A new statistical permutation analysis method is presented in this paper to efficiently and accurately localize regionally specific shape differences between groups of 3D biomedical images. It can improve the system’s efficiency by approximating the permutation distribution of the test statistic with Pearson distribution series. This procedure involves the calculation of the first four moments of the permutation distribution, which are derived theoretically and analytically without any permutation. Furthermore,bioequivalence testing aims for practical significances between the two groups that are statistically significant with the shape differences larger than a desired threshold. Experimental results based on both classical and bioequivalence hypothesis tests using simulated data and real biomedical images are presented to demonstrate the advantages of the proposed approach.