**4. Conclusions**

The similarity measurement of curves is an old problem. A lot of pattern recognition problems can be converted into curve similarity problems to study. In this research, we presented a novel signature verification based on the curve similarity model, which is equally competitive when compared to other approaches and leads to much simpler and easier matching procedures. Considering internal and external writing environments being always varied, signatures were effectively aligned to the reference signature curve by CSM and a curve similarity distance was proposed to make an assessment the similarity between test signatures and references. Open access signature datasets SUSIG, SVC2004 Task1&Task2, and MCYT-100 were used in our work, and several experiments were implemented. Experimental results illustrated that the best matching could be obtained by our proposed CSM method with one signature template. The error rates EERSUSIG = 3.47%, EERSVC1 = 12.30%, EERSVC2 = 12.25% and EERMCYT = 6.07% were provided, respectively, which demonstrated the effectiveness and robustness of our proposed method. The most important thing is the case that our method can use one signature to authenticate, and the performance of our method is not much different from that of multi-signature verification systems. Finally, this innovative method opens the door to new competitions on signature verification using a single signature as reference template.

**Author Contributions:** H.H. and J.Z. proposed the conception of this research and drafted this article. E.Z. and J.T. focused on the collection, analysis and interpretation of data. E.Z. and J.T. revised the whole content of this manuscript. All authors approved and agreed with the final paper version to be published.

**Funding:** This work was supported by the National Key R&D Program of China "The study on Load-bearing and Moving Support Exoskeleton Robot Key Technology and Typical Application" [grant numbers 2017YFB1300502]; the National Natural Science Fund "The mathematical model of natural computation and research" [grant numbers 61672319, 2017].

**Conflicts of Interest:** None of these authors has conflict of interest in this research.
