Accurate Inversion of 3-D Transformation Fields

This correspondence addresses the inversion of 3-D transformation fields, which is a problem that typically arises in image warping problems. A topology preserving parametric B-spline-based representation of the deformation field is considered. Topology preservation ensures that the transformation i...

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Bibliographic Details
Published in:IEEE transactions on image processing 2008-10, Vol.17 (10), p.1963-1968
Main Authors: Noblet, V., Heinrich, C., Heitz, F., Armspach, J.-P.
Format: Article
Language:English
Subjects:
Algorithms
Applied sciences
Brain
Brain - anatomy & histology
Brain modeling
Deformation
Exact sciences and technology
Image Enhancement - methods
Image Interpretation, Computer-Assisted - methods
Image processing
Image warping
Imaging, Three-Dimensional - methods
Information, signal and communications theory
Interpolation
interval analysis
Inversions
Magnetic Resonance Imaging - methods
Nonlinear equations
Parameter estimation
Preserving
Reproducibility of Results
resolution of systems of nonlinear equations
Sensitivity and Specificity
Signal processing
Stress
Telecommunications and information theory
Topology
transformation field inversion
Transformations
Yield estimation
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Summary:This correspondence addresses the inversion of 3-D transformation fields, which is a problem that typically arises in image warping problems. A topology preserving parametric B-spline-based representation of the deformation field is considered. Topology preservation ensures that the transformation is a one-to-one mapping and consequently that it is invertible. Inverting such transformation fields amounts to solving a system of nonlinear equations. To tackle this problem, we rely on interval analysis techniques. The proposed algorithm yields a solution whose accuracy is user-controlled. This method may be extended to any dense transformation field and also to deformations defined on a grid of points, by considering a projection in the space of topology preserving B-spline-based deformation fields. The performance of the algorithm is illustrated on transformation fields coming from intersubject brain registration.
ISSN:1057-7149
1941-0042
DOI:10.1109/TIP.2008.2002310