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Gems - Geometric Median Shapes

Cunha, Alexandre (2019) Gems - Geometric Median Shapes. In: 2019 IEEE 16th International Symposium on Biomedical Imaging. IEEE , Piscataway, NJ, pp. 1492-1496. ISBN 978-1-5386-3640-4. http://resolver.caltech.edu/CaltechAUTHORS:20190718-132254908

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Abstract

We present an algorithm to compute the geometric median of shapes which is based on the extension of median to high dimensions. The median finding problem is formulated as an optimization over distances and it is solved directly using the watershed method as an optimizer. We show that the geometric median shape faithfully represents the true central tendency of the data, contaminated or not. It is superior to the mean shape which can be negatively affected by the presence of outliers. Our approach can be applied to manifold and non manifold shapes, with single or multiple connected components. The application of distance transform and watershed algorithm, two well established constructs of image processing, lead to an algorithm that can be quickly implemented to generate fast solutions with linear storage requirement. We demonstrate our methods in synthetic and natural shapes and compare median and mean results under increasing outlier contamination.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
https://doi.org/10.1109/ISBI.2019.8759416DOIArticle
Additional Information:© 2019 IEEE. Funding supporting this work was provided by the Beckman Institute at Caltech, a research center endowed with funds from the Arnold and Mabel Beckman Foundation, to the Center for Advanced Methods in Biological Image Analsysis.
Funders:
Funding AgencyGrant Number
Caltech Beckman InstituteUNSPECIFIED
Arnold and Mabel Beckman FoundationUNSPECIFIED
Subject Keywords:Shape Analysis, Geometric Median, Median Shape, Average Shape, Segmentation Fusion
Record Number:CaltechAUTHORS:20190718-132254908
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20190718-132254908
Official Citation:A. Cunha, "Gems - Geometric Median Shapes," 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019), Venice, Italy, 2019, pp. 1492-1496. doi: 10.1109/ISBI.2019.8759416
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:97235
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:18 Jul 2019 20:53
Last Modified:18 Jul 2019 20:53

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