# Simulation Evaluation of Calligraphy Art Style Relying on Fuzzy Support Vector Machine Scientific Calculation Algorithm

Authors: Wei Cai
Journal: Scientific Programming
 (2022)

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## Abstract

With the comprehensive follow-up of the information age and the rise of digital technology, the collection of calligraphy art can be preserved in the form of image data. As a testimony to the Chinese 5,000-year history, calligraphy has formed its own genre in the long river of time and its style prevailed in different periods. Nowadays, the recognition technology of characters has become advanced, but there is no better method for the recognition and classification of the artistic style of calligraphy. In addition, there are more and more counterfeiting methods, and computers alone cannot completely replace human identification; therefore, the two need to be integrated and cooperated in the identification work. This article proposes an improved fuzzy support vector machine algorithm based on the aggregation algorithm, which uses the skeleton extraction of calligraphic fonts as the main method. It uses the extracted font style and font morphological characteristics to identify the style of the work and whether it is genuine. In the article, the improvement strategy of the traditional fuzzy support vector machine is proposed, and its detection accuracy is compared with that of the traditional fuzzy support vector machine. The experimental results of this article show that the discrimination rate of authenticity cannot reach 100% and there is a certain degree of error. Through repeated experiments for many times, the value has a certain change, and when the step size is 0.1, calculating the average value can get the value of the false rejection rate and the false recognition rate.


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## Body

## 1. Introduction

Calligraphy is not only a way of communication but also a traditional culture, showing how artists use mane and ink. Support vector machine (SVM) is a new data mining method developed on the basis of statistical learning theory and has been widely used in pattern recognition and regression analysis. Moreover, traditional SVMs are prone to overlearning due to the existence of noise teaching data, so it is necessary to eliminate the influence of noise. Based on the above considerations, this article proposes a fuzzy support vector machine model. The fuzzy support vector machine gives each sample a degree of membership on the basis of the support vector machine, thereby reducing the influence of outliers and noise on the optimal decision surface. It is used in the authenticity identification system, in which the feature extraction process is the most critical, which directly determines the final result of the identification. The calligraphy characters are soft pens, which are different from the characteristics of other handwritten Chinese characters to a large extent. The strokes of calligraphic characters are wider, and there are many variations, such as dry brushes and breaks. There are many typical features extracted, and different features have different characteristics and scope of application. For example, texture features and color features cannot well express the writing style of calligraphers, so they are not suitable for the feature category of calligraphy characters. Therefore, this article mainly chooses the characteristics of strokes and structural characteristics for research. The overall structural characteristics of calligraphy fonts mainly reflect the stable shape layout of each part of calligraphy characters when calligraphers create, and different structure layouts will produce calligraphy characters with different styles. Starting from the local details, the stroke characteristics of calligraphy characters can reflect the unique writing characteristics of each calligrapher.For a long time, people always could not do without the word “style” when judging the works of calligraphers. Each calligrapher has formed stable writing characteristics in the long-term writing process, showing their unique writing style, but no two people's styles are exactly the same. Different calligraphers have their own unique writing styles, for example, Yan Zhenqing created an aesthetic paradigm of regular script calligraphy that is stern, simple and majestic, and majestic, and his cursiveness also conveys a calm, happy, heroic and free and easy master atmosphere, and the description of the characteristics of each school of calligraphy is perceptual. There is no objective and quantitative scale, so computer assistance is needed to obtain a more objective and accurate “style.” The style features of calligraphic characters are extracted by computer and represented in a digital way, which has a very important influence on the identification of authenticity.Today’s society has a detailed classification of one of the Chinese heritage of calligraphy styles, but in today’s digital storage, there are still many shortcomings in the classification of styles realized by computers. Based on the classification of font styles, to study the fuzzy support vector classification method, many scholars at home and abroad have carried out research on it. For today’s mature digital technology, calligraphic character recognition is progressing smoothly, but there is a problem of lagging in automatic classification of calligraphic styles. Nagy G has developed a special style feature to measure the style similarity of calligraphic character images of different stroke configurations and GB (or Unicode) tags. When style mark samples of the same character (i.e., the same GB code) from the same work and scribe are available, it is easiest to identify the five main styles [1]. Shin J used the nib to change the ink to express light and shade. The system uses oriental paintbrushes that are affected by water and ink volume to show scratches and spreads. In this way, users can use oriental brushes to write calligraphy on the tablet, just like real brushes, expressing a more delicate feeling [2]. Samma et al. introduced a new fuzzy support vector machine (FSVM) combined with the memetic particle swarm optimization (MPSO) algorithm. The recognition model proposed includes a linear FSVM classifier used to locate two character windows for license plates, and also a new MPSO algorithm was constructed consisting of three layers: a global optimization layer, a component optimization layer, and a local optimization layer [3]. Zhou and Qin proposed an improved membership function method; through analysis and calculation of potential support vector sample points, the adjustment factor is obtained, and the nuclei are driven to adjust in the direction away from the outliers. In this way, the degree of membership of noise and outliers is reduced, and the degree of membership of support vectors will also increase [4]. The existing feature extraction technology only pays attention to the range contour of the original scale, which limits the cognitive level of the classifier. Jia et al. research goes beyond this limitation and introduces the scale-space theory in the feature extraction of the range profile. They extracted the edge points of the distance contour and proposed a new method of multiscale target classification based on fuzzy support vector machine classifier. The experimental results show that the addition of edge points is beneficial to improve the separability of the distance profile samples. According to the weighting factor developed by the secondary entropy, the membership degree distribution of the range profile samples is optimized, and the classification performance is further improved [5]. Yang et al. proposed a Fuzzy-SVM (Support Vector Machine) geotechnical risk analysis method based on Bayesian networks. The evaluation results show that this method can solve the problem of overfitting, which often appears when using machine learning methods for geotechnical risk assessment [6]. The above scholars mostly need more complex mathematical calculations, a professional understanding of the characteristics of related algorithms and their improvement methods for the experiments and application analysis of fuzzy support vector machines, as well as research on the classification of calligraphy styles because of the lack of understanding; it is difficult to control related experiments.In the evaluation and identification of calligraphy style based on a fuzzy vector support machine, the innovations of this article are mainly manifested in two aspects. First, on the basis of the support vector machine, a fuzzy support vector machine is proposed to discriminate and classify the calligraphy style, and to a certain extent, an improved method is proposed, and the representation is modified in the process of the classification and extraction algorithm. Second, in the extraction of calligraphy-based style features, calligraphy skeleton extraction is the main method, and the skeleton extraction method selected in this article is analyzed experimentally, and the accuracy of skeleton extraction can be determined.


## 2. Basic Calculation Principle of Fuzzy Support Vector Machine

### 2.1. Principle of Support Vector Machine

Support Vector Machine is a learning algorithm proposed based on problem classification, and its basic definition is to separate the two types of samples to the greatest extent [7]. Generally speaking, all classification problems can be transformed into two-category problems. The support vector classification machine is to find the function that can separate the two categories in the best way from the function set according to the principle of structural risk minimization and has good generalization [8]. For example, in Figure 1, there are many possible hyperplanes that can separate the two types of data, but only one hyperplane can separate the two types of data with the maximum interval (maximum interval refers to the distance between the closest point in each type of data and the hyperplane), and this hyperplane is the optimal hyperplane [9].Figure 1
Schematic diagram of optimal hyperplane classification in two-dimensional space.


### 2.2. Fuzzy Support Vector Machine

Since each training data of the support vector machine plays a different role in classification during the training process, some researchers have added a degree of membership to the samples in the process [10], the sample contains abnormal data, edge points, noise, etc., and a fuzzy support vector machine is proposed [11].Suppose the training set,L=A1,B1,B1,…,A1,B1,C2, which belongs to the training point An,Bn,Cn, n=1,…,i, a certain possibility of fuzzy membership Ln. The control parameter ϑn, which measures the degree of misclassification, together determines the degree of misclassification of samples with different importance degrees [12], and the main table is Lnϑn. Convert the establishment of the optimal hyperplane into an optimal solution problem:(1)min12φ2+R∑n=1iLnϑn,α⋅An+e+ϑn≥1,ϑn≥0,n=1,…,i..In (1), R > 0 represents the penalty parameter.(2)Gα,e,ϑ,β,χ=12α⋅α+R∑n=1iLnϑn−∑n=1iβnBnα⋅An+e−1+ϑn−∑n=1iLnϑn.According to Woife definition, perform the minimum evaluation ofφ, e, ϑn in the function.(3)δGδα=α−∑n=1iβnBnAn=0.δGδe=∑n=1iβnBn=0.δGδϑn=∑n=1iLnR−βn−χn=0.Substitute (3) into (2):(4)maxMβ=∑n=1iβn−12∑n=11∑n=11βnβjBnBjAn⋅Aj,s.t∑n=1iβnBn=0,0≤β≤LnRn=1,2,…,i..At this time, the solution of the optimal function is as follows:(5)sign∑n=1iβnBnKA,An+e.The classification importance of sampleAn in the training process is represented by LnR. The larger LnR is, the less likely the sample An is to be misclassified, and the smaller the distance between the sample and the classification hyperplane is. Conversely, the greater the probability of the sample being misclassified, the greater the distance between the sample and the classification hyperplane [13]. From the actual situation, the smaller the corresponding Ln is, the smaller the LnR will be affected by it. In this case, the contribution rate of isolated points and noise to the support vector machine is greatly reduced. It can be seen that the key factor to determine the fuzzy support vector machine is the fuzzy factor Ln 1 [14].Because the greatest influence on the computational complexity of the support vector machine is the number of training samples in it, selecting a part of the samples that can be trained less is also one of the ways to improve the fuzzy support vector machine [15]. The following are the characteristics of some support vectors:(1)
Support vector machines are concentrated outside the data set and are sparsely distributed. In general, data training obeys a normal distribution, which is mainly manifested in that most the same types of data are relatively concentrated. Only a small number of data are far away from the center, and this small number of data is easy to be misclassified and most likely to become support vectors [16].(2)
The data closer to another type of training center may also become a support vector [17].(3)
In actual applications, the least support vector is obtained, and the greatest capability is obtained [18].Based on the above introduction to the characteristics of support vectors and roughly judging its basic distribution, the second improvement method is proposed here, which is to deal with abnormal data reasonably. The treatment of abnormal data in this article is to regard the abnormal data as very important and easy to be misclassified samples and assign a larger penalty value to it during the training process [19]. Less important data with no meaning for constructing the classification hyperplane are given a smaller penalty value.


## 2.1. Principle of Support Vector Machine

Support Vector Machine is a learning algorithm proposed based on problem classification, and its basic definition is to separate the two types of samples to the greatest extent [7]. Generally speaking, all classification problems can be transformed into two-category problems. The support vector classification machine is to find the function that can separate the two categories in the best way from the function set according to the principle of structural risk minimization and has good generalization [8]. For example, in Figure 1, there are many possible hyperplanes that can separate the two types of data, but only one hyperplane can separate the two types of data with the maximum interval (maximum interval refers to the distance between the closest point in each type of data and the hyperplane), and this hyperplane is the optimal hyperplane [9].Figure 1
Schematic diagram of optimal hyperplane classification in two-dimensional space.


## 2.2. Fuzzy Support Vector Machine

Since each training data of the support vector machine plays a different role in classification during the training process, some researchers have added a degree of membership to the samples in the process [10], the sample contains abnormal data, edge points, noise, etc., and a fuzzy support vector machine is proposed [11].Suppose the training set,L=A1,B1,B1,…,A1,B1,C2, which belongs to the training point An,Bn,Cn, n=1,…,i, a certain possibility of fuzzy membership Ln. The control parameter ϑn, which measures the degree of misclassification, together determines the degree of misclassification of samples with different importance degrees [12], and the main table is Lnϑn. Convert the establishment of the optimal hyperplane into an optimal solution problem:(1)min12φ2+R∑n=1iLnϑn,α⋅An+e+ϑn≥1,ϑn≥0,n=1,…,i..In (1), R > 0 represents the penalty parameter.(2)Gα,e,ϑ,β,χ=12α⋅α+R∑n=1iLnϑn−∑n=1iβnBnα⋅An+e−1+ϑn−∑n=1iLnϑn.According to Woife definition, perform the minimum evaluation ofφ, e, ϑn in the function.(3)δGδα=α−∑n=1iβnBnAn=0.δGδe=∑n=1iβnBn=0.δGδϑn=∑n=1iLnR−βn−χn=0.Substitute (3) into (2):(4)maxMβ=∑n=1iβn−12∑n=11∑n=11βnβjBnBjAn⋅Aj,s.t∑n=1iβnBn=0,0≤β≤LnRn=1,2,…,i..At this time, the solution of the optimal function is as follows:(5)sign∑n=1iβnBnKA,An+e.The classification importance of sampleAn in the training process is represented by LnR. The larger LnR is, the less likely the sample An is to be misclassified, and the smaller the distance between the sample and the classification hyperplane is. Conversely, the greater the probability of the sample being misclassified, the greater the distance between the sample and the classification hyperplane [13]. From the actual situation, the smaller the corresponding Ln is, the smaller the LnR will be affected by it. In this case, the contribution rate of isolated points and noise to the support vector machine is greatly reduced. It can be seen that the key factor to determine the fuzzy support vector machine is the fuzzy factor Ln 1 [14].Because the greatest influence on the computational complexity of the support vector machine is the number of training samples in it, selecting a part of the samples that can be trained less is also one of the ways to improve the fuzzy support vector machine [15]. The following are the characteristics of some support vectors:(1)
Support vector machines are concentrated outside the data set and are sparsely distributed. In general, data training obeys a normal distribution, which is mainly manifested in that most the same types of data are relatively concentrated. Only a small number of data are far away from the center, and this small number of data is easy to be misclassified and most likely to become support vectors [16].(2)
The data closer to another type of training center may also become a support vector [17].(3)
In actual applications, the least support vector is obtained, and the greatest capability is obtained [18].Based on the above introduction to the characteristics of support vectors and roughly judging its basic distribution, the second improvement method is proposed here, which is to deal with abnormal data reasonably. The treatment of abnormal data in this article is to regard the abnormal data as very important and easy to be misclassified samples and assign a larger penalty value to it during the training process [19]. Less important data with no meaning for constructing the classification hyperplane are given a smaller penalty value.


## 3. Calligraphy Skeleton Extraction Based on Fuzzy Support Vector Machine

Chinese calligraphy fonts can be roughly divided into four parts due to fewer strokes: horizontal (including mention), vertical, skew, and na (including dot) [20]. This article first classifies the calligraphy fonts based on fuzzy support vector machine, and then finally recognizes the calligraphy strokes [21].Since the images of calligraphy characters are mostly black, and the writing methods are various, such as paper, bamboo slips, inscriptions, etc. [22], the color and texture characteristics of calligraphy characters are not suitable. Compared with features such as texture and color, its shape is more discriminatory to calligraphic characters [23]. The skeleton feature completely retains the shape features of the calligraphy characters, maintains the original topological structure of the calligraphy characters, and removes redundant information such as the length and thickness of the strokes [24]. People can recognize the word only based on the characteristics of the skeleton, and a complete skeleton should meet the following requirements:(1)
The skeleton is single-pixel wide [25](2)
The skeleton needs to be located in the center of the stroke [26](3)
The skeleton must maintain the topological structure of the original image [27]The skeleton extraction of calligraphy characters mostly borrows the skeleton extraction algorithm of ordinary Chinese characters, and the thinning algorithm is the first to be applied to the skeleton extraction of Chinese characters. Later, methods such as the axis transformation method and mathematical morphology were gradually used for skeleton extraction [28]. However, these algorithms have many shortcomings; for example, the central axis transformation method requires high resolution of the original image and high computational complexity and cannot be calculated in parallel; the skeleton of the mathematical morphology method may not be single-pixel wide, and the algorithm’s antinoise performance is very poor. Most of these algorithms are for general printed Chinese characters or handwritten Chinese characters with thin strokes. Therefore, for Chinese characters with a length and width of 64 pixels, these algorithms are not effective.


### 3.1. Shape Decomposition

The purpose of shape decomposition is to decompose a single calligraphy character into stroke segments with a certain shape meaning so that it is conducive to the extraction of the skeleton [29]. This section mainly uses the improved K-means fuzzy clustering algorithm for image segmentation. When the membership matrix is H, R represents the number of cluster centers and i is the number of sampling points. The fuzzy membership degree of point Qnj relative to Cn is represented by Hnj; namely,(6)Hnj=∑u=1Rbn.jbt,j2m−1−1.The distances from pointQnj to center Cn and Cn are bn,j and bu,j. m∈1,∞ shows the weighted index. The relationship between the function F and the center is as follows:(7)F=∑n=1R∑j=1ihnj2bn,j,Cn=∑j=1ihnj2bαj∑j=1ihnj.The coordinate value of the centerj point is αj, first obtain R as the initial center, and then set the threshold h. If the membership of the center point exceeds h, the point is assigned to the corresponding cluster center.The boundary of the model segmentation is determined by using the method of maximum flow and minimum. The font segmentation is shown in Figure2.Figure 2
Schematic diagram of calligraphy font segmentation.


### 3.2. Extraction of the Component Skeleton

As shown in Figure3, a single point is replaced by a directional line segment, and the center line segment also has directional information as a constraint condition for clustering, which can effectively reduce the amount of calculation.Figure 3
Schematic diagram of line segment selection of cluster center.Suppose a group of values for comparison isa1,a2,a3,…,ai, and then use the clustering algorithm proposed in this article to divide it into P groups of numbers, namely, P<iL=L1,L2,…,Lp, with the clustering square sum as the grouping standard, as follows:(8)arging∑i=1p∑a1=L1pai−qαi2.Equation (8) can represent the dividing line segment of the center.The initial skeleton extraction is mainly divided into three parts: one is to initialize the calligraphy, use a two-dimensional dot matrix to represent the calligraphy notes, and then calculate the principal component line segment after the data set is zero-averaged; the second is to add a new line segment to it and add it according to the maximum descent criterion of the objective function. And compare the number of data points in the updated Voronoi diagram; if >i, the procedure is completed; otherwise, go back to step one. The third part is to adjust the principal component line segment in the original area; the fourth is the continuous cycle process 2, 3, until the output skeleton is initially formed.


## 3.1. Shape Decomposition

The purpose of shape decomposition is to decompose a single calligraphy character into stroke segments with a certain shape meaning so that it is conducive to the extraction of the skeleton [29]. This section mainly uses the improved K-means fuzzy clustering algorithm for image segmentation. When the membership matrix is H, R represents the number of cluster centers and i is the number of sampling points. The fuzzy membership degree of point Qnj relative to Cn is represented by Hnj; namely,(6)Hnj=∑u=1Rbn.jbt,j2m−1−1.The distances from pointQnj to center Cn and Cn are bn,j and bu,j. m∈1,∞ shows the weighted index. The relationship between the function F and the center is as follows:(7)F=∑n=1R∑j=1ihnj2bn,j,Cn=∑j=1ihnj2bαj∑j=1ihnj.The coordinate value of the centerj point is αj, first obtain R as the initial center, and then set the threshold h. If the membership of the center point exceeds h, the point is assigned to the corresponding cluster center.The boundary of the model segmentation is determined by using the method of maximum flow and minimum. The font segmentation is shown in Figure2.Figure 2
Schematic diagram of calligraphy font segmentation.


## 3.2. Extraction of the Component Skeleton

As shown in Figure3, a single point is replaced by a directional line segment, and the center line segment also has directional information as a constraint condition for clustering, which can effectively reduce the amount of calculation.Figure 3
Schematic diagram of line segment selection of cluster center.Suppose a group of values for comparison isa1,a2,a3,…,ai, and then use the clustering algorithm proposed in this article to divide it into P groups of numbers, namely, P<iL=L1,L2,…,Lp, with the clustering square sum as the grouping standard, as follows:(8)arging∑i=1p∑a1=L1pai−qαi2.Equation (8) can represent the dividing line segment of the center.The initial skeleton extraction is mainly divided into three parts: one is to initialize the calligraphy, use a two-dimensional dot matrix to represent the calligraphy notes, and then calculate the principal component line segment after the data set is zero-averaged; the second is to add a new line segment to it and add it according to the maximum descent criterion of the objective function. And compare the number of data points in the updated Voronoi diagram; if >i, the procedure is completed; otherwise, go back to step one. The third part is to adjust the principal component line segment in the original area; the fourth is the continuous cycle process 2, 3, until the output skeleton is initially formed.


## 4. Calligraphy Style Stroke Extraction Based on Fuzzy Support Vector Machine

The stroke extraction of calligraphy characters faces many problems, mainly including the following. l) There are variations in the thickness of calligraphy characters: the writing tool of calligraphy characters is a brush, the strokes are relatively thick, and the order of the strokes leads to rich changes in the thickness of the strokes. (2) There are many changes in font shape: because the fonts of different calligraphy characters are very different in different font shapes, the strokes are often uneven horizontally and vertically, so it is very difficult to accurately find the inflection point. (3) Severe noise: due to long-term weathering and corrosion, the handed-down historical calligraphy works will leave many fuzzy places, resulting in obvious potholes in the borders of the strokes and severe damage due to time. Thus, it is unrealistic to automatically decompose clear and complete strokes just like printed ones, and the four-stroke primitives in calligraphy characters must be extracted based on the unique writing characteristics of calligraphy characters. Since the skeleton features of the characters have been extracted above, it provides a basis for extracting strokes, so this article adopts the skeleton-based stroke extraction method. The basic process is as follows: (1) extract the skeleton of the calligraphy character; (2) divide the strokes; (3) determine the intersection of the skeletons, and use the strokes to generate independent strokes according to the rule of stroke combination. The strokes are part of the strokes of Chinese characters; that is, the strokes are composed of strokes. The process of extracting strokes can be decomposed into two processes: the extraction of strokes and the synthesis of strokes, and the relationship between pens and paragraphs includes intersection and separation. Since the component skeleton is generated during the skeleton extraction, the process of the growth of the pen segment is as follows:(1)
Take the random unmerged skeleton segment in the dataset as the starting point. If an intersection point is encountered, it is adjacent to a cluster of intersection points atR>2, and the point has two adjacent points, and the rule of whether to include the next point is determined by the slope of the corner Hqit,qio,qout.(9)Hqit,qio,qout=argminBout−BioAout−Aio−Bio−BitAio−Ait.The point in the intersection cluster in the equation is represented asqio, and the point in the out point is qout, and the selection will include the point in the direction with the smallest value of the corner slope. The physical performance is that the writing of the font is always in the most convenient and fastest direction, which means that the intersection is in the direction with the largest angle.(2)
When encountering a common connection point, include the connection point, and track the sequence of pen segments where the connection point is located, and include all connection points in the sequence;(3)
When encountering the two situations of the endpoint or the adjacent cluster point of the current point, there is no point out of the adjacent cluster points, stop the growth and go to step (1); otherwise, exit after the current stroke growth is completed.


### 4.1. Morphological Characteristics of Calligraphy Strokes

In the computer field, the strokes are regarded as composed of many points and curve segments. Therefore, the model can be used to vividly represent the basic strokes, and the data structure can be used for storage so that the computer can recognize the primitives of the strokes. The extraction of calligraphic characters’ stroke features includes extracting the overall morphological features and local features of the calligraphic characters. The overall characteristics mainly include the shape of the structure, the position of the center of gravity, the distribution of geometric moments, and the distribution of ink marks; the local characteristics of the calligraphy stroke include the key points of the skeleton of the stroke, the characteristics between the skeleton segments, etc. Specifically, there are features, such as stroke entropy, pen pressure, elevation angle, perturbation degree, and curvature.


#### 4.1.1. Stroke Trajectory When Writing

Since during the writing process, the speed, rhythm, and strength of the pen will affect the generation of strokes, this article uses the concept of stroke entropy for the special writing method of calligraphy characters. Stroke entropy is used to measure the degree of twisting of a character’s stroke trajectory, covering a series of influencing factors such as speed, rhythm, and strength of holding the pen. The steps to describe stroke entropyFg are as follows:(10)Fg=∑n=18xbn×logxbn.(11)xbn=Δcot,=nleng.In (11), the code value cot in 8 directions has a certain correlation with the chain code length. When the writing stroke is a straight line, the entropy of the stroke is the minimum; when the proportion of the eight directions is equal, the entropy of the stroke Fg=0 is the maximum, and the writing trajectory is a perfect circle, indicating that the greater the curvature, the greater the value.


#### 4.1.2. Pen Pressure

In this section, we study the pressure characteristics of the strokes; the pen pressure reflects the intensity of the pen and the changes in the intensity of the pen when the author writes, which can be reflected indirectly by the changes in the thickness of the strokes. Therefore, it can be inferred that the pen pressure is linearly proportional to the thickness of the stroke, and the thickness change of the strokes can be obtained by the distance between the outlines of the strokes. In this article, a differential operator is used to extract the direction information of Chinese characters so as to calculate the change curve of pen pressure characteristics; in addition, the pen pressure feature is mainly for the running pen part, and the beginning and ending pen parts are not the research objects. Therefore, when measuring the width of the strokes, it should omit the part of the pen and the pen and only calculate the part of the pen. Take the feature extraction of “horizontal” strokes as an example, as shown in Figure4.Figure 4
Schematic diagram of calligraphy feature extraction. (a) Sketch of writing pen. (b) Sketch of handwriting measurement.
(a)(b)First, assume that the starting point of the calligraphy pen isQ and the ending point is P, and then the width of the two points is AQ and AP, respectively. To calculate the feature vector, first, find the points E and F where the maximum value AE and minimum value AF are located and the corresponding values. Namely, the distance between the start and endpoints AQP and the distance between the start point and the maximum and minimum values AQE, AQF can be expressed as follows:(12)K1=AQAP,K2=AQAE,K3=AQAF,K4=AQEAQP,K5=AQFAQP.Assume that theg value of the X-th feature sample of the nth writer is Knxg, of which n=1,2,3,…,i; g=1,2,3,…,i.


#### 4.1.3. Slope and Curvature

First, assume the coordinate points of the calligraphy skeleton, and the slopeX and curvature R of the written strokes should be defined using the starting point coordinate AE,BE and the ending point coordinate AF,BF of the skeleton:(13)X=AE−AEBE−BF,R=DEDE+1+⋯+DR−1DRDEDR.The Euclidean distance from pointDE to point DF is represented by DEDF.


#### 4.1.4. Elevation Angle and Disturbance

The elevation angle of the stroke is a feature that describes the degree of inclination of the stroke, and the style of the calligrapher Yan Zhenqing is horizontal and vertical. When a calligraphy character contains K strokes of the same type, the average elevation angle of the strokes can be expressed as follows:(14)Fn=1K∑n=1xBnE−BnFAnE−AnF.In the equation,AnE,BnE and AnF,BnF represent the starting point and ending point of the pen, respectively.Every calligrapher has their own pen-handling habits when they write. For example, when we press the pen, we will press it again, and we will be frivolous when we lift the pen. Different people have different pen strokes and directions. These actions make the strokes appear in a distorted form, and this kind of phenomenon is described as a disturbance.The degree of perturbation can be defined according to the stroke outline and skeleton, as shown in Figure5.Figure 5
Schematic diagram of the stroke distortion area ratio.The two endpoints of the pen areCs, Cz, and assume that the intersection point between the two endpoints and the skeleton is C, and then define the degree of disturbance according to(15)p=T1T2T2≠0,0T2=0..


#### 4.1.5. Jitter and Curve

Beginners will not do it all at once when copying the original but will observe the original while writing. Therefore, although the overall font of the copied work is very similar to the original, there will always be phenomena such as uneven strokes, uneven ink color, and wrinkles. Figure6(a) shows a copy of Wu Changshuo’s calligraphy characters and magnifies the jitter part of the strokes, while Figure 6(b) shows the authentic calligraphy characters. Comparing the magnified parts of the two characters, it is obvious that the copy works are more authentic, with more obvious jitter on the edges of the strokes and more wrinkles.Figure 6
An enlarged schematic diagram of handwriting jitter. (a) Imitator’s handwriting. (b) Authentic handwriting.
(a)(b)Consequently, the tiny wrinkles will be absorbed as the object gradually shrinks and thus disappear. Therefore, the jitter degree can be expressed as follows:(16)Jitterin=LengorigLengzoom.Among them,Lengorig, Lengzoom represent the contour length before and after the calligraphy scaling, respectively.


### 4.2. The Morphological Characteristics of Calligraphy Fonts

The structure feature of calligraphy characters refers to the structure of the square characters, such as Chinese characters, which reflects the overall structure of calligraphy characters. The characterization of the morphological structure of the knot played an important role in the writing style of the calligrapher. The morphological characteristics of calligraphy characters are mainly represented by the characteristics of the structure, the position of the center of gravity, the distribution of geometric moments, and the ink distribution ratio. The shape of the structure is expressed by the aspect ratio of the calligraphy; the location of the center of gravity reflects the structural characteristics of calligraphy characters; the ink changes of calligraphy characters indicate the changes in pen pressure and the tilt of the pen during writing. The width of the ink mark in the middle of the calligraphy strokes and the width in the horizontal direction are used to describe the density of ink marks.


#### 4.2.1. Knot Shape

It is very important to measure the shape of the font for the characteristics of calligraphy style, and the shape of the font written by different calligraphers is bound to be different. The average aspect ratio to express the structure shape is as follows:(17)ratiojq=1K∑heigwidt.


#### 4.2.2. The Position of the Center of Gravity

Most of the time, the position of the center of gravity is not at the center of the character, and there is a certain degree of deviation; however, the deviation will show a uniform trend for different writing habits. In the image function of F(A, B), for the font height H and width V, the second-order moment can be expressed as follows:(18)X=AE−AEBE−BF,R=DEDE+1+⋯+DR−1DRDEDR.At this time, the center of gravityA^,B^ of the font can be expressed as follows:(19)A^=H10H00,B^=H01H00.


#### 4.2.3. Geometric Moment Distribution

Because of the different writing habits, the inclination of the central axis is different. In order to measure the inclination, the defined central momentSmn is used; namely,(20)Smn=∑A=0A=H−1∑B=0B=V−1A−A^mB−B^nFA,B.Equation (20) can reflect the degree of ink change in the horizontal direction. After dividing the ink dots into positive Z30+ and negative Z30− on the horizontal axis, we can measure the weight of the pen on the left and right of the center axis of the calligraphy font:(21)Hs=Z30+Z30++Z30−.In the same way, measuring the pen pressure of the calligraphy font on the upper and lower axis is as follows:(22)Hy=Z30+Z30++Z30−.


#### 4.2.4. Ink Distribution Ratio

Based on the different pen-handling habits of different writers, there are certain differences in how many times the inks are distributed. The skeleton extraction divides it into two partsW1, W2 and assumes the ink distribution obtained by statistics to be T1, T2 to calculate the ratio of the ink:(23)T1=∑A,BAi,BimaxA−Ai∧B=Bi,B−Bi∧A=Ai,T2=∑A,BAi,BimaxA−Ai∧B=Bi,B−Bi∧A=Ai.The final ink distribution ratio isG:(24)G=T1HT2H.The numbers of center points of the two partsW1 and W2 are T and H.


## 4.1. Morphological Characteristics of Calligraphy Strokes

In the computer field, the strokes are regarded as composed of many points and curve segments. Therefore, the model can be used to vividly represent the basic strokes, and the data structure can be used for storage so that the computer can recognize the primitives of the strokes. The extraction of calligraphic characters’ stroke features includes extracting the overall morphological features and local features of the calligraphic characters. The overall characteristics mainly include the shape of the structure, the position of the center of gravity, the distribution of geometric moments, and the distribution of ink marks; the local characteristics of the calligraphy stroke include the key points of the skeleton of the stroke, the characteristics between the skeleton segments, etc. Specifically, there are features, such as stroke entropy, pen pressure, elevation angle, perturbation degree, and curvature.


### 4.1.1. Stroke Trajectory When Writing

Since during the writing process, the speed, rhythm, and strength of the pen will affect the generation of strokes, this article uses the concept of stroke entropy for the special writing method of calligraphy characters. Stroke entropy is used to measure the degree of twisting of a character’s stroke trajectory, covering a series of influencing factors such as speed, rhythm, and strength of holding the pen. The steps to describe stroke entropyFg are as follows:(10)Fg=∑n=18xbn×logxbn.(11)xbn=Δcot,=nleng.In (11), the code value cot in 8 directions has a certain correlation with the chain code length. When the writing stroke is a straight line, the entropy of the stroke is the minimum; when the proportion of the eight directions is equal, the entropy of the stroke Fg=0 is the maximum, and the writing trajectory is a perfect circle, indicating that the greater the curvature, the greater the value.


### 4.1.2. Pen Pressure

In this section, we study the pressure characteristics of the strokes; the pen pressure reflects the intensity of the pen and the changes in the intensity of the pen when the author writes, which can be reflected indirectly by the changes in the thickness of the strokes. Therefore, it can be inferred that the pen pressure is linearly proportional to the thickness of the stroke, and the thickness change of the strokes can be obtained by the distance between the outlines of the strokes. In this article, a differential operator is used to extract the direction information of Chinese characters so as to calculate the change curve of pen pressure characteristics; in addition, the pen pressure feature is mainly for the running pen part, and the beginning and ending pen parts are not the research objects. Therefore, when measuring the width of the strokes, it should omit the part of the pen and the pen and only calculate the part of the pen. Take the feature extraction of “horizontal” strokes as an example, as shown in Figure4.Figure 4
Schematic diagram of calligraphy feature extraction. (a) Sketch of writing pen. (b) Sketch of handwriting measurement.
(a)(b)First, assume that the starting point of the calligraphy pen isQ and the ending point is P, and then the width of the two points is AQ and AP, respectively. To calculate the feature vector, first, find the points E and F where the maximum value AE and minimum value AF are located and the corresponding values. Namely, the distance between the start and endpoints AQP and the distance between the start point and the maximum and minimum values AQE, AQF can be expressed as follows:(12)K1=AQAP,K2=AQAE,K3=AQAF,K4=AQEAQP,K5=AQFAQP.Assume that theg value of the X-th feature sample of the nth writer is Knxg, of which n=1,2,3,…,i; g=1,2,3,…,i.


### 4.1.3. Slope and Curvature

First, assume the coordinate points of the calligraphy skeleton, and the slopeX and curvature R of the written strokes should be defined using the starting point coordinate AE,BE and the ending point coordinate AF,BF of the skeleton:(13)X=AE−AEBE−BF,R=DEDE+1+⋯+DR−1DRDEDR.The Euclidean distance from pointDE to point DF is represented by DEDF.


### 4.1.4. Elevation Angle and Disturbance

The elevation angle of the stroke is a feature that describes the degree of inclination of the stroke, and the style of the calligrapher Yan Zhenqing is horizontal and vertical. When a calligraphy character contains K strokes of the same type, the average elevation angle of the strokes can be expressed as follows:(14)Fn=1K∑n=1xBnE−BnFAnE−AnF.In the equation,AnE,BnE and AnF,BnF represent the starting point and ending point of the pen, respectively.Every calligrapher has their own pen-handling habits when they write. For example, when we press the pen, we will press it again, and we will be frivolous when we lift the pen. Different people have different pen strokes and directions. These actions make the strokes appear in a distorted form, and this kind of phenomenon is described as a disturbance.The degree of perturbation can be defined according to the stroke outline and skeleton, as shown in Figure5.Figure 5
Schematic diagram of the stroke distortion area ratio.The two endpoints of the pen areCs, Cz, and assume that the intersection point between the two endpoints and the skeleton is C, and then define the degree of disturbance according to(15)p=T1T2T2≠0,0T2=0..


### 4.1.5. Jitter and Curve

Beginners will not do it all at once when copying the original but will observe the original while writing. Therefore, although the overall font of the copied work is very similar to the original, there will always be phenomena such as uneven strokes, uneven ink color, and wrinkles. Figure6(a) shows a copy of Wu Changshuo’s calligraphy characters and magnifies the jitter part of the strokes, while Figure 6(b) shows the authentic calligraphy characters. Comparing the magnified parts of the two characters, it is obvious that the copy works are more authentic, with more obvious jitter on the edges of the strokes and more wrinkles.Figure 6
An enlarged schematic diagram of handwriting jitter. (a) Imitator’s handwriting. (b) Authentic handwriting.
(a)(b)Consequently, the tiny wrinkles will be absorbed as the object gradually shrinks and thus disappear. Therefore, the jitter degree can be expressed as follows:(16)Jitterin=LengorigLengzoom.Among them,Lengorig, Lengzoom represent the contour length before and after the calligraphy scaling, respectively.


## 4.1.1. Stroke Trajectory When Writing

Since during the writing process, the speed, rhythm, and strength of the pen will affect the generation of strokes, this article uses the concept of stroke entropy for the special writing method of calligraphy characters. Stroke entropy is used to measure the degree of twisting of a character’s stroke trajectory, covering a series of influencing factors such as speed, rhythm, and strength of holding the pen. The steps to describe stroke entropyFg are as follows:(10)Fg=∑n=18xbn×logxbn.(11)xbn=Δcot,=nleng.In (11), the code value cot in 8 directions has a certain correlation with the chain code length. When the writing stroke is a straight line, the entropy of the stroke is the minimum; when the proportion of the eight directions is equal, the entropy of the stroke Fg=0 is the maximum, and the writing trajectory is a perfect circle, indicating that the greater the curvature, the greater the value.


## 4.1.2. Pen Pressure

In this section, we study the pressure characteristics of the strokes; the pen pressure reflects the intensity of the pen and the changes in the intensity of the pen when the author writes, which can be reflected indirectly by the changes in the thickness of the strokes. Therefore, it can be inferred that the pen pressure is linearly proportional to the thickness of the stroke, and the thickness change of the strokes can be obtained by the distance between the outlines of the strokes. In this article, a differential operator is used to extract the direction information of Chinese characters so as to calculate the change curve of pen pressure characteristics; in addition, the pen pressure feature is mainly for the running pen part, and the beginning and ending pen parts are not the research objects. Therefore, when measuring the width of the strokes, it should omit the part of the pen and the pen and only calculate the part of the pen. Take the feature extraction of “horizontal” strokes as an example, as shown in Figure4.Figure 4
Schematic diagram of calligraphy feature extraction. (a) Sketch of writing pen. (b) Sketch of handwriting measurement.
(a)(b)First, assume that the starting point of the calligraphy pen isQ and the ending point is P, and then the width of the two points is AQ and AP, respectively. To calculate the feature vector, first, find the points E and F where the maximum value AE and minimum value AF are located and the corresponding values. Namely, the distance between the start and endpoints AQP and the distance between the start point and the maximum and minimum values AQE, AQF can be expressed as follows:(12)K1=AQAP,K2=AQAE,K3=AQAF,K4=AQEAQP,K5=AQFAQP.Assume that theg value of the X-th feature sample of the nth writer is Knxg, of which n=1,2,3,…,i; g=1,2,3,…,i.


## 4.1.3. Slope and Curvature

First, assume the coordinate points of the calligraphy skeleton, and the slopeX and curvature R of the written strokes should be defined using the starting point coordinate AE,BE and the ending point coordinate AF,BF of the skeleton:(13)X=AE−AEBE−BF,R=DEDE+1+⋯+DR−1DRDEDR.The Euclidean distance from pointDE to point DF is represented by DEDF.


## 4.1.4. Elevation Angle and Disturbance

The elevation angle of the stroke is a feature that describes the degree of inclination of the stroke, and the style of the calligrapher Yan Zhenqing is horizontal and vertical. When a calligraphy character contains K strokes of the same type, the average elevation angle of the strokes can be expressed as follows:(14)Fn=1K∑n=1xBnE−BnFAnE−AnF.In the equation,AnE,BnE and AnF,BnF represent the starting point and ending point of the pen, respectively.Every calligrapher has their own pen-handling habits when they write. For example, when we press the pen, we will press it again, and we will be frivolous when we lift the pen. Different people have different pen strokes and directions. These actions make the strokes appear in a distorted form, and this kind of phenomenon is described as a disturbance.The degree of perturbation can be defined according to the stroke outline and skeleton, as shown in Figure5.Figure 5
Schematic diagram of the stroke distortion area ratio.The two endpoints of the pen areCs, Cz, and assume that the intersection point between the two endpoints and the skeleton is C, and then define the degree of disturbance according to(15)p=T1T2T2≠0,0T2=0..


## 4.1.5. Jitter and Curve

Beginners will not do it all at once when copying the original but will observe the original while writing. Therefore, although the overall font of the copied work is very similar to the original, there will always be phenomena such as uneven strokes, uneven ink color, and wrinkles. Figure6(a) shows a copy of Wu Changshuo’s calligraphy characters and magnifies the jitter part of the strokes, while Figure 6(b) shows the authentic calligraphy characters. Comparing the magnified parts of the two characters, it is obvious that the copy works are more authentic, with more obvious jitter on the edges of the strokes and more wrinkles.Figure 6
An enlarged schematic diagram of handwriting jitter. (a) Imitator’s handwriting. (b) Authentic handwriting.
(a)(b)Consequently, the tiny wrinkles will be absorbed as the object gradually shrinks and thus disappear. Therefore, the jitter degree can be expressed as follows:(16)Jitterin=LengorigLengzoom.Among them,Lengorig, Lengzoom represent the contour length before and after the calligraphy scaling, respectively.


## 4.2. The Morphological Characteristics of Calligraphy Fonts

The structure feature of calligraphy characters refers to the structure of the square characters, such as Chinese characters, which reflects the overall structure of calligraphy characters. The characterization of the morphological structure of the knot played an important role in the writing style of the calligrapher. The morphological characteristics of calligraphy characters are mainly represented by the characteristics of the structure, the position of the center of gravity, the distribution of geometric moments, and the ink distribution ratio. The shape of the structure is expressed by the aspect ratio of the calligraphy; the location of the center of gravity reflects the structural characteristics of calligraphy characters; the ink changes of calligraphy characters indicate the changes in pen pressure and the tilt of the pen during writing. The width of the ink mark in the middle of the calligraphy strokes and the width in the horizontal direction are used to describe the density of ink marks.


### 4.2.1. Knot Shape

It is very important to measure the shape of the font for the characteristics of calligraphy style, and the shape of the font written by different calligraphers is bound to be different. The average aspect ratio to express the structure shape is as follows:(17)ratiojq=1K∑heigwidt.


### 4.2.2. The Position of the Center of Gravity

Most of the time, the position of the center of gravity is not at the center of the character, and there is a certain degree of deviation; however, the deviation will show a uniform trend for different writing habits. In the image function of F(A, B), for the font height H and width V, the second-order moment can be expressed as follows:(18)X=AE−AEBE−BF,R=DEDE+1+⋯+DR−1DRDEDR.At this time, the center of gravityA^,B^ of the font can be expressed as follows:(19)A^=H10H00,B^=H01H00.


### 4.2.3. Geometric Moment Distribution

Because of the different writing habits, the inclination of the central axis is different. In order to measure the inclination, the defined central momentSmn is used; namely,(20)Smn=∑A=0A=H−1∑B=0B=V−1A−A^mB−B^nFA,B.Equation (20) can reflect the degree of ink change in the horizontal direction. After dividing the ink dots into positive Z30+ and negative Z30− on the horizontal axis, we can measure the weight of the pen on the left and right of the center axis of the calligraphy font:(21)Hs=Z30+Z30++Z30−.In the same way, measuring the pen pressure of the calligraphy font on the upper and lower axis is as follows:(22)Hy=Z30+Z30++Z30−.


### 4.2.4. Ink Distribution Ratio

Based on the different pen-handling habits of different writers, there are certain differences in how many times the inks are distributed. The skeleton extraction divides it into two partsW1, W2 and assumes the ink distribution obtained by statistics to be T1, T2 to calculate the ratio of the ink:(23)T1=∑A,BAi,BimaxA−Ai∧B=Bi,B−Bi∧A=Ai,T2=∑A,BAi,BimaxA−Ai∧B=Bi,B−Bi∧A=Ai.The final ink distribution ratio isG:(24)G=T1HT2H.The numbers of center points of the two partsW1 and W2 are T and H.


## 4.2.1. Knot Shape

It is very important to measure the shape of the font for the characteristics of calligraphy style, and the shape of the font written by different calligraphers is bound to be different. The average aspect ratio to express the structure shape is as follows:(17)ratiojq=1K∑heigwidt.


## 4.2.2. The Position of the Center of Gravity

Most of the time, the position of the center of gravity is not at the center of the character, and there is a certain degree of deviation; however, the deviation will show a uniform trend for different writing habits. In the image function of F(A, B), for the font height H and width V, the second-order moment can be expressed as follows:(18)X=AE−AEBE−BF,R=DEDE+1+⋯+DR−1DRDEDR.At this time, the center of gravityA^,B^ of the font can be expressed as follows:(19)A^=H10H00,B^=H01H00.


## 4.2.3. Geometric Moment Distribution

Because of the different writing habits, the inclination of the central axis is different. In order to measure the inclination, the defined central momentSmn is used; namely,(20)Smn=∑A=0A=H−1∑B=0B=V−1A−A^mB−B^nFA,B.Equation (20) can reflect the degree of ink change in the horizontal direction. After dividing the ink dots into positive Z30+ and negative Z30− on the horizontal axis, we can measure the weight of the pen on the left and right of the center axis of the calligraphy font:(21)Hs=Z30+Z30++Z30−.In the same way, measuring the pen pressure of the calligraphy font on the upper and lower axis is as follows:(22)Hy=Z30+Z30++Z30−.


## 4.2.4. Ink Distribution Ratio

Based on the different pen-handling habits of different writers, there are certain differences in how many times the inks are distributed. The skeleton extraction divides it into two partsW1, W2 and assumes the ink distribution obtained by statistics to be T1, T2 to calculate the ratio of the ink:(23)T1=∑A,BAi,BimaxA−Ai∧B=Bi,B−Bi∧A=Ai,T2=∑A,BAi,BimaxA−Ai∧B=Bi,B−Bi∧A=Ai.The final ink distribution ratio isG:(24)G=T1HT2H.The numbers of center points of the two partsW1 and W2 are T and H.


## 5. Calligraphy Style Feature Recognition Analysis Based on FSV

The identification system is roughly divided into five steps: data collection, preprocessing, feature extraction, diagnosis matching, and performance evaluation. The style of calligraphy works can be divided into three levels from overall to partial: overall layout style, structure style, and stroke style. The overall layout style refers to the row and column spacing, layout, etc., of the calligraphy characters in the whole work; synthetic style refers to the structural characteristics of the character, such as the ratio of length to width, the position of the center of gravity, the distribution of ink marks, etc.; stroke style refers to the characteristics of the stroke level, such as stroke width, stroke pressure, stroke entropy, and features between small strokes. The workflow for calculating the probability of authenticity of suspicious works is shown in Figures7 and 8.Figure 7
Schematic diagram of the authenticity identification process of calligraphy works.Figure 8
Calligraphy appraisal evaluation process.


### 5.1. Experimental Analysis of Calligraphy Font Skeleton Extraction

The calculation effect of the actual algorithm in this article is explored, and the central axis transformation method is used as the comparison algorithm, and the skeleton feature of the font is extracted from 100 samples.As shown in Table1 and Figure 9, the running time of the improved algorithm in this article is about 30% lower than that of the central axis transformation method, which improves the calculation speed to a certain extent. In terms of space complexity, the improved algorithm in this article is equivalent to the central axis transformation algorithm. Although the algorithm in this article has performed a step-by-step calculation, it does not increase the space complexity and is still O(n2). Therefore, the improved algorithm in this article can effectively reduce the computing time without increasing the space complexity.Table 1
Comparison of experimental methods.
AlgorithmNumber of imagesAverage refinement timeRefinement effectAxis exchange algorithm1000.87Obvious distortion at the bifurcation, with small burrsAlgorithm1000.83The skeleton is more reasonableFigure 9
Comparison of two algorithms. (a) Algorithm running time. (b) Comparison of the time of the two algorithms.
(a)(b)


### 5.2. Experimental Analysis of the Advancing Strategy of FSVM

Based on the characteristics of calligraphy and handwriting, the recognition accuracy of the improved FSVM model in this article is compared with the recognition accuracy of SVMs based on linear aggregation:As shown in Figure10, through the comparison of the training accuracy of the two, the training accuracy and testing accuracy of the improved FSVM are both higher than those of SVMs. In this article, the K-means clustering algorithm is used in the recognition and classification of calligraphy fonts. Here, the traditional K-means aggregation algorithm and FCM method are used for all the data to experiment on the operating efficiency and accuracy of the system. As shown in Table 2, focus on reducing the impact of redundant information on later classification.Figure 10
Comparison of training accuracy between (a) FSVMs and (b) SVMs.
(a)(b)Table 2
The influence of FMC weight index on classification accuracy.
GroupWeight indexAccuracy1.1.079.22.1.580.53.1.783.64.2.085.35.2.287.66.2.484.97.2.585.38.2.785.79.3.084.4As shown in Figure11, it is the detection accuracy of handwritten font recognition by FSVMs.Figure 11
Traditional and improved FSVMs recognition performance: (a) traditional FSVMs; (b) improved FSVMs.
(a)(b)As shown in Figure11, the traditional fuzzy support vector machine is not the best classifier, and the improved fuzzy support vector machine performs better. The improved fuzzy support vector machine only needs 398 data in 455 training samples to form a better classification hyperplane, and the calculation time is also significantly reduced.


### 5.3. Results of System Identification and Evaluation of Authenticity

This article uses false recognition rate and false rejection rate to define system performance, and the choice of threshold directly determines the effect of feature selection. The definition of false recognition rate is the probability that the actual product is a fake but is misjudged as a genuine product; the definition of rejection rate is the probability that the actual product is a genuine product is misjudged as a fake. Starting from the definition of false recognition rate and false rejection rate, if all the works to be tested are judged to be fakes, the rejection rate is 100%, and the false recognition rate is 0%; if the works to be tested are judged to be genuine, the false recognition rate is 100%, and the rejection rate is 0%. If the false recognition rate and the false rejection rate are both 0%, the system reaches the ideal state. However, in actual operation, it is impossible for the false recognition rate and the rejection rate to be 0% at the same time.The optimal value obtained by calculation, as shown in Figure12, is a representation of the distribution of calligraphic features, from which the optimal threshold point can be seen.Figure 12
Schematic diagram of the optimal threshold.The style of today’s calligraphy works is basically a legacy of history. Therefore, the available research samples are limited, which makes the samples for model training relatively insufficient. Therefore, the discrimination rate of authenticity cannot reach 100%, and there is a certain degree of error. Through repeated experiments many times, the value has a certain change, and when the step size is 0.1, calculating the average value can get the value of the false rejection rate and the false recognition rate.As shown in Figure13(a), the more discriminatory the style features, the better the discriminating effect.Figure 13
Appraisal and evaluation chart: (a) comparison chart of authenticity rate; (b) change of accuracy rate with grid window.
(a)(b)The preprocessed calligraphy images are all normalized images, and the selection of the grid window size is involved in the feature extraction process at this time. If the selected window is too small, it will cause insufficient information to be obtained. As shown in Figure13(b), a 13 × 13 grid window is better for extracting feature information.


## 5.1. Experimental Analysis of Calligraphy Font Skeleton Extraction

The calculation effect of the actual algorithm in this article is explored, and the central axis transformation method is used as the comparison algorithm, and the skeleton feature of the font is extracted from 100 samples.As shown in Table1 and Figure 9, the running time of the improved algorithm in this article is about 30% lower than that of the central axis transformation method, which improves the calculation speed to a certain extent. In terms of space complexity, the improved algorithm in this article is equivalent to the central axis transformation algorithm. Although the algorithm in this article has performed a step-by-step calculation, it does not increase the space complexity and is still O(n2). Therefore, the improved algorithm in this article can effectively reduce the computing time without increasing the space complexity.Table 1
Comparison of experimental methods.
AlgorithmNumber of imagesAverage refinement timeRefinement effectAxis exchange algorithm1000.87Obvious distortion at the bifurcation, with small burrsAlgorithm1000.83The skeleton is more reasonableFigure 9
Comparison of two algorithms. (a) Algorithm running time. (b) Comparison of the time of the two algorithms.
(a)(b)


## 5.2. Experimental Analysis of the Advancing Strategy of FSVM

Based on the characteristics of calligraphy and handwriting, the recognition accuracy of the improved FSVM model in this article is compared with the recognition accuracy of SVMs based on linear aggregation:As shown in Figure10, through the comparison of the training accuracy of the two, the training accuracy and testing accuracy of the improved FSVM are both higher than those of SVMs. In this article, the K-means clustering algorithm is used in the recognition and classification of calligraphy fonts. Here, the traditional K-means aggregation algorithm and FCM method are used for all the data to experiment on the operating efficiency and accuracy of the system. As shown in Table 2, focus on reducing the impact of redundant information on later classification.Figure 10
Comparison of training accuracy between (a) FSVMs and (b) SVMs.
(a)(b)Table 2
The influence of FMC weight index on classification accuracy.
GroupWeight indexAccuracy1.1.079.22.1.580.53.1.783.64.2.085.35.2.287.66.2.484.97.2.585.38.2.785.79.3.084.4As shown in Figure11, it is the detection accuracy of handwritten font recognition by FSVMs.Figure 11
Traditional and improved FSVMs recognition performance: (a) traditional FSVMs; (b) improved FSVMs.
(a)(b)As shown in Figure11, the traditional fuzzy support vector machine is not the best classifier, and the improved fuzzy support vector machine performs better. The improved fuzzy support vector machine only needs 398 data in 455 training samples to form a better classification hyperplane, and the calculation time is also significantly reduced.


## 5.3. Results of System Identification and Evaluation of Authenticity

This article uses false recognition rate and false rejection rate to define system performance, and the choice of threshold directly determines the effect of feature selection. The definition of false recognition rate is the probability that the actual product is a fake but is misjudged as a genuine product; the definition of rejection rate is the probability that the actual product is a genuine product is misjudged as a fake. Starting from the definition of false recognition rate and false rejection rate, if all the works to be tested are judged to be fakes, the rejection rate is 100%, and the false recognition rate is 0%; if the works to be tested are judged to be genuine, the false recognition rate is 100%, and the rejection rate is 0%. If the false recognition rate and the false rejection rate are both 0%, the system reaches the ideal state. However, in actual operation, it is impossible for the false recognition rate and the rejection rate to be 0% at the same time.The optimal value obtained by calculation, as shown in Figure12, is a representation of the distribution of calligraphic features, from which the optimal threshold point can be seen.Figure 12
Schematic diagram of the optimal threshold.The style of today’s calligraphy works is basically a legacy of history. Therefore, the available research samples are limited, which makes the samples for model training relatively insufficient. Therefore, the discrimination rate of authenticity cannot reach 100%, and there is a certain degree of error. Through repeated experiments many times, the value has a certain change, and when the step size is 0.1, calculating the average value can get the value of the false rejection rate and the false recognition rate.As shown in Figure13(a), the more discriminatory the style features, the better the discriminating effect.Figure 13
Appraisal and evaluation chart: (a) comparison chart of authenticity rate; (b) change of accuracy rate with grid window.
(a)(b)The preprocessed calligraphy images are all normalized images, and the selection of the grid window size is involved in the feature extraction process at this time. If the selected window is too small, it will cause insufficient information to be obtained. As shown in Figure13(b), a 13 × 13 grid window is better for extracting feature information.


## 6. Conclusion

This article extracts the calligraphic character stroke-level and structure-level features and obtains multiple feature parameters to construct the authentic model of the calligrapher, which provides a comparison basis for the calligraphy work identification of the calligrapher. The number of feature parameters is uncertain, and each feature has a different weight in its corresponding feature vector, and different style vectors need to be formed through continuous learning. When new features are discovered, further learning and updating make the real model more perfect. The main focus of this article is to carry out simulation experiments on the algorithms involved in the steps of feature extraction and identification and select the extracted features for weight estimation to construct the true vector. It has established a system of authentic models to conduct multiple experiments to detect suspicious points in suspicious works and give the probability of authenticity. This system provides a quantitative evaluation standard for calligraphy identification and enables the development of the field of computer-aided calligraphy works authenticity identification. However, the system is still in the preliminary research stage, and a lot of work needs to be done to improve the system before it can be applied to the field of more than ten degrees of identification. In today’s society, fake calligraphy and painting, imitations, and fish eyes are mixed, and the level of counterfeiting tricks is getting higher and higher, making it difficult to distinguish the authenticity. It is difficult to distinguish the traces of fraud with the naked eye alone. Therefore, this article applies image processing methods to the field of calligraphy identification to provide an objective and quantitative reference standard for calligraphy identification. However, the functions contained in the calligraphy authenticity identification system in this article are relatively preliminary, and there is still a lack of strict evaluation criteria for the pros and cons of the system’s performance. This article only gives a rough estimate of the probability that the suspicious work is authentic, and its function needs to be further improved to give convincing data conclusions.



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*Source: 8484609-2022-04-09.xml*