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 problems, 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 aligning all the images. Our approach is based on M-estimation and we

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... the consistency of the resulting estimators. A small scale simulation study and real examples are used to illustrate the numerical performances of our procedure. Ackowledgements We gratefully acknowledge Stephane Derrode for providing the butterflies database. They are also grateful to the Associate Editor and to the referees for their helpful suggestions concerning the presentation of this paper. and remark that M ǫ (α) is the sum of three terms using (4.9): Consequently from Assumption (4.18) and Assumption (4.24-4.25), Consequently, ǫ 2 Q ǫ converges uniformly to zero. Finally, the arguments used to prove that (I I I) j converges to zero, can also be used to derive that 1 J ∑ J j=1 |ω|≤ω ǫ |Ẑ j (ω)| 2 dω converges to N 1 , which finally proves that N ǫ (b) converges uniformly to N(b).