# Fingerprint Classification Based on Multilayer Extreme Learning Machines
## 3 Theoretical Foundations
### Feature Descriptors  
Fingerprint classification is the most commonly employed technique to reduce the penetration rate in fingerprint identification datasets [40]. Most researchers adopt the five-class system proposed by [PERSON] [26], which categorizes fingerprints based on distinct visual patterns. These classes are unevenly distributed as follows: arch (3.7%), left loop (33.8%), right loop (31.7%), tented arch (2.9%), and whorl (27.9%). Fingerprint classification algorithms typically rely on global fingerprint features, such as OM, ridge structures, and singular points (SPs). Singular points are commonly detected using the Poincare method. While OMs are generally extracted through gradient-based methods, alternative approaches, such as cleft-based or skeleton-tracking techniques, have also been proposed. Based on several analyses, Peralta already compared various fingerprint extraction (FE) methods (SVM, 5 NN, 10 NN, and Kappa) across multiple databases. These evaluations consistently show that the Capelli02, Hong08, and Liu10 methods deliver the best performance [3; 41]. Hong08 maintains an accuracy of 93.55% and a Kappa of 0.9083 using K-NN (k = 5, Euclidean distance), suggesting that K-NN may be more suitable for low-quality fingerprint classification than SVM. The Jain method, also using K-NN, shows similar performance, with an accuracy of 93.47% and a Kappa of 0.9072. As the database difficulty increases, the extraction of the new features introduced by Hong08 becomes more challenging. Nevertheless, Hong08 remains the best option compared to other methods, demonstrating a strong ability to handle fingerprints of varying quality. Capelli02 [24] is a method based on the fingerprint OM; the OM is aligned using a central point detected by the Poincare method. A dynamic mask is applied to each class, generating a five-element vector. The orientations are also recorded as part of the feature set. The authors combined two distinct approaches for feature extraction and classification. Additionally, features from the earlier Capelli99a [42] method were incorporated into the feature vector. Once the OM is registered, it is enhanced following the procedure described in Capelli99a. Finally, orientations are recorded in radians within the feature vector, whose size depends on the original image dimensions. These features are then processed using the Multi-space KL (MKL) classification method [43]. The Hong08 [14] method extends the FingerCode feature vector (derived from Gabor filters) by incorporating pseudo-ridges traced from the fingerprint center, along with the number of singular points (nucleus and deltas), and their distance and location. This approach builds upon the FingerCode method proposed by [PERSON], adding ten new features derived from the SPs and pseudo-ridges. SPs are extracted using the Karu method [44], while the pseudo-ridge is based on the Zhang04 method [45]. In this case, pseudo-ridges are traced from the center of the fingerprint, which is defined as the closest central point detected or remains unchanged if no central point is identified. Once the SP and pseudo-ridge are calculated, ten additional features are added to the FingerCode feature vector. These features include the number of nuclei and deltas, as well as the relative location and distance of the deltas and the endpoints of pseudo-ridges in relation to the fingerprint center. It should be noted that these features are categorical, as distances and relative locations are discretized into four and six values, respectively. The Liu10 approach [25] differs significantly from other methods by exclusively considering relative measures of SPs as features. A total of 16 features are extracted at four different scales to enhance robustness against noise. All features are related to the primary central point, including its position, orientation, and degree of freedom. Additional features are defined as relative measures between the central point and the other SPs. The Liu10 method can be summarized in four main steps.