Template Shape Estimation: Correcting an Asymptotic Bias

Abstract : We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation using the stratified geometry of the shape space. We give a Taylor expansion of the bias with respect to a parameter σ describing the measurement error on the data. We propose two bootstrap procedures that quantify the bias and correct it, if needed. They are applicable for any type of shape data. We give a rule of thumb to provide intuition on whether the bias has to be corrected. This exhibits the parameters that control the bias' magnitude. We illustrate our results on simulated and real shape data.
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SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, 10 (2), pp.808 - 844. <10.1137/16M1084493>
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Contributeur : Nina Miolane <>
Soumis le : jeudi 2 février 2017 - 13:50:27
Dernière modification le : vendredi 16 juin 2017 - 13:40:56
Document(s) archivé(s) le : vendredi 5 mai 2017 - 12:25:09

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Nina Miolane, Susan Holmes, Xavier Pennec. Template Shape Estimation: Correcting an Asymptotic Bias. SIAM Journal on Imaging Sciences, Society for Industrial and Applied Mathematics, 2017, 10 (2), pp.808 - 844. <10.1137/16M1084493>. <hal-01350508v2>

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