# Fingerprints Classification through Image Analysis and Machine Learning Method
## 3 Proposed Method
### Types of Fingerprint and Features Extraction  
In this work, we classify types of fingerprint into 3 classes--arch, loop and whorl.  
\(\bullet\)**Arch**: These occur in about 5% of the encountered fingerprints. The identifying features of this arch are that the fingerprints have overlapping shapes that form layers and have a mountain-like peak. Arch of fingerprints are divided into several categories--AS (the lines are stacked on top of each other, unconcerned, no intersection.), AE (a combination of whorl and arch group, the distance from the center to the intersection of eagles is less than 5 veins), AU, AR (the combination of the loop group with arch, the distance from the center to the intersection is less than 5 fringe lines) as shown in Figure 3.  
\(\bullet\)**Loop**: It is called the loop (can be seen in almost 60% to 65% of fingerprints worldwide) fingerprint because it is shaped like a water wave with the following features--the ridges make a backward turn in loops, triangular with a center and an intersection. Divided into two types: _RL--Radial Loop_: Top of the triangle facing the pinky finger. It looks like a stream of water flowing downwards (on the little finger). This type accounts for about 6% of fingerprints worldwide. _UL--Ulmar Loop_: The top of the triangle faces the thumb. It is shaped like a stream of water flowing backward (thumb direction). This form only accounts for 2% of fingerprints worldwide. A loop pattern has only one delta as shown in Figure 4.  
\(\bullet\)**Whorl**: This fingerprint only accounts for about 25% to 35% of fingerprints worldwide. Whorl pattern identification is that they have one circuit and 2 Delta (intersection) as shown in Figure 5.  
Figure 4: Example type of fingerprint is loop.  
Figure 3: Example type of fingerprint is arch.  
Feature extraction of singularityOn the fingerprint there are areas with unusual structures compared to other areas. They often have a parallel structure called a singularity. There are two types of singularity--core and delta. To extract singularity characteristics, we proceed as follows:  
* Step 1. Input image then resize image to \(256\times 256\)
* Step 2. Fingerprint pre-processing and enhancement
* Step 3. At each pixel, the gradient is calculated in two directions x and y are \(G_{x}\) and \(G_{y}\) based on the Formula (1): \[\varphi=\frac{1}{2}\tan^{-1}\left[\frac{\sum_{i=1}^{W}\sum_{j=1}^{W}2G_{x}\left( i,j\right)G_{y}\left(i,j\right)}{\sum_{i=1}^{W}\sum_{j=1}^{W}\left(G_{x}^{2} \left(i,j\right)-G_{y}^{2}\left(i,j\right)\right)}\right]\] (1)
* Step 4. Identify singularity points using the Pointcare index [15]. Pointcare index at the pixel with coordinates \(\left(i,j\right)\) is the sum of the deviations of direction of adjacent points, calculated as follows in Equation (2): \[PC\left(i,j\right)=\sum_{k=0}^{N_{p}-1}\Delta\left(k\right)\] (2) \[\Delta\left(k\right)=\left\{\begin{array}{l}d\left(k\right);\left|d\left(k \right)\right|<\frac{\pi}{2}\\ d\left(k\right)+\pi;d\left(k\right)\leq-\frac{\pi}{2}\end{array}\right.\begin{array} []{l}d\left(k\right)=\varphi\left(x_{k+1},y_{k+1}\right)-\varphi\left(x_{k}, y_{k}\right),\end{array}\] (3) where \(\varphi\) is the gradient at pixels in two directions.  
Based on the Pointcare index, we can identify singularity points as follows in Equation (4):  
\[PC(i,j)=\left\{\begin{array}{l}0^{0};\left(i,j\right)\text{ is not singularity}\\ 360^{0};\left(i,j\right)\text{ is whorl}\\ 180^{0};\left(i,j\right)\text{ is loop}\\ -180^{0};\left(i,j\right)\text{ is delta}\end{array}\right. \tag{4}\]  
* Step 5. Save and create fingerprint features vector.