Estimating topology preserving and smooth displacement fields

IEEE Transactions on Medical Imaging
Bilge Karaçali, Christos Davatzikos

Abstract

We propose a method for enforcing topology preservation and smoothness onto a given displacement field. We first analyze the conditions for topology preservation on two- and three-dimensional displacement fields over a discrete rectangular grid. We then pose the problem of finding the closest topology preserving displacement field in terms of its complete set of gradients, which we later solve using a cyclic projections framework. Adaptive smoothing of a displacement field is then formulated as an extension of topology preservation, via constraints imposed on the Jacobian of the displacement field. The simulation results indicate that this technique is a fast and reliable method to estimate a topology preserving displacement field from a noisy observation that does not necessarily preserve topology. They also show that the proposed smoothing method can render morphometric analysis methods that are based on displacement field of shape transformations more robust to noise without removing important morphologic characteristics.

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Citations

Aug 30, 2011·Medical Image Analysis·Nai-Xiang Lian, Christos Davatzikos
Dec 9, 2015·Annual Review of Biomedical Engineering·Michael I MillerLaurent Younes
May 1, 2007·Magnetic Resonance Imaging·Shan ShenAnnette Sterr
Jan 9, 2009·Cytometry. Part a : the Journal of the International Society for Analytical Cytology·Tiehua Du, Martin Wasser
Jan 5, 2013·IEEE Transactions on Medical Imaging·Ivor J A SimpsonJulia A Schnabel
Sep 12, 2008·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Vincent NobletJean-Paul Armspach
May 13, 2006·IEEE Transactions on Medical Imaging·Bilge Karaçali, Christos Davatzikos
Oct 15, 2011·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Lucilio Cordero-GrandeCarlos Alberola-López
Dec 14, 2011·IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society·Carole Le GuyaderChristian Gout
Feb 1, 2009·IEEE Journal of Selected Topics in Signal Processing·Se Young Chun, Jeffrey A Fessler
Feb 21, 2013·Computational and Mathematical Methods in Medicine·XiangBo LinDongMei Guo
May 2, 2009·NeuroImage·Evangelia I ZacharakiChristos Davatzikos
Mar 25, 2017·Physics in Medicine and Biology·Angelica I AvilesHabib Ammari

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