Hybrid permutation test with application to surface shape analysis

This paper presents a new statistical surface analysis framework that aims to accurately and efficiently localize regionally specific shape changes between groups of 3D surfaces. With unknown distribution and small sample size of the data, existing shape morphometry analysis involves testing thousands of hypotheses for statistically significant effects through permutation. In this work, we develop a novel hybrid permutation test approach to improve the system's efficiency by approximating the permutation distribution of the test statistic with a Pearson distribution series that involves the calculation of the first four moments of the permutation distribution. We propose to derive these moments theoretically and analytically without any permutation. Detailed derivations and experimental results using two different test statistics are demonstrated using simulated data and brain data for shape morphometry analysis. Furthermore, an adaptive procedure is utilized to control the False Discovery Rate (FDR) for increased power of finding significance.