## 5 Discussion and Conclusion  
In this paper, we introduced a hybrid method of dorsal hand vein and dorsal geometry modality for human recognition. We designed a hand vein pattern acquisition that is immune to ambient light disturbance. The captured infrared image is then preprocessed using a median filter, closing morphological process, thinning morphological process, pruning morphological process and minutia detection. To find correspondences between the minutia points of two vein pattern images, a set of geometric invariants was determined based on the triangles constructed from sets of the minutia point triplets. After the correspondences were established, the parameters of a relevant transformation  
\begin{table}
\begin{tabular}{l l l c} \hline \hline
**References** & **Year** & **Methodology** & **Performance (EER)** \\ \hline [PERSON] et al. [54] & 2020 & wave atom transform & 1.49\% \\  & & & (self-built database) \\ \hline [PERSON] et al. [55] & 2020 & cross-spectral matching & 0.472\% \\ \hline [PERSON], [PERSON], [PERSON], \& [PERSON] [56] & 2018 & Haarwavelet decomposition and partial least squares algorithm & 0.4058\% \\ [PERSON] \& [PERSON] [30] & 2018 & Multibiometric fusion based on serial methodology \\ \hline [PERSON] et al. [32] & 2009 & Triangulation of hand vein images and simultaneous extraction of knuckle & EER is 1.14\%, EER of fusion is 0.38\% for left hand and shape information & 0.28\% for right hand \\ \hline [PERSON] \& [PERSON] [57] & 2011 & Neighborhood Matching Random & 0.51\% \\  & & & \\ \hline [PERSON] \& [PERSON] [58] & 2010 & Hessian Phase & 2.24\% \\  & & Local Radon Transform & 1.03\% \\ [PERSON] \& [PERSON] [58] & 2010 & Ordinal Code & 2.00\% \\  & & The Laplacian palm & 5.00\% \\  & & Score Combined of above four methods & 0.38\% \\ \hline [PERSON] \& [PERSON] [31] & 2014 & Improved LBP Method on mutual foreground & 0.267\% \\ \hline Proposed algorithm & & & 0.243\% \\ \hline \hline \end{tabular}
\end{table}
Table 2: Performance comparison of our algorithm with other matching algorithms at EER.  
Figure 30: Detection-error tradeoff (DET) curve plotted between FMR against FNMR.  
were estimated and the two images were aligned. The performance of our method was demonstrated by its ability to register the two vein pattern images scanned under a host of shape transformations. The results of the vein pattern alignment revealed that our proposed method can be used to find the corresponding minutiae and align any two vein patterns in the case of affine transformation. This makes our system applicable under varying conditions that differ from those under which the database of vein pattern was constructed. For vein pattern verification, we also proposed a rule that combines the geometric distance map error with the barcoded features to verify the query vein pattern against the reference vein pattern. Our performance yielded an area of 0.99842 under the ROC curve. Our algorithm compares favorably to other methods, resulting in an EER of 0.243%.  
Conceptualization, Y.P. and C.P.; data curation, Y.P.; formal analysis, Y.P. and C.P.; investigation, Y.P.; methodology, Y.P.; project administration, C.P.; resources, N.T.; software, Y.P.; supervision, C.P.; validation, H.A. and C.P.; visualization, Y.P.; writing--original draft, Y.P.; writing--review & editing, H.A., C.P. and Y.P. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors would like to show our gratitude to [PERSON] and [PERSON], Rangsit University, who provided insight and expertise that greatly assisted the research, as well as [PERSON], King Mongkut's Institute of Technology Ladrakang, for assistance with English language editing and proofreading.  
The authors declare no conflict of interest.