# Fractal Visual Art Graphic Design Based on Computer-Aided Algorithms

Authors: Qihao Zhou; Teng Liu; Guorong Wu; Xuhui Chen
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

Embedded machine vision algorithm development platform is of great significance. Based on the elaboration of visual communication design, this paper further details the design of fractal visual art graphics based on computer-aided algorithms to design edge detection schemes, where edges represent sudden changes in the signal and are able to characterize the rich information of an image. In response to the problems of poor robustness and difficult parameter selection of the currently widely used edge detection algorithms, the platform encapsulates joint edge detection graphic components in a higher-order processing library to achieve the requirements of high-precision detection and to realise enhanced edge detection effects. Finally, the experimental analysis shows that the proposed algorithm has a more accurate detection effect and can meet the user's high-precision detection requirements.


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## Body

## 1. Introduction

As the times have developed, Internet information technology has also developed rapidly and has become popular in many areas of society, especially in the application of mathematical and web design [1]. With the rapid development of society, people’s needs are constantly growing, and in the specific visual communication design, the individual needs of web users need to be taken into account, as well as the rationality of web design and other requirements [2]. For this reason, visual communication design in the Internet era often requires consideration of a wider range of requirements The so-called visual communication design mainly refers to the implementation of information-based communication design based on the combination of art and communication, while the use of visual symbols for auxiliary expression is also very important and has a strong application type [3]. At the beginning of visual communication design, a variety of forms of expression exist, which, in summary, include four main forms: painting, sculpture, architecture and design [4]. As the development of visual communication design is inevitably linked to many media, it has been influenced to a certain extent by the rapid development of the Internet, which has also given rise to a variety of new forms [5]. For this reason, in the specific visual communication design, the visual intention needs to be fully considered, including its own intention as well as the client's intention [6]. Only in this way can designers be comprehensive in their visual communication design and thus help to ensure that the visual communication design meets the individual needs of web users.There are two main types of machine vision systems available, one relying on general purpose computers for processing and computing, and the other based on embedded architectures [7]. Commonly used machine vision systems generally carry out data processing via general-purpose computers, but with the increase in the number of inspection objects and the demand for real-time inspection, machine vision systems based on embedded architectures help to reduce the burden on data transmission and computer resources, enabling real-time monitoring, multipoint detection, distributed computing, and highly modular multitasking [8], and are increasingly being used in manufacturing industries.Existing algorithm development platforms are often incompatible with system versatility and ease of use [9]. Some platforms use sequential function diagrams and ladder diagrams in order to meet generality, which still require a certain level of programming literacy on the part of the developer, and the design process is more complex and the interaction is more cumbersome, not intuitive or easy to use. The algorithm development platforms that can meet the ease of use are often industry-specific platforms, which cannot be downloaded across platforms and have to be redesigned by software developers for functional iterations, and generally suffer from poor generality and low reuse rate [10]. As users’ needs are polymorphic and algorithms are designed for thousands of people, the value of personalised services and customised solutions is increasingly evident in the manufacturing industry, with more and more customised solutions being used to replace standardised products in the field of machine vision. Existing platforms can no longer meet the requirements of a wide range of applications for embedded systems [11]. The ideal vision algorithm development platform should reduce the difficulty and complexity of machine vision system development for developers, enable easy iteration and updating of system functions, and meet the diverse functional requirements of different situations [12].Therefore, the research of an algorithm development platform for embedded machine vision is of great significance. Users can perform interactive programming in a graphical development environment, complete the rapid development of vision systems, and download them to the embedded devices with a single click, with low error rate, high versatility, and high reliability, which has become the future development trend of embedded machine vision systems [13]. In this study, a machine learning-like algorithm was used to develop a high-precision tool recognition system to meet the requirements of high-precision detection and achieve enhanced edge detection. Aiming at the problems of poor robustness and difficult parameter selection of the currently widely used edge detection algorithms, this research designs an edge detection scheme, combined with edge detection graphics components and encapsulated in a high-level processing library to meet the requirements of high-precision detection.


## 2. Joint Edge Detection Graphic Element

The joint edge detection graphical element not only solves the problem of poor algorithm robustness by using a composite wrapper model and an adaptive algorithm, but also solves the problem of difficult selection of edge detection threshold parameters by using an automatic parameter finding algorithm, making it very adaptable to images that change due to irresistible factors [14].The graphical component combines the common Roberts, Sobel, and Prewitt edge detection operators in a composite package, and uses the Canny algorithm to perform non-maximum suppression and double thresholding on the gradient images obtained under the different operators to output more accurate single-edge results [15]. First, the target image is segmented by N equal parts (default is four equal parts) based on the adaptive algorithm, and the segmented subimages are processed separately. Then, the gradient image is obtained for each subimage under different operators, and the upper and lower threshold combinations corresponding to the Canny algorithm are automatically found based on the gradient image, respectively [16]. Finally, more accurate single-edge information is obtained based on the Canny algorithm, and the optimal edge of each subimage is selected by an objective evaluation method and combined to obtain the complete output edge as shown in figure 1 [17].Figure 1
Flowchart of edge detection algorithm.


### 2.1. Automatic Parameter Optimization

The aim of the automatic parameter finding algorithm is to solve the problem of difficult parameter selection during the actual development of the algorithm and to improve the dynamic adaptability of the algorithm. Although not all graphical elements are suitable for automatic parameter selection, and human debugging of some image algorithms is still irreplaceable, the parameter auto-optimisation algorithm encapsulated by the joint edge detection graphical element is a good solution to the problem of difficult threshold selection in Canny edge detection.The parameter optimization algorithm of the joint edge detection graphic element introduces the image entropy [18], which can characterize the aggregation property of the image grey-scale distribution, and proposes the method of maximum entropy ratio of class groups to achieve the automatic threshold optimization of the Canny algorithm. According to the maximum entropy theory, it is known that the greater the variation of the grayscale value of a class group, the greater the entropy, so the optimal segmentation threshold is found by calculating the maximum value of the entropy ratio between intraclass and interclass.Let the number of image pixels beN, the range of gray levels be [0, L − 1], and the number of pixels corresponding to gray level i be ni, with probability.(1)pi=niN,i=0,1,2,…,L−1.In the gray level range,k is set as the most segmentation threshold, and the threshold k is used to classify the nonedge C0 and the edge C1 into two categories, C0 in the range [0, k] and C1 in the range [k, L − 1]. Then, the image entropy of nonedge C0 and edge C1 is expressed as(2)H0=−∑i=0kPlogPiρ0;H1=−∑i=k+1L−1PlogPiρ1,where the probabilities ρ0 and ρ1 of nonedge C0 and edge C1 are(3)ρ0=∑i=0kPi,ρ1=∑i=k+1L−1Pi.The total mean image entropyH is(4)H=−∑i=0L−1PilogPi.The expression for the entropy ratioΔη of the nonedge class to the edge class is(5)Δη=η22kη12k,where the interclass entropy variance η22k is defined as(6)η22k=ρ0H0−H2+ρ1H1−H2.The intraclass entropy varianceη12k is defined as(7)η12k=ρ0∑i=0ki−H02+ρ0∑i=k+1L−1i−H12.Whenk is the optimal partitioning threshold such that the interclass entropy is maximized while the intraclass entropy is minimized, the derivative of k in (7) is therefore(8)∂Δηk∂k=0.Thek value solved according to (8) is used as the upper threshold TH1 in Canny’s algorithm, while the lower threshold is chosen based on the empirical coefficient of proportionality, i.e., TH2 = αTH1, and the final α value was chosen as 0.4 after several experiments.


### 2.2. Edge Evaluation Model

The selection of the best edge in the joint edge detection graphical component relies on a reference-free evaluation method, i.e., there is no baseline reference edge information, and an evaluation model is built to objectively score the edge result image and select the highest score as the final output. The edge detection evaluation model is based on the connected component analysis method [19], where the ratio of the 4- to 8-connected component scores reflects the degree of edge line connectivity, and the influence of the degree of edge line connectivity on edge detection is reflected in the error and miss detection.In order to score the edge result image specifically, the quantitative model fitting of the principle of connected components is used as an evaluation model to complete the selection of the edge algorithm in this paper. An edge map is a binary image with pixel values consisting of only 0 and 1. For the total number of edges A, 4-connected components B, and 8-connected components C in the edge map, mathematical induction shows that the magnitude of the values of C/A and C/B is linearly and positively correlated with the effect of the extracted edges.Let the edge score beG, the edge evaluation index be M = B/C, N = A/C, and the weight coefficients be α and β, respectively; then, the linear model of the edge score G with M and N can be expressed as(9)G=α×M+β×N.For each set of edge results, the ratio of 4- to 8-connectedness scoreM and the ratio of total number of edges to 8-connectedness score N were calculated, and a subjective score was assigned to each of the 100 edge results and fitted to the model. The final ratio of α to β is approximately (4.8e2)e2:1. The evaluation model formula in equation (10) shows that the ratio of 4- to 8-linked scores M is the main variable for the edge score G, with a correlation coefficient r of 0.98.(10)G=4.8M+e−2N.


## 2.1. Automatic Parameter Optimization

The aim of the automatic parameter finding algorithm is to solve the problem of difficult parameter selection during the actual development of the algorithm and to improve the dynamic adaptability of the algorithm. Although not all graphical elements are suitable for automatic parameter selection, and human debugging of some image algorithms is still irreplaceable, the parameter auto-optimisation algorithm encapsulated by the joint edge detection graphical element is a good solution to the problem of difficult threshold selection in Canny edge detection.The parameter optimization algorithm of the joint edge detection graphic element introduces the image entropy [18], which can characterize the aggregation property of the image grey-scale distribution, and proposes the method of maximum entropy ratio of class groups to achieve the automatic threshold optimization of the Canny algorithm. According to the maximum entropy theory, it is known that the greater the variation of the grayscale value of a class group, the greater the entropy, so the optimal segmentation threshold is found by calculating the maximum value of the entropy ratio between intraclass and interclass.Let the number of image pixels beN, the range of gray levels be [0, L − 1], and the number of pixels corresponding to gray level i be ni, with probability.(1)pi=niN,i=0,1,2,…,L−1.In the gray level range,k is set as the most segmentation threshold, and the threshold k is used to classify the nonedge C0 and the edge C1 into two categories, C0 in the range [0, k] and C1 in the range [k, L − 1]. Then, the image entropy of nonedge C0 and edge C1 is expressed as(2)H0=−∑i=0kPlogPiρ0;H1=−∑i=k+1L−1PlogPiρ1,where the probabilities ρ0 and ρ1 of nonedge C0 and edge C1 are(3)ρ0=∑i=0kPi,ρ1=∑i=k+1L−1Pi.The total mean image entropyH is(4)H=−∑i=0L−1PilogPi.The expression for the entropy ratioΔη of the nonedge class to the edge class is(5)Δη=η22kη12k,where the interclass entropy variance η22k is defined as(6)η22k=ρ0H0−H2+ρ1H1−H2.The intraclass entropy varianceη12k is defined as(7)η12k=ρ0∑i=0ki−H02+ρ0∑i=k+1L−1i−H12.Whenk is the optimal partitioning threshold such that the interclass entropy is maximized while the intraclass entropy is minimized, the derivative of k in (7) is therefore(8)∂Δηk∂k=0.Thek value solved according to (8) is used as the upper threshold TH1 in Canny’s algorithm, while the lower threshold is chosen based on the empirical coefficient of proportionality, i.e., TH2 = αTH1, and the final α value was chosen as 0.4 after several experiments.


## 2.2. Edge Evaluation Model

The selection of the best edge in the joint edge detection graphical component relies on a reference-free evaluation method, i.e., there is no baseline reference edge information, and an evaluation model is built to objectively score the edge result image and select the highest score as the final output. The edge detection evaluation model is based on the connected component analysis method [19], where the ratio of the 4- to 8-connected component scores reflects the degree of edge line connectivity, and the influence of the degree of edge line connectivity on edge detection is reflected in the error and miss detection.In order to score the edge result image specifically, the quantitative model fitting of the principle of connected components is used as an evaluation model to complete the selection of the edge algorithm in this paper. An edge map is a binary image with pixel values consisting of only 0 and 1. For the total number of edges A, 4-connected components B, and 8-connected components C in the edge map, mathematical induction shows that the magnitude of the values of C/A and C/B is linearly and positively correlated with the effect of the extracted edges.Let the edge score beG, the edge evaluation index be M = B/C, N = A/C, and the weight coefficients be α and β, respectively; then, the linear model of the edge score G with M and N can be expressed as(9)G=α×M+β×N.For each set of edge results, the ratio of 4- to 8-connectedness scoreM and the ratio of total number of edges to 8-connectedness score N were calculated, and a subjective score was assigned to each of the 100 edge results and fitted to the model. The final ratio of α to β is approximately (4.8e2)e2:1. The evaluation model formula in equation (10) shows that the ratio of 4- to 8-linked scores M is the main variable for the edge score G, with a correlation coefficient r of 0.98.(10)G=4.8M+e−2N.


## 3. Enhanced Effect Validation

After obtaining a dataset with a sufficient number of samples, the image needs to be preprocessed first; the purpose of which is to improve the image quality and exclude the redundant images other than the tool, to segment the tool from the complex background; the program flowchart is shown in Figure2.Figure 2
Image preprocessing and feature extraction.In order to remove the redundant parts other than the backpack part, the backpack region is first segmented from the background using binarization. Then, the backpack location is further determined based on the maximum contour extraction method, and the image is cropped according to the location coordinates to achieve the backpack region extraction. In the next step, the image is scaled to a uniform size of 128 × 128 by dragging and dropping the image crop graphic component, taking into account the uniform size of the training samples of the machine learning model. Finally, the tool is separated from the backpack using a colour tracking method. The image is first converted to the HSV colour space, which is more suitable for tracking a given colour as HSV is an intuitive colour model that describes the image by hue H, saturation S, and luminance V. In the X-ray image, the tool colours are distributed in the range (70, 43, 46) to (130, 255, 255), and the tool segmentation is achieved using the threshold settings in the colour tracking graphic element.To verify whether the above joint edge detection graphic element provides enhanced edge detection, two experiments were selected for analysis and testing. The house image shown in Figure3 was selected for the edge detection experiment. Figure 3 shows the results of the Robert’s operator, Prewitt operator and Sobel operator edge detection combined with the Otsu threshold selection method compared to the edge detection algorithm encapsulated by the graphical element, respectively. It can be seen visually that the composite edge detection elements of the platform can effectively suppress spurious edges and obtain better continuity of edge results.Figure 3
Comparison of edge detection results of Experiment 1.Experiment 2 selected Figure3 for contrast edge detection, and the experimental comparison results are shown in Figure 4. Since the pixel values of an edge image consist of only 0 and 1, the edge detection algorithm to be evaluated can be considered as a binary classifier, and the result of its classification is also the result of edge detection. In order to better characterize the edge detection performance of the detection algorithm, a receiver operating characteristic (ROC) curve was introduced for algorithm performance evaluation, which was used to illustrate the relationship between the correct and incorrect edge detection rates [20–22].Figure 4
Comparison of the edge detection results of Experiment 2.The measure of correct edge detection results is the edge information reference map, which represents an ‘ideal’ edge detection effect and often requires constant debugging and subjective judgement by the human visual system. The reference map for Experiment 2 is shown in Figure5 and the total number of benchmark edges is calculated to be 2066 [23–25].Figure 5
ROC plot of edge detection algorithm.A comparison of the performance of the four algorithms based on the ROC curve is shown in Table1, where the area enclosed by the axes under the ROC curve is defined as the metric AUC for the mathematical morphological gradient method, and the closer the value is to 1, the more realistic the detection algorithm is. As can be seen, although the edge detection algorithm in this paper sacrifices runtime to a certain extent, the detected edges are more accurate than the single operator Canny edge detection combined with the Otsu threshold selection method.Table 1
Algorithm performance comparison table.
Evaluating indicatorRobertsPrewittSobELPrimitive algorithmAUC0.7070.7120.7620.854Running time/s0.9950.8741.231.854


## 4. Conclusions

In summary, in the network era, visual communication design is not only very rich in content but also has very significant features, specifically navigation design content, page and graphic design, features specifically freedom, and interactivity and timeliness. Traditional recognition methods generally achieve the classification problem through image feature description and detection, but due to the high complexity of images in practical applications, traditional methods are difficult to perform the detection work. This paper therefore builds on traditional vision algorithms to develop a high-precision tool recognition system using machine learning-like algorithms in an algorithm development platform. In this way, in the rapidly developing information technology network era, to better visual communication design, designers need to continuously conduct in-depth research in order to improve the level of visual communication design.



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*Source: 3345037-2022-05-27.xml*