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The problem of curve registration appears in many different areas of applications ranging from neuroscience to road traffic modeling. In the present work, 1 1 This paper was presented in part at the AI-STATS 2012 conference. we propose a nonparametric testing framework in which we develop a generalized likelihood ratio test to perform curve registration. We first prove that, under the null hypothesis, the resulting test statistic is asymptotically distributed as a chi-squared random variable. This result, often referred to as Wilks’ phenomenon, provides a natural threshold for the test of a prescribed asymptotic significance level and a natural measure of lack-of-fit in terms of the p -value of the χ 2 -test. We also prove that the proposed test is consistent, i.e. , its power is asymptotically equal to 1. Finite sample properties of the proposed methodology are demonstrated by numerical simulations. As an application, a new local descriptor for digital images is introduced and an experimental evaluation of its discriminative power is conducted. [ABSTRACT FROM AUTHOR]