Abstract
In this paper we focus on estimating the deformations that may exist between similar images in the presence of additive noise when a reference template is unknown. The deformations are modeled as parameters lying in a finite dimensional compact Lie group. A general matching criterion based on the Fourier transform and its well known shift property on compact Lie groups is introduced. M-estimation and semiparametric theory are then used to study the consistency and asymptotic normality of the resulting estimators. As Lie groups are typically nonlinear spaces, our tools rely on statistical estimation for parameters lying in a manifold and take into account the geometrical aspects of the problem. Some simulations are used to illustrate the usefulness of our approach and applications to various areas in image processing are discussed.
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Bigot, J., Loubes, JM. & Vimond, M. Semiparametric estimation of shifts on compact Lie groups for image registration. Probab. Theory Relat. Fields 152, 425–473 (2012). https://doi.org/10.1007/s00440-010-0327-2
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DOI: https://doi.org/10.1007/s00440-010-0327-2
Keywords
- Image registration
- Lie group
- Semi-parametric estimation
- M-estimation
- Fourier transform
- Statistical inference on manifolds
- White noise model
Mathematics Subject Classification (2000)
- Primary 62F12
- Secondary 65Hxx