Researchers proposed several criteria to assess the quality of predicted protein structures because it is one of the essential tasks in the Critical Assessment of Techniques for Protein Structure Prediction (CASP) competitions. Popular criteria include root mean squared deviation (RMSD), MaxSub score, TM-score, GDT-TS and GDT-HA scores. All these criteria require calculation of rigid transformations to superimpose the the predicted protein structure to the native protein structure. Yet, how to obtain the rigid transformations is unknown or with high time complexity, and, hence, heuristic algorithms were proposed.In this work, we carefully design various small structure patterns, including the ones specifically tuned for local pockets. Such structure patterns are biologically meaningful, and address the issue of relying on a sufficient number of backbone residue fragments for existing methods. We sample the rigid transformations from these small structure patterns; and the optimal superpositions yield by these small structures are refined and reported. As a result, among 11, 669 pairs of predicted and native local protein pocket models * To whom all correspondence should be addressed (email: shuaicli@cityu.edu.hk). † To whom all correspondence should be addressed (email: xin.gao@kaust.edu.sa).Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from permissions@acm.org. BCB '15, September 9-12, 2015 from the CASP10 dataset, the GDT-TS scores calculated by our method are significantly higher than those calculated by LGA. Moreover, our program is computationally much more efficient.Source codes and executables are publicly available at