  The problem of curve registration appears in many different areas of
applications ranging from neuroscience to road traffic modeling. In the present
work, 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 $\chi^2$-test. We also prove that the proposed test is
consistent, \textit{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.
