anatomical structures. Conversely, topological “defects” or departures from the true topology of a structure due to segmentation errors can greatly reduce the utility of anatomical models. In this chapter we cover methods for integrating topological constraints into segmentation procedures in order to generate geometrically accurate and topologically correct models, which is critical for many clinical and research applications.

Support for this research was provided in part by the National Center for Research Resources (P41-RR14075, R01 RR16594-01A1 and the NCRR BIRN Morphometric Project BIRN002, U24 RR021382), the National Institute for Biomedical Imaging and Bioengineering (R01 EB001550, R01EB006758), the National Institute for Neurological Disorders and Stroke (R01 NS052585-01) as well as the Mental Illness and Neuroscience Discovery (MIND) Institute, and is part of the National Alliance for Medical Image Computing (NAMIC), funded by the National Institutes of Health through the NIH Roadmap for Medical Research, Grant U54 EB005149.

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Notes

  1. 1.

    The human cerebral cortex is a highly folded ribbon of gray matter (GM) that lies inside the cerebrospinal fluid (CSF) and outside the white matter (WM) of the brain. Locally, its intrinsic “unfolded” structure is that of a 2D sheet, several millimeters thick. In the absence of pathology and assuming that the midline hemispheric connections are artificially closed, each cortical hemisphere can be considered as a simply-connected 2D sheet of neurons that carries the simple topology of a sphere - see Fig. 1-b

  2. 2.

    In the case of multiple surfaces involving K connected components, the total genus is related to the total Euler-characteristic by the formula: \( \chi \) = 2(K − g).

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Authors and Affiliations

  1. Department of Radiology, MGH/Harvard Medical School, Building 149, 13th Street, Charlestown, MA, 02129, USA

    F. Ségonne & B. Fischl

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  1. F. Ségonne
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  2. B. Fischl
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Correspondence to F. Ségonne .

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Editors and Affiliations

  1. Department of Applied Mathematics, École Centrale de Paris / INRIA Saclay, Île De France, Chatenay-Malabry, France

    Nikos Paragios

  2. Department of Biomedical Engineering, Diagnostic Radiology and Electrical Engineering, Yale University, New Haven, Connecticut, USA

    James Duncan

  3. INRIA Sophia Antipolis - Méditerranée, Sophia Antipolis Cedex, France

    Nicholas Ayache

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Ségonne, F., Fischl, B. (2015). Integration of Topological Constraints in Medical Image Segmentation. In: Paragios, N., Duncan, J., Ayache, N. (eds) Handbook of Biomedical Imaging. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-09749-7_13

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  • DOI: https://doi.org/10.1007/978-0-387-09749-7_13

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