# Invariant Feature Encoding for Contact Handprints Using Delaunay Triangulated Graph
## 2 Related Work  
### Fingerprint  
Fingerprint recognition systems are categorized into minutiae-based, texture-based, and correlation-based [12]. In the minutiae-based approach, a set of minutiae that correspond to one another between two fingerprint images is used to compute a match score, whereas in the correlation-based approach, the cross-correlation between the two images after geometrical transformations to obtain the best fit provides a match score. On the other hand, selected points and their surrounding areas are passed through texture extraction filters, and the filter outputs are used to obtain a match score in the texture-based approach. Minutiae, as features, have the attributes of simplicity and some tolerance to non-linear distortion [13] and are hence widely used, which leads the minutiae to be accepted as a discriminative feature of choice in fingerprint systems. Existing minutiae-matching structures are distinguished as: (i) nearest-neighbor-based; (ii) fixed-radius-based; (iii) minutiae-triangle-based; and (iv) texture-based local structures. Nearest-neighbor-based structures use minutiae with their x, y coordinates and orientation information for one-to-one minutiae matching. This leads to non-linear deformation and does not guarantee the best performance in existing systems [14]. [PERSON] and [PERSON] [15] proposed a fixed-radius-based minutiae-star structure, while [PERSON] et al. [16] introduced minutiae cylinder code (MCC), where angles between neighboring minutiae and their relative positions are described by Gaussian filters. However, methods that match only using minutiae coordinates and angle are not robust against geometrical variations or distortion. The work in [17] used a variable distance approach using K-nearest neighbors, the distance between the core points, and the distance between the minutiae. Since the core point is difficult to define in the arch-type fingerprints, and it is not always visible due to the degradation and noise, the work in [18] used a faster region-based convolutional neural network (R-CNN) to find its own reference point. The existing works using neighboring edges and core points are suitable only for images with good quality [19] and will fail if there is an error in detecting the core point. Since minutiae topological structure provides inadequate information to overcome geometrical transformations of the matching images, many researchers exploited minutiae-related local structures, such as ridge frequency, ridge orientation, relationship and curvature [20; 21]. The methods of minutiae-based fingerprint matching represented in the literature involve the use of minutiae pairs, minutiae triplets [9; 19], Delaunay triangles [8; 10], and minutiae quadruplets where minutiae direction and coordinate information are commonly used for the matching of two fingerprint images. This information, however, is sensitive to geometric transformations which necessitate image alignment before the matching process. In the minutiae-based polygon approach, pairs of minutiae and surrounding textures were used in the past, which needs an additional alignment step as one minutiae pair can match many pairs of minutiae located on different regions of the compared image. On the other hand, [PERSON] [9] exploited minutiae triplets where the feature vector consists of angles and distances between minutiae of a triangle. However, one triangle on an image can still possibly match more than one triangle on the counterpart or compared image. Further, using distance between two minutiae as a feature is not always feasible if there is a scale change during image capture. [PERSON] and [PERSON] [10] exploited Delaunay triangles, where one pair of minutiae was used for alignment of an edge, and then the matching process was performed. In this work, a local structure was formed by the selected concerned minutia and its adjacent minutiae.