Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fourier-Mellin Transform

Jérémie Bigot , Fabrice Gamboa , Myriam Vimond (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this paper we focus on extended Euclidean registration of a set of noisy images. We provide an appropriate statistical model for this kind of registration problem, and a new criterion based on Fourier-type transforms is proposed to estimate the translation, rotation, and scaling parameters to align a set of images. This criterion is a two-step procedure which does not require the use of a reference template onto which all the images are aligned. Our approach is based on M-estimation, and we prove the consistency of the resulting estimators. A small-scale simulation study and real examples are used to illustrate the numerical performances of our procedure.

Mots clés: image registration; extended Euclidean transformation; semiparametric estimation; white noise model; M-estimation; Fourier transform; Fourier-Mellin transform

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Jérémie Bigot, Fabrice Gamboa, Myriam Vimond. Estimation of Translation, Rotation, and Scaling between Noisy Images Using the Fourier-Mellin Transform. SIAM Journal on Imaging Sciences, 2009, 2 (2), pp.614-645. ⟨10.1137/070691231⟩. ⟨hal-00776806⟩