# Invariant Feature Encoding for Contact Handprints Using Delaunay Triangulated Graph
## 3 Proposed Method  
In this section, the proposed algorithm is briefly explained. When there is a triangle match between a pair of images, there is a possibility of having a match between neighboring triangles of the initially matched. These all-matched triangle sets are known as sub-graphs. The sub-graph is formed by connecting minutiae with the initial triangle and extended until there is a match among the neighboring triangles. At a point, the sub-graph may stop without growing due to the presence of partial occlusion or degradation.  
Now, if one triangle on an image matches with two triangles on another image due to the spurious minutiae, then there would be a possibility of forming many distinct independent sub-graphs in different locations of the counterpart of the image. Further, in a handprint, one minutiae- -triangle-based sub-graph may be formed in finger segment, while the other sub-graph may be in palm segment. The region between these two sub-graphs could be distorted or not clear due to the degradation. Therefore, there would be a problem to extend such sub-graphs further. In the end, there would be many sub-graphs, and all of these sub-graphs may not be reliable. That means, one sub-graph can match with two or more sub-graphs in different locations of the counter image due to the bombardment of spurious minutiae. Then, there should be a mechanism to make such sub-graphs grow further and select the best reliable sub-graphs among them to form an authentic minutia-based graph. This is the base idea of the proposed algorithm.  
In the literature, [PERSON] et al. [51] worked with latent palm prints using a single graph which is connected from a set of neighboring triangles. But the graph can be extended until there is a match among the neighboring triangles. And it is noted that the work used manually marked minutiae information for the image alignment process. There are a few questions left in this work: (i) What if the graph stops at a certain point without growing due to the presence of occlusion or degradation? (ii) How would the bombardment of spurious minutiae be eliminated? (iii) How would geometrical alignment of the images be achieved? (iv) How would the matched triangles and graph be validated? (v) How could the computational complexity be compromised (due to the spurious minutiae present on image)? These questions highlight the gaps, and the work in [51] concluded without addressing these issues. Further, their feature vector used the distance of a triangle side that can be affected by skin stretch.  
In this context, the following aspects are introduced in the proposed method:  
1. Invariant feature representation--a feature vector of a triangle is proposed to tolerate scale and rotation variations of images (distance of a triangle side or ridge count are eliminated in feature vector).
2. Geometrical alignment--image alignment is achieved using initial triangle matching and the matched triangles are used as reference locations. This process helps to automatically align the images.
3. Computational complexity in processing a larger surface area--Delaunay triangulation is used to lower the computational complexity of the minutiae-based triangles in an increased hand size with a large number of spurious minutiae.
4. Elimination of spurious minutiae--this is achieved by verification of independent matched triangles and validation of sub-graphs. Since spurious minutiae can generate false triangles on handprints, we can discard some of the sub-graphs formed from the false triangle match after validity checking. The sub-graphs are validated based on the number of minutiae each graph holds (threshold).