# Handwritten Signature Verification Method Based on Improved Combined Features
## 3 Proposed Work
### Data Acquisition  
This paper uses a smart pen with a camera and pressure sensor to sign on a piece of paper filled with tiny dots. While writing the signature, the image and trajectory data of the signature can be obtained in real time. A total of 20 authors' signatures were collected, including 30 authentic signatures and 30 forged signatures for each author, a total of 1200 signatures. The forged signature used in this paper is to find 2-3 experimenters, provide the real signature, and then perform the forgery after pre-training to obtain the forgery. The forged signature is reliable and practical. The data set used in this article is entirely composed of Chinese signatures, but the experimental methods used can be widely applied to other languages. Each signature data collected includes both offline signature image and online signature data. The creation of this data set itself is a bold attempt. We hope to achieve a more scientific and reliable signature verification by combining signature online data and offline images. The online data contains six columns, namely X coordinate, Y coordinate, whether the stroke starts or not, whether the stroke ends or not, and pressure. Table 1 lists the signature data of the two authors. Each signature has a corresponding offline image and online data. The online curve in the table is obtained based on the X coordinate of the signature data. The abscissa of the graph represents time, and the ordinate represents the change of the X coordinate or Y coordinate of the online signature over time during the writing process. The red curve represents the real signature and the blue curve represents forged signatures, it is obvious that there is a big difference in the curve. The data will be processed, verified and fused separately in the subsequent steps.  
Figure 1: System overview.  
interval, and the change of gray scale can be obtained, which is the basis for analyzing the local pattern and arrangement rules of the image.  
Let \(f\left(x,y\right)\) denote a signature image, \(\left(x1,y1\right)\) and \(\left(x2,y2\right)\) are two points in the image, the interval is d, and the angle between the two points and the horizontal axis of the coordinate is \(\theta,f\left(x1,y1\right)=i,f\left(x2,y2\right)=j\). In this way, a matrix \(P\left(i,j,d,\theta\right)\) of various pitches and angles can be obtained. This paper analyzes the gray space position from horizontal, vertical, bottom left to top right, bottom right to top left, namely \(\theta=0\), 45, 90, 135. At the same time, this paper uses four parameters to reflect the matrix situation, namely: contrast, correlation, energy and homogeneity, as shown in the following.  
\[Con=\sum\limits_{i}\sum\limits_{j}{(i-j)^{2}P(i,j)} \tag{1}\]  
\[Corr=\left[\sum\limits_{i}\sum\limits_{j}((ij)P(i,j)-\mu x\mu y)/\sigma x\sigma y\right. \tag{2}\]  
\[Ene=\sum\limits_{i}\sum\limits_{j}{P(i,j)^{2}} \tag{3}\]  
\[Hom=\sum\limits_{i}\sum\limits_{j}{P(i,j)}/\left(1+|i-j|\right) \tag{4}\]  
HOG is used to calculate the direction statistical value of the local image gradient. The main idea is to segment the signature image, calculate the value of the gradient in each direction in the cell unit, and accumulate to form a histogram. In this paper, the cell size is set to 20 \(\times\) 20. The equations are as follows, where \(Gx(x,y)\), \(Gy(x,y)\), \(H(x,y)\) respectively represent the horizontal gradient, vertical gradient and pixel value at the pixel (\(x\),\(y\)) in the image.  
\[Gx(x,y) =H(x+1,y)-H(x-1,y) \tag{5}\] \[Gy(x,y) =H(x,y+1)-H(x,y-1)\] (6) \[G(x,y) =\sqrt{Gx(x,y)^{2}+Gy(x,y)^{2}}\] (7) \[\alpha(x,y)=cot\bigg{(}\frac{Gy(x,y)}{Gx(x,y)}\bigg{)} \tag{8}\]  
In addition, 9 geometric features are extracted, which is used to represent the global information of the image. The equations are in Table 2, where d represents the distance from point \(x1\) to \(x2\). In the subsequent experiment process, the effect of each static feature will be evaluated.