# Invariant Feature Encoding for Contact Handprints Using Delaunay Triangulated Graph
## 2 Related Work
### Palm Prints
#### 2.2.1 Match between Full Palm Prints  
Most of the existing works in contact-based palm prints use the structural approach. The researchers in [24] proposed a system using the fusion of multiple features, particularly palm lines, ridge density, ridge orientation, and minutiae. The limitations of this work are: (i) images need a manual alignment for geometrical transformations, and (ii) features are not robust to distortions, are time consuming, and have a high complexity as they are still analogous to fingerprinting techniques.  
[PERSON] et al. [24] attempted a segment-based approach for a full-palm print system. However, it needs a manual segmentation before processing. [PERSON] et al. [25] addressed a minutiae-based approach for full palm prints. Since the full palm print was crowded with a large number of minutiae and image distortion, region-wise or segment-based palm prints were processed to minimize such issues. Radial triangulation of minutiae was used for feature representation, which can practically be affected by skin stretch. [PERSON] et al. [26] exploited fingerprint-based methods using minutiae where palm prints were manually segmented into thenar, hypothenar, and interdigital segments. The segments were separately processed as individual prints, and scores from each segment match were fused.  
It is outlined in the literature that minutiae-based palm print matches either adopted manual alignment of images before the match or manual segmentation of the full palm prints into distinct regions before processing. Therefore, the existing minutiae-based approaches in such prints have some limitations to overcome the geometrical transformations of the impressions in a real-time scenario. In the work proposed by [PERSON] et al. [27], a general matching process starts with one-to-one minutiae match and followed by their neighboring minutiae recursively. The work in [28] used minutiae quadruplets where four minutiae together worked as a set for the match. In complexity perspective, the orders of complexity for minutiae-triplets, quadruplets and Delaunay triangles are \(O(n^{3})\), \(O(n^{4})\) and \(O(n)\) respectively (where \(n\) = total number of minutiae) [11]. Therefore, minutiae quadruplets have higher complexity.  
The majority of the contact-based palm print feature representation is based on minutiae. However, fewer investigations are noted in the literature that experimented with minutiae-based triangles in contact palm prints. It would be advantageous if we used minutiae-triangle-to-triangle matches instead of minutiae quadruplet matches (in the complexity perspective) or one-to-one minutiae matches (alignment perspective). This approach can help to mitigate the issues that arise from the accumulation of spurious minutiae and the process of region-wise palm print segmentation. For instance, one minutiae can match with many spurious minutiae, while one minutiae triangle can match with a smaller number of false triangles compared to minutiae matches. On the other hand, one triangle-based graph can match with a much lower number of false minutiae-based graphs compared to all of the above.