#### Abstract

A signature is a useful human feature in our society, and determining the genuineness of a signature is very important. A signature image is typically analyzed for its genuineness classification; however, increasing classification accuracy while decreasing computation time is difficult. Many factors affect image quality and the genuineness classification, such as contour damage and light distortion or the classification algorithm. To this end, we propose a mobile computing method of signature image authentication (SIA) with improved recognition accuracy and reduced computation time. We demonstrate theoretically and experimentally that the proposed golden global-local (G-L) algorithm has the best filtering result compared with the methods of mean filtering, medium filtering, and Gaussian filtering. The developed minimum probability threshold (MPT) algorithm produces the best segmentation result with minimum error compared with methods of maximum entropy and iterative segmentation. In addition, the designed convolutional neural network (CNN) solves the light distortion problem for detailed frame feature extraction of a signature image. Finally, the proposed SIA algorithm achieves the best signature authentication accuracy compared with CNN and sparse representation, and computation times are competitive. Thus, the proposed SIA algorithm can be easily implemented in a mobile phone.

#### 1. Introduction

Artificial intelligence influences the information technology being developed in today’s world. People use artificial intelligence digital information technology almost anywhere and at any time. This supports daily social life and economic activities and contributes greatly to the sustainable growth of the economy and solves various social problems [1]. A signature is a commonly used human feature for identity authentication [2–4]. Artificial intelligence approaches to signature authentication have been evolving from offline methods to online methods to meet modern demands.

Regarding offline methods, researchers have developed signature recognition methods using a fusion algorithm involving distance and centroid orientation [5]. Additionally, the single optimized dehazing method has been proposed to estimate atmospheric light and remove the haze from an image [6], and methods to ensure consistency of signature verification have been proposed [7–10]. Dissimilarity normalization, shape features, and complex network spectrums have also been developed to assist in signature verification [11–14]. In addition, scientists presented a multitask metric learning recognition method that uses true and fake samples to calculate the similarity and dissimilarity of a signature [15]. Fine geometric structures were encoded by using a mesh template and splitting the area of the subset of features to analyze and verify a signature [16, 17].

Regarding online methods, scientists have utilized fast Fourier transform (FFT) [18] and dynamic time warping (DTW) [19] methods for on-air signature verification based on video, leading to the discrete cosine transform developed for online signature verification [20]. Researchers have also developed a signature alignment verification method to obtain a best match effect on the basis of a Gaussian mixture algorithm [21]. Scientists have further developed various image-processing approaches, such as image descattering, color restoration, and image quality assessments that support signature verification activities.

Current state-of-the-art methods include deep learning and artificial intelligence. Recently, the convolutional neural network (CNN) method has become a popular research topic in many applications. Additionally, researchers have proposed deep probabilistic neural networks and optimal parameters determined by particle swarm optimization (PSO) as a signature method design. In more modern applications, the traditional template signature has been replaced by the hidden signature to minimize the mean misalignment. Scientists have applied CNN to establish a fast level set algorithm to solve the color distortion problem for wound image intensity correction and segmentation processing, which could have applications in signature verification [22].

Deep CNN was originally developed for object classification, and reinforcement learning was developed to detect abnormal information [23]. For signature image authentication (SIA), scientists have proposed the improved CNN method to process distorted samples and decrease the distortion [24, 25]. Sparse representation (SR) has been proposed for a separate feature-level fusion to integrate multiple feature representation [26]. Also, the local SR was proposed to improve robustness in cases of partial occlusion, deformation, and rotation in visual tracking [27]. The hierarchical SR was developed for synthetic aperture radar image classification [28]. In addition, researchers have developed the probabilistic class structure [29] and the sparse exponent batch processing method [30] combined with artificial intelligence methods for signature verification.

Meanwhile, mobile systems have been developing rapidly, and the above methods have not considered signature authentication applications for mobile systems, especially mobile phones. Based on the lack of such research, this paper addresses the problems of contour damage and light distortion as well as the classification accuracy of signature images. A combination of CNN and SR is proposed as a potential signature authentication method for mobile phones.

The organization of this paper is as follows: Section 2 presents the basic design for the signature authentication system, the golden global-local (G-L) filtering algorithm to solve the contour damage problem, the minimum probability threshold (MPT) segmentation algorithm to obtain the minimum error result, the CNN design for decreasing the light distortion, and the SIA algorithm to increase the recognition accuracy and obtain better speed performance. Section 3 discusses the experiments and comparisons. Finally, Section 4 concludes the paper.

#### 2. Materials And Methods

The proposed system collects signature image samples using a mobile phone with the CamScanner app. Then ACDSee software is used for image cutting creating an image size of 64 × 128 pixels. Furthermore, MATLAB is used to conduct the CNN training and the SR method design. Finally, the SIA result is obtained and presented as output.

We design the signature authentication system scheme as shown in Figure 1. First, true signature images are collected by the mobile phone. Then, the signature verification system is applied on the basis of the deduced golden G-L filtering algorithm, the proposed MPT algorithm, and the proposed SIA algorithm. Finally, the application program of the SIA is installed in a mobile phone.

##### 2.1. Derivation Of Golden G-L Filtering Algorithm For Contour Damage Mending

In order to mend the contour damage, remove noise, and smooth the signature image, a filtering process is needed first. Filtering is a convolution process of the input signature image with a core. Commonly used filtering methods are Gaussian filtering and mean filtering.

However, the Gaussian filtering effect should be improved, while mean filtering lacks scaling properties in variance and rotation symmetry. Therefore, we developed the golden G-L filtering algorithm below.

An original signature image, , occupies the total area . The global mean gray value of image iswhere is the gray value of a pixel and are the coordinates of a pixel, and and are the row number and the column number of the original signature image , respectively.

The gray value variance of the original signature image iswhere is the global mean gray value of image , is the local mean gray value of a pixel, and and were defined previously.

In order to obtain a better filtering effect, we define the G-L mean parameter by a combination of the mean filtering method with a golden section number .

The local neighbor area of a pixel is selected to be five rows and five columns, so it occupies the local area . The local mean gray value of image is thenwhere the pixel coordinates are and is the gray value of a pixel.

According to experiments we conducted, a new parameter of the G-L mean gray value is defined below.where , , is the golden section number (), and are the global area and the local area of a pixel, respectively, and , , and represent pixel coordinates.

The G-L mean is defined as the weighted sum of the global mean gray value and the local mean gray value with the golden section , and the local mean gray value is the main component of the G-L mean .

Thus, we determine the pixel positions where the gray values are equal to . where are the coordinates of a pixel of the original signature image , is the gray value of a pixel, is the global mean gray value of image , and are the pixel coordinates where the gray value is equal to .

Then, we design the improved Gaussian template as below.Finally, the G-L filtering algorithm can be described on the basis of the defined parameter and the improved Gaussian template as outlined in Table 1.

Note that salt and pepper noise is added to the original signature image in Step 5. This operation is used for mending any contour damage in the signature.

The deduced golden G-L filtering algorithm has scaling advantages in variance and rotation symmetry as well as the contour damage mending effect. This is because of the combination of the mean filtering, the Gaussian filtering and golden section of the global and local information, and the mending operation using salt and pepper noise, respectively.

##### 2.2. Proposed MPT Algorithm For Minimum Error Segmentation

To achieve the minimum error binary segmentation of a signature image, we propose the MPT algorithm on the basis of signature image analysis and the developed optimal threshold for binary segmentation.

Image segmentation sets all pixel values to 0 or 1 while the pixel positions remain invariant. This operation simplifies postprocessing. Using this technique, the binary threshold influences the result dramatically. For example, Figure 2 shows the gray signature image and the histogram as well as the influence of a threshold on the segmentation results.

For a signature image, the gray degree histogram has two peaks. One is for the background of the signature, and the other is for the signature itself. Between these two peaks, there must be a minimum point where the gray degree value corresponds to the minimum histogram value. We select this minimum gray degree value to be the threshold for binary segmentation of the filtered image . To ensure the minimum error segmentation of a signature image, the proposed MPT algorithm is described in Table 2.

##### 2.3. CNN Design For Decreasing Light Distortion

To ignore the light distortion and extract the frame construction and the special details of a signature, a CNN structure is designed, as shown in Figure 3. The CNN has the obvious advantages of local sensing, a hierarchical structure, and integration of the feature extraction and the classification. It is mainly used to verify the two-dimensional graph invariance if displacement, zoom, and other forms of distortion occur. This CNN structure is designed specifically for solving any light distortion problems.

First, the true 64 × 128 signature image is used as the input for CNN training. Second, we design the six convolution kernels (9 × 9) for the first stage of feature extraction of the true signature. The convolution layer C_{1} is composed of six images (56 × 120). Third, the sampling kernel S_{1} is selected with a size of 2 × 2 to obtain the pooling layer P_{1} which serves as the first part of the inputs to the SR classifier. Then, we design three convolution kernels (5 × 5) for feature extraction by the second stage.

The pooling layer is mapped to the convolution layer to extract the second level of features , which serves as the second part of the inputs of the SR. In the pooling layers and , the different images focus on different types of features. Some focus on the signature frame, some focus on the key points of a signature, and others focus on the changing areas of a signature. The designed CNN extracts relatively complete features from the original signature features. In this signature authentication system, the image features and work together and serve as the inputs of the SR. This CNN is applied to extract the frame construction and the special details of a signature, and eliminates any light distortion problems in a signature image.

##### 2.4. Proposed SIA Algorithm To Increase The Recognition Accuracy

In this section, we design the SIA algorithm based on CNN and SR for signature authentication. The SIA algorithm is described in Table 3.

The SR uses the least number of suitable features for reconstruction of the most complete information. Therefore, the speed of the SR classifier is relatively high. The difficulty with the SR method is to determine the solution of the optimal objective function. Thus, we must solve the two problems of obtaining the supercomplete dictionary and the nontrivial solution for sparse coefficients.

After the true signature image template SR is reconstructed, the test signature can be classified as true if the difference between the test signature image* TSI* and the reconstructed true signature image template SR is smaller than the error parameter . Otherwise, the test signature is classified as false.

#### 3. Experiments And Analysis

In this section, we demonstrate three experiments of the G-L algorithm, the MPT algorithm, and the SIA algorithm followed by comparisons and discussion. The training and testing datasets of signatures are collected from 300 students. The students include 150 males and 150 females. The true signature number is 300 and the false signature number is also 300.

##### 3.1. G-L Algorithm and MPT Algorithm Experiments

In Section 2.1, a new filtering algorithm, G-L, is developed, and the novel segmentation algorithm MPT is proposed in Section 2.2. Figure 4 shows the original signature image of the true signature and the fake signature. Figure 5 presents comparisons of the G-L filtering algorithm and the MPT segmentation algorithm to traditional methods.

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The developed G-L filtering algorithm with added salt and pepper noise has the best filtering effect compared to traditional mean filtering, medium filtering, and Gaussian filtering. The developed G-L filtering algorithm decreases the influence of signature contour damage.

The proposed MPT segmentation algorithm produces a better segmentation effect than the traditional methods of maximum entropy and iterative segmentation and has the minimum segmentation error.

##### 3.2. SIA Algorithm Experiment

For the new SIA signature authentication algorithm, 90 true signature images and 72 false signature images for each user are considered. Two-thirds of the samples of true and false images are used for CNN training, and the remaining one-third samples are used for CNN testing. Then, and obtained from the CNN are selected as the inputs of the SR. Figure 6 shows the signature features and . , and retain the frame features and the special detail features of the signature, ignoring any light distortion of the signature image.

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For the SR of the SIA, the overcomplete dictionary and the sparse coefficients are essential. They are shown in Figures 7 and 8, respectively.

The process and result interface of the signature recognition system is shown in Figure 9. First, the CNN is trained using the training samples and the test samples. Then, the six signature frame features and the 18 detailed features are obtained, and the total 24 image features (which avoid the light distortion problem) serve as the inputs of the SR.

Finally, the dictionary and the sparse coefficients* N* of the true signature are calculated, and the true signature template SR can be reconstructed. In Figure 9, a signature is input to the system to be judged as true or false by the proposed SIA algorithm. The right part shows the sparse coefficients of the 8th chancel of the* SR*, the central part is the first 36 dictionaries of the SIZE, and the left pan shows the signature authentication result.

##### 3.3. Comparisons and Discussion

Based on the theoretical analysis and the experiments, the comparison of traditional filtering methods and the developed golden G-L filtering algorithm is given in Table 4, the comparison of traditional segmentation methods and the developed MPT segmentation algorithm is given in Table 5, and the performance comparison of the traditional signature authentication methods and the proposed SIA algorithm is given in Table 6. The performance comparisons are shown in Table 7.

From Table 4, the proposed golden G-L filtering algorithm has the best signature contour damage mending and filtering result compared with the traditional methods of mean filtering, medium filtering, and Gaussian filtering. From Table 5, the developed MPT segmentation algorithm has the minimum segmentation error and produces the best signature segmentation compared with the traditional maximum entropy and iterative methods. From Table 6, the performance comparison results indicate that the proposed SIA algorithm has the highest signature authentication accuracy and acceptable time consumption performance compared with the traditional single CNN method and single SR method.

#### 4. Conclusions

It is theoretically and experimentally verified that the proposed golden G-L algorithm has the best filtering result compared with the traditional methods of mean filtering, medium filtering, and Gaussian filtering in the case where the original signature contour is damaged. Meanwhile, the developed MPT algorithm has the best segmentation results with minimum error compared with the maximum entropy and iterative segmentation methods. In addition, the designed CNN can solve the light distortion problem for the feature extraction of the frame features and the detailed features of signature images. Finally, the proposed SIA algorithm achieves the highest average signature authentication accuracy of 97%. In contrast, the average accuracies of the single CNN method and the single SR method are 95% and 94%, respectively. Consumption times are 0.8, 1.0, and 0.7 s, respective to the proposed SIA, CNN, and SR. Future work will focus on balancing and/or improving the performance between the signature authentication accuracy and the computation time of the proposed SIA algorithm.

#### Conflicts of Interest

The authors declare that they have no conflicts of interest.

#### Acknowledgments

This research was sponsored by the Natural Science Foundation of China (61300179), Key Scientific and Technological Project of Shaanxi Province (2016GY-040), and the Science Foundation of Xi’an University of Science and Technology (104-6319900001). We also thank Master students Huan Li and Min Sun for their support of data set collection.