2011/04/21 by Olivier Collier, Collier, Olivier, Arnak S. Dalalyan +1
Computer Science · Mathematics · #Digital Image Processing Techniques #FOS: Mathematics #Medical Image Segmentation Techniques #Point processes and geometric inequalities #Statistics Theory (math.ST) #math.ST #stat.TH
paper · pdf · doi:10.48550/arxiv.1104.4210
openalex publication_date 2011/04/21 · arxiv created 2015/02/19 · arxiv updated 2015/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 χ2-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.