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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.

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 [

Regarding offline methods, researchers have developed signature recognition methods using a fusion algorithm involving distance and centroid orientation [

Regarding online methods, scientists have utilized fast Fourier transform (FFT) [

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 In more modern applications, the traditional template signature has been replaced by the hidden signature to minimize the mean misalignment.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 [

Deep CNN was originally developed for object classification, and reinforcement learning was developed to detect abnormal information [

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

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

Signature authentication scheme.

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,

The gray value variance

In order to obtain a better filtering effect, we define the G-L mean parameter

The local neighbor area

According to experiments we conducted, a new parameter

The G-L mean

Thus, we determine the pixel positions

Then, we design the improved Gaussian template

Deduced golden G-L filtering algorithm for mending contour damage of signature image.

Input: | The original signature image |

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Output: | The filtered image |

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Step 1: | For each pixel of |

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Step 2: | Calculate the local mean gray value |

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Step 3: | Calculate the G-L mean gray value |

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Step 4: | Calculate the improved Gaussian template according to ( |

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Step 5: | Add salt and pepper noise signature image |

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Step 6: | For each pixel, filter the noise signature image |

Note that salt and pepper noise is added to the original signature image

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.

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

Gray signature image and the histogram program as well as the influence of a threshold on the segmentation result.

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

Proposed MPT segmentation algorithm with minimum error.

Input: | The filtered image |

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Output: | The binarized image |

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Step 1: | Calculate the gray degree distribution of the filtered signature image |

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Step 2: | Calculate the two gray values |

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Step 3: | Seek the gray value |

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Step 4: | Segment the filtered image |

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

Designed CNN to solve the light distortion problem and extract the detailed frame features of a signature.

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

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

SIA algorithm for signature authentication.

Input: | Training samples of the true signature images, testing samples of the signature images, and the given error parameter |

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Output: | The recognition result for the unknown signature. |

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Step 1: | Filter each sample by using the proposed golden G-L filtering algorithm and obtain the sample set |

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Step 2: | Segment each sample of |

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Step 3: | Design the CNN structure parameters as per Figure |

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Step 4: | Build the CNN using the sample set |

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Step 5: | Calculate the over-complete dictionary |

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Step 6: | Reconstruct the true signature template |

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Step 7: | Reconstruct the unknown signature |

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Step 8: | If |

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

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.

In Section

Original signature images: (a) true and (b) fake.

Experimental result comparisons of traditional methods and developed methods: (a) the filtering and (b) the segmentation.

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.

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,

Image features obtained from the designed CNN: (a)

For the SR of the SIA, the overcomplete dictionary

The first 64 overcomplete dictionaries

Sparse coefficients

The process and result interface of the signature recognition system is shown in Figure

Signature authentication process and results.

Finally, the dictionary

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

Signature authentication comparisons.

Filtering algorithm | Contour damage mending | Filtering result for signature |
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Mean filtering | No | Better |

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Medium filtering | No | Ordinary |

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Gaussian filtering | No | Good |

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G-L filtering | Yes | Best |

Signature authentication comparisons.

Segmentation algorithm | Error rate | Segmentation effect |
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Maximum entropy | Modest | Better |

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Iterative method | Maximum | Ordinary |

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MPT algorithm | Minimum | Best |

Comparison of signature authentication algorithms.

Authentication algorithm | Accuracy | Time consumption |
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CNN | Higher | Modest |

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RS | Modest | Shortest |

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SIA algorithm | Highest | Short |

Performance comparisons.

Test No. | CNN | RS | SIA | |||
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A(%) | T(s) | A(%) | T(s) | A(%) | T(s) | |

1 | 96 | 0.8 | 93 | 0.6 | 99 | 0.6 |

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2 | 95 | 0.9 | 87 | 0.9 | 95 | 1.1 |

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3 | 94 | 1.0 | 95 | 0.5 | 99 | 0.7 |

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4 | 92 | 1.2 | 92 | 0.7 | 96 | 0.9 |

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5 | 93 | 1.1 | 91 | 0.8 | 96 | 0.7 |

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Mean value | 95 | 1.0 | 94 | 0.7 | 97 | 0.8 |

From Table

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.

The authors declare that they have no conflicts of interest.

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.