# Invariant Feature Encoding for Contact Handprints Using Delaunay Triangulated Graph
In the existing literature related to minutiae-based feature representation, one-to-one minutiae match between two fingerprints has been exploited. This approach, however, cannot be applied for geometrically transformed image segments, which will additionally require a manual image alignment before such a match. Therefore, a pair of minutiae, minutiae triangles, and minutiae polygons have been exploited to mitigate the issue of geometrical normalization in the past [8; 9; 10]. However, one minutiae-based triangle may match with another triangle that is located in a different region of the  
Figure 2: Extremely low-quality hypothenar segments of palm prints acquired from THUPALMLAB database. Images in each row represent four instances of a single palm from one individual. Four rows represent images acquired from four individuals. Note that the data set used in this category shows low-quality prints nearly similar to latent prints. An enlarged portion of the degraded image is shown to illustrate the quality level of the image. compared print. To tackle this issue, Delaunay triangles that are formed from the set of minutiae can be extended as a graph and utilized as Delaunay triangulated graph. This can result the matching as a sub-graph to sub-graph instead. The probability of matching a triangle in one image with a false triangle in another image increases during the triangle match. In contrast, the probability of matching a sub-graph in one image with a false sub-graph in another image reduces because the sub-graph becomes large and comprises multiple Delaunay triangles. Further, the complexity of matching a set of minutiae from one image segment arbitrarily to another similar set in a compared image segment is vastly reduced because of the Delaunay triangulation. This is particularly advantageous because the number of minutiae can be very large in handprint systems which consist of multiple fingers and multiple regions of the palm [11]. This research presents an alternate approach based on a graph incorporated with the Delaunay triangulations. An extended graph with a set of minutiae-based triangles imparts invariance to similarity transformations, such as translation, rotation, and scale changes. This work investigates if the proposed algorithm can be used in handprints and presents an invariant feature representation in a common framework so that the algorithm can be applied for any segment of the hand acquired using touch-based sensors from any surfaces. The proposed algorithm eliminates the effect of geometrical variations in the handprints without any manual pre-alignment process and can be extended to the forensic domain where only parts of handprints are available. The outline of this work is summarized as follows:  
* Introducing the algorithm based on new variant of graph matching with triangles using invariant feature representation. * Evaluating the algorithm using fingerprints with geometrical variations and investigating palm prints with geometrical variation, partial-quality, and extremely degraded impressions that resemble latent prints. * Comparing the method with the state-of-the-art scale-invariant feature transform (SIFT) features. The remaining of the article is organized as follows: Section 2 discusses minutiae-based related work in touch-based fingerprints and palm prints; Section 3 illustrates methodology with the algorithm description, data preparation, and experimental setup; Section 4 discusses experimental results. A conclusion and the future direction are provided in Section 5.