Title :
Estimating topology preserving and smooth displacement fields
Author :
Karaçali, Bilge ; Davatzikos, Christos
Author_Institution :
Dept. of Radiol., Univ. of Pennsylvania, Philadelphia, PA, USA
fDate :
7/1/2004 12:00:00 AM
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.
Keywords :
Jacobian matrices; adaptive signal processing; biomedical MRI; image matching; medical image processing; smoothing methods; Jacobian matrix; adaptive smoothing; biomedical MRI; biomedical image matching; cyclic projection framework; morphometric analysis methods; shape transformations; smooth displacement field; topology preserving displacement field; Biomedical imaging; Deformable models; Image analysis; Jacobian matrices; Monitoring; Noise shaping; Radiology; Rendering (computer graphics); Smoothing methods; Topology; Algorithms; Brain; Computer Simulation; Humans; Image Enhancement; Image Processing, Computer-Assisted; Imaging, Three-Dimensional; Linear Models; Male; Phantoms, Imaging;
Journal_Title :
Medical Imaging, IEEE Transactions on
DOI :
10.1109/TMI.2004.827963