Digital Color Images as a Tool for the Sustainable Use of Embroidery Elements from Folk Costumes

Abstract

The aim of the research is to improve the public’s assessment and understanding of the cultural values and history of Bulgaria. The main issues related to the sustainable use of elements of the cultural heritage are defined, and the accessible literary sources related to the digitization of the folklore heritage are reviewed. Shape indices, color, and textural characteristics were obtained from digital color images of the elements of Bulgarian folk costumes. The most informative indices of these features were selected. A kernel variant of the principal component analysis (kPCA) method was used to reduce the data volume of the feature vector. A Naïve Bayes classifier, discriminant analysis, and the support vector method (SVM) were used for classification. The classification accuracy was assessed. In the analysis of the decorative elements of Bulgarian costumes, it was found that the accuracy of classification depended both on the method for reducing the volume of data and on the separability of the classes of data, depending on the classifier used. In the analysis of microscopic images of textile fabrics from Bulgarian costumes, it was found that the accuracy of classification for the studied objects depended both on the method for reducing the volume of data and on the used classifier. In the considered cases, a classification error below 10% was obtained using a non-linear kPCA kernel and SVM with a non-linear partition function. It was proven that the results of this development can be used in the creation of modern cross-stitch patterns, textile patterns, and clothing. The practical application of these research findings has the potential to benefit various stakeholders, including cultural heritage institutions, researchers, artisans, designers, and the general public, promoting a deeper appreciation and sustainable use of costume embroidery elements. Research can continue in the direction of the sustainable use and preservation of embroidery elements of Bulgarian costumes, enriching the understanding of cultural heritage and promoting appreciation for it in future generations.

1. Introduction

The preservation of cultural heritage is a priority task in modern society. Museums, libraries, and art exhibitions are used for this purpose. Preserving and deriving added value from this heritage era is a priority for specialists in the subject area.

Heritage sites are not only revered, but the very buildings that house them are often a symbol of the cultural integrity of the community to which they belong.

An important place in modern scientific research is occupied by issues of sustainable development. This is reflected in the links among research, sustainability, and related cultural heritage conservation activities [1].

A significant obstacle to cultural sustainability is the preservation of textile fabrics over time. For this purpose, proper storage, maintenance, and the use of suitable preservative biochemical substances for their conservation are necessary [2]. Last but not least is the problem of financing these activities. A priority task in ensuring the sustainability of the use of cultural heritage is the reduction and even elimination of costs for this activity, where possible [3].

Interest in sustainable textile production and fashion design is high among scholars from various fields due to the benefits it brings to modern society and the outlook for the future. Major textile companies have been using recycling since 2010 to create products with minimal negative impacts on the environment. Also, the use of textile raw materials with minimal residue is of interest to these manufacturers [4].

Clothing design is one of the significant factors in its sustainable production. Regardless of how many of the other sustainability requirements are met, if the design of the garment is not attractive to consumers, then it also becomes a waste of resources. Clothing should be designed to last, remain stylish, and be desirable without being swayed by fast-moving fashion trends.

One of the significant elements of cultural heritage is clothing. The Bulgarian costume is an example of this. It is a typical illustration of the use of woven, sewn, and embroidered garments with minimal material residue. The simplified construction, using simple elements such as belts, scarves, and shirts, is richly decorated with embroidery, decorations, and embroidery.

The decoration of folk costumes is part of their overall composition. Through these decorations, people expressed their identity. The elements reflect the relevant folklore area, for example, whether the woman was married, and the financial status of the person [5]. The elements of the costumes show modern researchers the beliefs, traditions, aesthetics, and moral norms of the society in which these costumes were used.

Preserving the beauty of costumes is possible by digitizing them and creating arrays of text and metadata about them. Historical data can be described textually, and metadata can be represented by numerical values. Obtaining numerical data on costumes and decorative elements applied to them is realized by video sensors, colorimeters, spectrophotometers, and scanning electron microscopes. The obtained results can be used to create digital collections containing photographic material, 3D-scanned objects, and numerical values from measurements. They can be used in modern developments related to interior and fashion design.

The main goal of this research is to contribute to the preservation, digitization, and popularization of the Bulgarian cultural heritage, with particular attention given to the fabrics and elements of Bulgarian costumes. In this way, this research aims to improve the public’s assessment and understanding of the cultural values and history of Bulgaria.

The contributions that can be defined include the following: Preserving and obtaining added value from cultural heritage is a priority task for specialists and the public. Thanks to the richness and diversity of the Bulgarian cultural heritage, the present work contributes to the digitization and popularization of Bulgarian cultural values. Non-destructive tests of the textile fabrics and elements of Bulgarian costumes were carried out. Contemporary textile patterns and garments with elements of Bulgarian costumes are offered.

The work is organized in the following order: After defining the main issues related to the sustainable use of elements of the cultural heritage (Section 1), a review of the available literary sources related to the digitization of the folklore heritage was carried out (Section 2). The material and methods used are presented (Section 3). The results of receiving, processing, and analyzing the data of elements of Bulgarian costumes are indicated. Contemporary textile patterns and garments with elements of these costumes are offered. They are compared with the available literature sources (Section 4). Conclusions and summaries are made (Section 5). Guidelines for further research and recommendations for using the obtained results in practice are indicated.

2. Related Works

In recent years, the creation of digital collections and the design of methods and technical means for their organization have received strong interest. The results of such research are useful both for the preservation of difficult-to-maintain folk costumes and for their application in contemporary textile, interior, and fashion design.

Kuo et al. [6,7], as a result of a series of studies, summarized that the three-dimensional effect of decorative elements can be achieved by changing the embroidery stitches. The authors proposed a new method of obtaining, processing, and analyzing images to obtain, in digital form, elements of embroidery and their numerical description through color and geometric features. The presented work was limited to obtaining only patterns of decorative elements from textiles, without making a detailed numerical analysis of these elements.

Shih et al. [8] developed and investigated an automated inspection system for Tatami-type embroidered fabrics. The authors used an image analysis method. When processing the RGB images, wavelet transforms and an averaging filter were used. Then, clustering by fuzzy c-means was carried out. When analyzing the shape of an embroidered fabric element, its individual components were segmented by the separated colors. Regardless of the complex analysis applied, the data were mainly obtained on the colors of the embroidered elements, and to a lesser extent, a numerical analysis of these elements by geometric, textural, and topological features was conducted.

Elnashar and Boneva [9] developed software tools for obtaining, processing, and analyzing geometric features from decorative elements on traditional Egyptian carpets. The authors combined the resulting forms with contemporary colors. According to the authors, the results of the application of the proposed software tools are suitable for the transfer of knowledge and visual forms from the field of traditional Egyptian carpets into modern textiles and their use as innovations in fashion design. A disadvantage of this development is that the developed technical means are presented without showing examples of their application in modern textile, interior, or fashion design.

Arora et al. [10] proposed a methodology for capturing images of the decorative elements of folk costumes. The methodology can be used to organize these items in online catalogs. A major limitation of this development is that no automated algorithms or procedures were proposed to facilitate the process of collecting and systematizing the captured images of folklore elements.

Baeva and Baev [11] proposed a semantic approach for organizing the elements of folklore costumes in digital databases. The model the authors proposed includes the following: specifying the purpose and scope of the ontological model of decorative elements; the retrieval of object data; structuring the received data; data integration; the choice of a programming environment for ontology implementation; documenting and storing the results. A limitation of the model thus proposed is that it covers only the theoretical foundations for creating digital databases of folklore elements.

Florea-Burduja et al. [12] proposed an accessible method for obtaining data on decorative elements in traditional textiles. The resulting images are converted into embroidery patterns. Thus, the proposed method combines the values of the past with modern technologies. The results of this research are suitable for application in clothing decoration, the ornamentation of textiles, and interior elements with traditional decorations. Also, the numerical form in which the stitches are obtained is suitable for use in electronic databases with traditional elements. Also, the results can be used to promote cultural heritage values. As a shortcoming of the presented work, one can point out the limitation of obtaining only patterns of the decorative elements of antique textiles without making a detailed numerical analysis of these elements.

Baeva [5] created a formalized model of semantic information for embroidered elements in Bulgarian costumes. This model contains descriptive data, including historical information, folklore region, type of embroidery, colors, and symbolism. Also included in the model are metadata such as a description, image, file name, catalog number, and a short summary of the item. A drawback of this study is that a way to organize embroidered elements of costumes is not proposed. Most of the data used are purely descriptive.

Indrie et al. [13] proposed a method to analyze Romanian folk motifs through two main algorithms: radius–vector function and principal component analysis. For greater accuracy of the analysis, a combination of these methods was proposed. For this purpose, the authors used a method for obtaining, processing, and analyzing images. A disadvantage of this development is that the developed software tools are presented, but only geometric signs are used to describe the objects, and no examples of their application in modern textile, interior, or fashion design are shown.

Kalita et al. [14] proposed a linear ontological model through which folk costumes and dances in India can be systematized. In this way, they often implemented the recommendations made during the Convention on the Intangible Cultural Heritage (ICH) of the United Nations Educational, Scientific, and Cultural Organization (UNESCO). According to the authors, additions to and development of the model proposed by them are necessary since the specific study mainly focused on folk dances. More research is needed related to the traditional textile fabrics used, which will enrich the knowledge of folk dances and costumes.

Ilieş et al. [1] used an X-radiography method to assess the conditions of Romanian costumes. An advantage of the method used is that it is non-destructive, and images that can be analyzed are obtained quickly enough. A major limitation of the method is that it is not widely available and requires well-trained specialists to work with the technical equipment. The reason for the non-wide application of the method is the relatively high cost of the technical equipment used.

Elnashar et al. [15] conducted research on the possibility of extracting data from elements of Romanian costumes and their use in the field of contemporary sustainable fashion. An advantage of the presented results is that the authors used available technical means, such as an optical microscope and techniques for acquiring, processing, and analyzing digital color images, to extract data about textile fabrics. A limitation of these results is that global textural features were used, which did not sufficiently describe the condition of the textile fabric. Additionally, these features were not invariant to the conditions under which the antique textile images were acquired.

The analysis made of existing solutions in the subject area related to the digitization, processing, and analysis of data on the elements of folk costumes, with the aim of their application in the creation of digital libraries and the design of modern textiles, clothing, and interior components, can be summarized as follows: The data on costume items are presented descriptively. There is a lack of numerical data that can be objectively used to describe the elements. Such data are indices obtained from color components, spectral characteristics, textural characteristics, and the shape of costume elements. Numerical data on these elements can be used in classification to distinguish historical regions, in the creation of contemporary clothing with folk motifs, and in the study of consumer preferences. The research on the elements of Bulgarian costumes is very limited.

Some of the research uses complex and difficult-to-operate service equipment that is not widely available and has a relatively high cost.

Along with spectral analysis and determining the properties and composition of fabrics, one of the main methods for extracting data about the elements of costumes are image acquisition, processing, and analysis techniques. This method is affordable, video sensors are widespread, and images can be easily obtained and processed, both on commercial software products and on those that are free and open to use.

3. Material and Methods

Data obtained from costumes from south-eastern Bulgaria were used. These types of costumes are made of woolen and cotton fabrics with beautiful embroidery that is characteristic of the area. Black woolen fabric with rich embroidery on the bodice and skirt was used to make the sukman. The sukman is a thick, dark-colored woolen garment with a closed, tunic-like cut. The same technique is seen with the shirt. White cotton fabric was used to make the short shirt. It has embroidery on the sleeves and, less often, on the bodice. It is only available on the front apron. It stands out sharply against the background of the cloth. The apron is made of colored woolen fabric with embroidery. Also, the apron can be red, green, yellow, or, in some cases, white. The embroidered sash is a woolen fabric, about 25 cm wide. It can be red, orange, or burgundy.

Figure 1 shows a general view of a costume and its main parts. Its base is a sukman (dress), shirt, apron, skirt, girdle, belt, headscarf, and waistcoat. A characteristic element of the costumes from this part of Bulgaria is the bodice. On the cloth of the bodice, the embroidery is called “gazi”. A headscarf is a square piece of cloth that is tied on the head and serves as protection or as a decorative element. An apron is a waist garment that is part of the costume. It is made of thick, homemade woolen fabric. It covers the front lower part of the body and has practical and aesthetic functions. The “sukman” is a long, loose, sleeveless dress. The difference with the dress is that the sukman is worn over a shirt. It is made of a strong fabric, most often a thick woolen fabric, but it is also sewn from linen and cotton fabric. A shirt refers to traditional clothing that is usually worn as part of a costume and is an integral part of it. The belt of the folk costume, also known as “poyas”, is a traditional accessory worn around the waist. “Pafti” are decorated metal buckles for belts, which also have the role of ornaments in the costume. The “brim” is the fabric at the lower end of the cloth that is richly decorated with embroidery.

3.1. Digital Color Images

The digital color images of costume decorative elements were obtained with a Huawei P20 Pro mobile phone video sensor (Huawei Technologies Co., Ltd., Shenzhen, China). The characteristics of the video sensor included the following: focal length: 28 mm; maximum resolution: 40 MP; aperture size: F1.8. The video sensor used Leica Vario-Summilux-H1:1.6-24/27-80 ASPH optical lenses (Leica Camera AG, Wetzlar, Germany). Homogeneous illumination of the filmed scene was provided by a light source that consisted of a dome-shaped part in which white LEDs with cold white light (6400 K), model VT-3528-60 (V-TAC Europe Ltd., Plovdiv, Bulgaria), were installed, with the maximum emitted light intensity at 450 nm. Color adjustment was performed with a 24-field Danes Picta Color Chart BST11 (Danes-Picta, Praha, Czech Republic).

A König Electronic CMP-USB Micro 10 magnifying video camera (Nedis B.V.’s-Hertogenbosch, The Netherlands) was used to analyze the structure of textile fabrics and their fibers in the costumes. Magnification: 10–200×; optical image resolution: 640 × 480 pixels. The illumination of the object was by means of 4 white LEDs, with the greatest intensity of emitted light at 450 nm. The images were obtained with the textile fabric oriented along the main textile thread.

3.2. Determining the Thickness of the Fabric

An electronic digital caliper SEB-DC-023 was used, with an accuracy of 0.05 mm and a maximum measured length of 150 mm (Shanghai Shangerbo Import and Export Co., Ltd., Shanghai, China).

3.3. Form Indexes

The main parameters of the costume elements from their digital images were determined with the regionprops function in the MATLAB programming environment (Mathworks Inc., Natick, MA, USA). Through this function, the following were determined: area of object A; perimeter P; major axis D; minor axis d; the ideal area A_ideal; area of the minimum rectangle circumscribed around object A_mr; standard volume V_sb.

$$V=\frac{4}{3}\pi \frac{D}{2}{\left(\frac{d}{2}\right)}^2$$

(1)

$$A_{ideal}=\frac{\pi dD}{4}$$

(2)

$$A_{mr}=d.D$$

(3)

$$V_{sb}=\frac{d^2.D}{2}$$

(4)

Indices for describing the forms of costume elements that are available in the available literature are presented by Biggins et al. [16]. In the present work, they are used with some modifications. They are calculated by the major and minor axes of the object, and the perimeter, area, and volume. They include the indices of elongation, shape, asymmetry, ellipticity, sharpness, funneling, taper, polarity, complementarity, strength, and ovality.

$$i_1=\frac{V}{V_{sb}}$$

(5)

$$i_2=\frac{P^2}{A}$$

(6)

$$i_3=\frac{D}{d}.100, \%$$

(7)

$$i_4=\frac{P^2}{4\pi A}$$

(8)

$$i_5=\frac{1}{c}$$

(9)

$$i_6=\frac{A}{A_{ideal}}$$

(10)

$$i_7=\frac{A}{A_{mr}}$$

(11)

$$i_8=\left(\sqrt{\frac{D}{2}}+\sqrt{\frac{d}{2}}\right)\frac{\sqrt{\frac{D}{2}}}{d}-1$$

(12)

$$i_9=\left(\frac{D}{2}-\frac{d}{2}\right)\frac{D}{d^2}$$

(13)

$$i_{10}=\frac{d}{D}-1$$

(14)

$$i_{11}=\frac{\left(\frac{D}{2}-\frac{d}{2}\right)}{d}$$

(15)

$$i_{12}=\frac{D-d}{D}$$

(16)

$$i_{13}=\frac{dD}{2}-1$$

(17)

$$i_{14}=\frac{(D+2)(d+2)}{2D^2(-dD+D+2)}$$

(18)

$$i_{15}=\frac{P^2}{4\pi A}-1$$

(19)

$$i_{16}=\frac{d}{D}$$

(20)

$$i_{17}=\frac{D}{d}-1$$

(21)

$$i_{18}=\frac{D}{d}$$

(22)

$$i_{19}=\frac{dD}{2}$$

(23)

$$i_{20}=\frac{D-d}{2d}$$

(24)

$$i_{21}=\frac{P}{D}$$

(25)

$$i_{22}=\frac{3V}{4\pi D{d}^2}$$

(26)

$$i_{23}=\frac{P}{D-P}$$

(27)

$$i_{24}=\frac{D}{D-P}$$

(28)

3.4. Color Components

Digital color images were obtained in the RGB color model, which was converted to the Lab color model, according to CIE 1976. Color component conversion functions were used at observer 2° and illuminance D65 (average daylight with UV component, 6500 K). Color components from the 8-bit RGB (RGB [0 255]) model were converted to Lab (L [0 100], a [−86.18 98.23], b [−107.86 94.47]).

The color components from the Lab model are represented as a color sphere. Figure 2 shows the transition from a color sphere to a four-color circle. The color circle is a projection of the color sphere along the two horizontal axes corresponding to the coordinates “a” and “b”. An advantage of using a color sphere is that the L-component of the colors can be observed to change, whereas, with the color wheel, this is not possible. The color sphere was obtained using the sphere function in the MATLAB programming environment. A sphere of dimensions [1 1 1] was generated and then used to create the large sphere in the graph and the small spheres showing the color coordinates in three-dimensional space. The small spheres are colored in the color they show.

3.5. Color Indices

Color component values from the Lab model were converted to LCh. It was taken into account that L(Lab) = L(LCh). The remaining two color components (C and h) were converted according to the following formulas:

$$C=\sqrt{a^2+b^2}{h}^o=atan\left(\frac{b}{a}\right)$$

(29)

The obtained values from the Lab and LCh color models were used in the calculation of the color indices. The indices were determined according to the formulas summarized by Pathare and colleagues [17]. These indices depended on the changes in the brown, yellow, and white colors of the examined samples. They also present the relationships among the color components of the specified patterns. The color indices used were determined by the following formulas:

$$c_1=L$$

(30)

$$c_2=a$$

(31)

$$c_3=b$$

(32)

$$c_4=C$$

(33)

$$c_5=h$$

(34)

$$c_6=\frac{142.86b}{L}$$

(35)

$$c_7=100-\sqrt{{(100-L)}^2+a^2+b^2}$$

(36)

$$c_8=\frac{x-0.31}{0.17}x=\frac{a+1.75L}{5.645L+a-0.012b}$$

(37)

$$c_9=\sqrt{a^2+b^2}$$

(38)

$$c_{10}=\frac{180-h}{L+C}$$

(39)

$$c_{11}=\frac{2000a}{LC}$$

(40)

$$c_{12}=\frac{a}{b}$$

(41)

$$c_{13}=\frac{a}{b}+\frac{a}{L}$$

(42)

$$c_{14}=L-b$$

(43)

$$c_{15}=\frac{L}{b}$$

(44)

$$c_{16}=\frac{1000a}{L+h}$$

(45)

3.6. Texture Characteristics

Digitally scaled color images of costume elements were used. The pictures were in *.PNG file format. They had a resolution of 640 × 480 pixels.

In the analysis of images of historical textiles, the most commonly used method of representing their digital representation is through their textural features [18]. The advantage of using texture features in digital image analysis is that they can be used to analyze, model, and process the texture. In this way, human vision is simulated by distinguishing the elements in images. Texture features provide sufficient information about objects in digital images suitable for their classification, clustering, identification, and predictive modeling.

It is necessary to make a selection of textural features that are sufficiently informative and can be used to classify the types of costume fabrics. Twenty-two textural features were used and are described in detail in [19]. They are generally described by their formulas, as represented in Equations (46)–(67), where μ_x, μ_y and σ_x, σ_y—the mean values and standard deviations of px and p_y, respectfully—represent the partial probability density function; x and y are the coordinates (rows and columns) of a common matrix; probability “p”, p_{x + y}(i) is the probability of the total matrix; HX and HY are entropies of p_x and p_y; N is the number of gray levels in the image. The equations for the calculation of the textural features have the following forms:

$$t_1=\sum _i\sum _j\left(ij\right)p(i,j)$$

(46)

$$t_2={\sum }_{n=0}^N{n}^2\left\{{\sum }_{i=1}^N{\sum }_{j=1}^{N}p(i,j)\right\},\left|i-j\right|$$

(47)

$$t_3=\sum _{i,j}\frac{(i-{\mu }_i)(j-{\mu }_j)p(i,j)}{{\sigma }_i{\sigma }_j}$$

(48)

$$t_4=\frac{\sum _i\sum _j\left(ij\right)p\left(i,j\right)-{\mu }_x{\mu }_y}{{\sigma }_x{\sigma }_y}$$

(49)

$$t_5=\sum _i\sum _j{\left(i+j-{\mu }_x-{\mu }_y\right)}^{4}p(i,j)$$

(50)

$$t_6=\sum _i\sum _j{\left(i+j-{\mu }_x-{\mu }_y\right)}^{3}p(i,j)$$

(51)

$$t_7=\sum _i\sum _j\left|i-j\right|p(i,j)$$

(52)

$$t_8=\sum _i\sum _j{p(i,j)}^2$$

(53)

$$t_9=-\sum _i\sum _{j}p\left(i,j\right)\mathrm{l}\mathrm{o}\mathrm{g}(p\left(i,j\right))$$

(54)

$$t_{10}=\sum _{i,j}\frac{p(i,j)}{1+\left|i-j\right|}$$

(55)

$$t_{11}=\sum _i\sum _j\frac{1}{1+{\left(i-j\right)}^2}p(i,j)$$

(56)

$$t_{12}=\underset{i,j}{\max }p(i,j)$$

(57)

$$t_{13}=\sum _i\sum _j{\left(i-\mu \right)}^{2}p(i,j)$$

(58)

$$t_{14}=\sum _{i=2}^{2N_g}i{p}_{x+y}(i)$$

(59)

$$t_{15}=\sum _{i=2}^{2N_g}{\left(i-cshad\right)}^2{p}_{x+y}(i)$$

(60)

$$t_{16}=-\sum _{i=2}^{2N_g}{p}_{x+y}\left(i\right)\mathrm{l}\mathrm{o}\mathrm{g}\left\{p_{x+y}\left(i\right)\right\}$$

(61)

$$t_{17}=\sum _{i=0}^{N_g-1}{i}^2{p}_{x-y}(i)$$

(62)

$$t_{18}=-\sum _{i=0}^{N_g-1}{p}_{x-y}\left(i\right)\mathrm{l}\mathrm{o}\mathrm{g}\left\{p_{x-y}\left(i\right)\right\}$$

(63)

$$t_{19}=\frac{HXY-{HXY}_1}{\mathrm{m}\mathrm{a}\mathrm{x}\{HX,HY\}}$$

(64)

$$t_{20}=\sqrt{1-e^{-2\left(HXY2-HXY\right)}}$$

(65)

$$t_{21}=\sum _{i=1}^{N_g}\sum _{j=1}^{N_g}\frac{p(i,j)}{1+\left(\frac{{\left|i-j\right|}^2}{{N_g}^2}\right)}$$

(66)

$$t_{22}=\sum _i\sum _j{p(i,j)}^2$$

(67)

3.7. Method for Selection of Informative Features

The RelieFf method used has consistently improved ratings. It is suitable for selecting informative features when creating classification procedures [20]. The algorithm is suitable for use in determining the informativeness of features that are used for distance-based models.

3.8. Method for Reducing the Volume of Data

In the present work, a kernel variant of the principal components (kPCA) with linear (simple), polynomial, and Gaussian kernel functions was used. All notations and descriptions in the following chapters refer to this method of reducing the volume of received data. The kernel model can be directly constructed from the data {x_i}. Linear and non-linear methods are more commonly used:

$$\mathrm{K}(x,y)={({\times }^{T}y+c)}^d$$

(68)

where c > 0 is a constant. A Gaussian kernel can also be defined:

$$\mathrm{K}(x,y)=exp(-{‖x-y‖}^2/2{\sigma }^2)$$

(69)

with parameter σ.

3.9. Classification Methods

The naïve Bayesian classifier was used as a benchmark. Through it, a suitable method for reducing the volume of data on the decorative elements of costumes was selected. The data were then classified using discriminant analysis and the support vector method. Linear and non-linear partition functions were used. The sample size selected 40% of the data for training the classifiers and 60% for classifying them.

3.9.1. Naïve Bayesian Classifier (NB)

This classifier is based on Bayes’ rule [21]. It determines the probabilities of the classes based on the data from various measurements. In this classifier, it is assumed that the variables used are independent of the class. For this reason, it is called “naïve”. Bayes’ theorem has the following form:

$$P\left(y=c|x\right)=\frac{P\left(x|y=c\right)P(y=c)}{P(x)}$$

(70)

where P(y = c|x) is the probability that an object belongs to class “c”; P(x|y = c) is the probability that object “x” is in the middle of the object of the class “c”; P(y = c) is the unconditional probability that object “y” is in class “c”; P(x) is the unconditional probability of object “x”. The purpose of this classification is to find a probability class of object “x” so that the maximum probability P(y = c|x) is selected from all classes.

3.9.2. Discriminant Analysis (DA)

This classification method is a multidimensional analysis method [22]. It can be implemented by linear (LDA) and non-linear analysis, for example, quadratic divisive functions (QDA). LDA is suitable for the classification of small datasets, while QDA is applicable to larger datasets. Also, QDA is suitable in cases where the data have higher variation. In a generalized form, the partition function suitable for practical purposes has the following form:

$$\delta \left(x\right)=K+v.L+v^{\prime }.Q.v)$$

(71)

where K is a constant; L is the linear coefficient; Q is the quadratic coefficient; v = [x;y] is the matrix of the signs describing the objects; x and y are the coordinates of the signs along the two axes; v’ is the transpose matrix of v. By removing the non-linear part of the equation, this function is converted to a linear one.

3.9.3. Support Vector Machines Method (SVM)

In the present work, a kernel variant of the kSVM method was used. In this variant of the method, a nonlinear transformation of the data into a new feature space is performed. In kSVM, reference points are defined for a given class of data in the feature space in such a way that the distance between the boundaries of two classes is maximal. Depending on the type of kernel function chosen, several types of classifiers are constructed (linear (L), polynomial (P), or radial basis function (RBF)). We choose a width σ, and a kernel function with the following general form:

$$K\left(x,y\right)={(x^{T}y+c)}^d$$

(72)

where K is a kernel function; x and y are input vectors (vectors of features determined by the training sample; c > 0 is a constant. At c = 0, the kernel is homogeneous.

3.10. Assessment of Classification Accuracy

Basic e_i, actual g_i and total e₀ classification errors were used. They have the following equations:

$$e_i=\frac{{FN}_i}{{TP}_i+{FN}_i}\times 100,\%$$

(73)

$$g_i=\frac{{FP}_i}{{TP}_i+{FP}_i}\times 100,\%$$

(74)

$$e_0=\frac{\sum _{i=1}^m{FN}_i}{\sum _{i=1}^m{TP}_i+\sum _{i=1}^m{FN}_i}\times 100,\%$$

(75)

where FN is incorrect; FP is incorrect correct; TP is actually correct.

3.11. Application of Costume Elements in Contemporary Clothes and Textiles

The application of folk costume elements in modern clothes and textiles is possible through the realization of clothes and accessories, the design of constructions and patterns, artistic drawing, three-dimensional models, online simulators for personalizing clothes, etc. [23].

In the present work, to present the application of the researched elements and motifs of costumes in modern fashion and textiles, methods for the online simulation of clothes and artistic drawings were chosen.

4. Results

4.1. Analysis of Decorative Elements of Folk Costumes

Figure 3 shows the main elements of throne costume cloths: bodices. The presented bodices are decorated with mainly geometric elements embroidered on them. They also feature stylized floral motifs. In the lower part, a geometric or stylized element is located, which occupies the entire lower part of the bodice. It is surrounded by smaller elements that can also be floral, geometric, or combinations thereof. Mirror-identical elements are located on both sides, towards the shoulders. In addition to the mentioned geometric or stylized floral elements, there can also be faunal elements. The colors that stand out are yellow, red, green, and, to a lesser extent, blue.

Figure 4 shows the basic elements of “Tronska” costume cloths—the “skirt” decoration. This group of elements is miniature, measuring about 1.5 cm. They are mainly floral, but there are also variants with geometric designs. In the case of floral elements, the green parts of the flowers mainly consist of three to four green leaves, and in some cases, there are inflorescences among the green leaves. The colors are more numerous, e.g., yellow and different shades of blue and green, red, orange, and white.

Figure 5 shows the basic elements of the robes of “Tronska” aprons. Here, mainly floral elements prevail, and in fewer cases, geometric ones. The elements are about 5 cm in size. The variety of colors is also significant, similar to the previous items. Of course, here again, the basic white, yellow, blue, green, and red are preserved. To a lesser extent, purple and orange are observed.

Figure 6 shows the basic elements of “Tronska” folk costume shirts. The embroidery is mainly geometric, and, to a lesser extent compared to the other parts of the costumes, floral elements are present. The embroidery is monochromatic, and in some cases, two, three, or more colors are observed. The same element is repeated to form the overall look of the embroidery. The colors are mainly red and blue, and to a lesser extent, they are supplemented with yellow, green, purple, and pink.

The thickness of textile fabrics with applied embroidery was determined. The results of these measurements are presented in Figure 7. The skirts were the thickest compared to the textile fabrics of the other parts of the costumes. After them were the aprons and bodices. The shirts had the smallest thickness of the textile fabrics used.

Table 1. Coefficients of form values of folk costume decorative elements. The values are significantly different at p < 0.05.

FCP	Brim	Bodice	Apron	Shirt	FCP	Brim	Bodice	Apron	Shirt
ix					i
i1	1.05 ± 0	1.05 ± 0	1.05 ± 0	1.05 ± 0	i13	1 ± 1.07	1 ± 0.28	1 ± 0.55	1 ± 0.71
i2	1 ± 0.52	1 ± 0.26	1 ± 1.25	1 ± 1.08	i14	0 ± 0	0 ± 0	0 ± 0	0 ± 0
i3	1 ± 0.22	1 ± 0.16	1 ± 0.28	1 ± 0.5	i15	7.52 ± 4.47	2.15 ± 0.83	8.7 ± 12.12	3.6 ± 4.99
i4	1 ± 1.07	1 ± 0.28	1 ± 0.55	1 ± 0.71	i16	0.38 ± 0.11	0.65 ± 0.1	0.71 ± 0.14	0.31 ± 0.23
i5	0.16 ± 0.1	0.33 ± 0.07	0.5 ± 1.13	12.63 ± 34.35	i17	1.75 ± 0.62	0.58 ± 0.25	0.47 ± 0.41	3.7 ± 2.37
i6	0.69 ± 0.11	0.8 ± 0.06	0.79 ± 0.12	0.72 ± 0.15	i18	2.75 ± 0.62	1.58 ± 0.25	1.47 ± 0.41	4.7 ± 2.37
i7	0.54 ± 0.09	0.63 ± 0.05	0.62 ± 0.1	0.57 ± 0.12	i19	1 ± 1.07	1 ± 0.28	1 ± 0.55	1 ± 0.71
i8	1.2 ± 0.4	0.42 ± 0.17	0.34 ± 0.28	2.4 ± 1.48	i20	0.87 ± 0.31	0.29 ± 0.12	0.24 ± 0.21	1.85 ± 1.19
i9	2.57 ± 1.37	0.49 ± 0.27	0.43 ± 0.6	11.28 ± 10.99	i21	4.49 ± 1.2	3.93 ± 0.27	5.9 ± 2.7	2.31 ± 2.41
i10	0.62 ± 0.11	0.35 ± 0.1	0.29 ± 0.14	0.69 ± 0.23	i22	0.13 ± 0	0.13 ± 0	0.13 ± 0	0.13 ± 0
i11	0.87 ± 0.31	0.29 ± 0.12	0.24 ± 0.21	1.85 ± 1.19	i23	1.33 ± 0.15	1.34 ± 0.03	1.92 ± 2.91	0.92 ± 0.76
i12	0.62 ± 0.11	0.35 ± 0.1	0.29 ± 0.14	0.69 ± 0.23	i24	0.33 ± 0.15	0.34 ± 0.03	0.92 ± 2.91	0.75 ± 0.41

FCP—Folk costume part; i—form index.

shows the calculated values of the shape coefficients for the presented decorative elements of costumes. As can be seen in the table, the coefficients of the body elements had the smallest differences relative to the rest of the costume elements. Greater differences were seen between the shirts and aprons.

The Lab color component values of costume element groups were determined. They are shown in Figure 8 as color spheres. The elements of the skirts and bodices had a similar character of change. A gradient of yellow color prevailed, changing from darker to lighter. The skirts also showed smooth transitions from darker to lighter gray-white colors. The blue, red, and green colors were significantly lighter in the skirts than the bodices. The second group, with similar color characteristics, that can be formed was from the colors of the elements of the shirts and aprons. In the aprons, the colors were more striated and lighter compared to those of the shirts. This is because, in the aprons, there were much more complex and colorful floral and geometric elements, while in the shirts, in most cases, monochromatic embroidery was observed, with darker colors of the textile fibers used from which they are made.

Table 2. Color index (c_x) values for folk costume decorative elements. The values are significantly different at p < 0.05.

FCP	Brim	Bodice	Apron	Shirt	FCP	Brim	Bodice	Apron	Shirt
cx					cx
c1	36.05 ± 24.81	48.65 ± 28.43	45.04 ± 24.63	30.99 ± 24.24	c9	18.66 ± 17.61	30.88 ± 24.13	25.48 ± 18.75	19.46 ± 13.73
c2	7.7 ± 8.94	7.6 ± 9.83	13.4 ± 13.21	12.11 ± 11.59	c10	0 ± 0	0 ± 0	0 ± 0	0 ± 0
c3	15.52 ± 16.7	28.17 ± 24.25	18.97 ± 16.96	13.4 ± 10.34	c11	0 ± 0	0 ± 0	0 ± 0	0 ± 0
c4	3.36 ± 2.25	4.73 ± 2.58	3.77 ± 2.27	3.66 ± 2.26	c12	0 ± 0	0 ± 0	0 ± 0	0 ± 0
c5	0 ± 0	0 ± 0	0 ± 0	0 ± 0	c13	0 ± 0	0 ± 0	0 ± 0	0 ± 0
c6	0 ± 0	0 ± 0	0 ± 0	0 ± 0	c14	28.84 ± 23.92	21.46 ± 19.94	34.98 ± 27.67	32.5 ± 25.23
c7	30.59 ± 22.66	32.24 ± 19.63	36.1 ± 23.1	27.46 ± 24.93	c15	0 ± 0	0 ± 0	0 ± 0	0 ± 0
c8	332.93 ± 3284.45	266.17 ± 568.24	254.46 ± 1383.63	49.21 ± 207.66	c16	0 ± 0	0 ± 0	0 ± 0	0 ± 0

FCP—Folk costume part; c_x—color index.

shows the values of the calculated color indices. The largest differences in color index values were observed for the shirt items. The bodices and the aprons had close values in the color components. The skirts also differed in value in this type of index from other parts of the costumes.

A selection of informative geometric and color indices of the costume elements was made. The results of this selection are shown in Figure 9. The indices that had weight coefficient values above 0.6 were taken into account. As can be seen in the figure, a total of 13 features were selected, which changed according to the part from which the costume elements were taken and which had no correlation with each other.

The vector of the selected features consisted of six colors and seven geometric indices. It has the following form:

FV = [c₁ c₄ c₅ c₇ c₉ c₁₄ i₂ i₃ i₆ i₇ i₁₃ i₁₅ i₂₁]

(76)

Figure 10 shows a representation of the reduced data in the resulting feature vector by the kPCA method. The greatest overlap of the data was observed after reducing them with kPCA with a Gaussian kernel, followed by those with a simple kernel. The data reduced with kPCA with a polynomial kernel had less overlap compared to the other two methods.

The following data classes were defined: c1—brim; c2—bodice; c3—apron; c4—shirt. These were used to denote groups of elements in classification.

Table 3. Classification results from Naïve Bayesian classifier (e, %).

kPCA	Simple			Polynomial			Gaussian
Error	ei	gi	e0	ei	gi	e0	ei	gi	e0
Class
c1-c2	62%	36%	43%	31%	3%	17%	85%	41%	48%
c1-c3	37%	29%	32%	59%	38%	44%	5%	50%	49%
c1-c4	35%	51%	53%	18%	43%	40%	6%	50%	53%
c2-c3	31%	31%	32%	1%	12%	7%	5%	49%	49%
c2-c4	28%	41%	40%	0%	26%	18%	6%	50%	49%
c3-c4	9%	30%	26%	13%	34%	29%	94%	52%	50%

shows the classification results with a naïve Bayesian classifier. It can be seen that the highest error rates (over 70%) were observed when using a Gaussian kernel. This was followed by the simple kernel. The lowest error values compared to the other two methods were obtained when using a polynomial kernel.

Using the data reduced by the three variants of kPCA, it can be seen that the lowest values (up to 10%) were obtained for the basic classification error. This is indicative that the first-class data were correctly classified. High levels of actual and total classification errors indicate that data from the second class were misclassified into the first, which in turn increased the total classification error values.

From the obtained results, it can be seen that the classification accuracy depended both on the data volume reduction method and on the separability of the data classes. A reason for the high classification errors is that the classification algorithm set spherical boundaries among the classes. The boundaries among the data classes were different from a circle. This caused some of the data to fall into a class to which they did not belong. Using kPCA with simple and Gaussian kernels resulted in relatively high levels of resulting classification errors. Therefore, these methods were not used in the following analyses.

Table 4. Classification results from discriminant analysis (e, %).

Classifier	LDA			QDA
Error	ei	gi	e0	ei	gi	e0
Class
c1-c2	11%	55%	12%	7%	21%	9%
c1-c3	11%	55%	12%	7%	21%	9%
c1-c4	11%	55%	12%	7%	21%	9%
c2-c3	14%	55%	16%	7%	21%	9%
c2-c4	14%	55%	16%	7%	21%	9%
c3-c4	14%	56%	38%	9%	25%	12%

shows the classification results with discriminant analysis. Reduced data from the feature vector with the polynomial kPCA method were used. In LDA, high levels of actual classification errors indicate that some of the data from the second class were misclassified into the first, which in turn increased the overall classification error. The same trend was observed when using QDA to separate the classes, but the fundamental and total errors were at levels lower than 10%. This indicates that the data were not linearly separable from each other.

Table 5. Classification results using the support vector machines method (e, %).

Separation Function	Linear			Polynomial			RBF
Error	ei	gi	e0	ei	gi	e0	ei	gi	e0
Class
c1-c2	0%	14%	12%	0%	11%	9%	0%	14%	9%
c1-c3	0%	15%	12%	0%	15%	9%	0%	15%	9%
c1-c4	0%	14%	12%	0%	14%	9%	0%	14%	9%
c2-c3	0%	8%	16%	0%	8%	9%	0%	8%	9%
c2-c4	0%	8%	16%	0%	8%	9%	0%	8%	9%
c3-c4	0%	10%	38%	0%	8%	9%	0%	10%	11%

shows the classification results using the support vector method. Data from the vector with selected features, reduced with the polynomial kPCA method, were used. The trend in the classification error values was similar to that of the previous two cases. When using a linear partition function, high levels of actual classification error indicate that some of the data from the second class were misclassified into the first, which in turn increased the overall classification error. On the other hand, when using a single SVM, zero basic classification error rates were observed, and when using non-linear discriminant functions, the overall classification error was below 10%.

From the analyses made and the classifiers used, it can be summarized that the data for the groups of costume elements were not linearly separable among themselves. Linear partitioning functions have a simplified mathematical implementation, but they assume that the four classes for costume decorative elements have compact and non-intersecting regions, which, in practice, is not the case. The resulting error when using linear partitioning functions was e = 12–38%, as in both DA and SVM.

With the lowest values of the total classification error, the support vector method worked (e₀ = 9–11%). The separation of the groups of decorative elements of costumes, depending on their color and geometric indices, was possible using non-linear separation functions (polynomial and RBF).

4.2. Analysis of the Structure of Textile Fabrics of Folk Costumes

Figure 11 shows photographs of the more common structures of the textile fabric of costumes. Textile fabrics are basically woven and have embroidery applied to them. In skirts, there are densely woven fabrics and looser ones. The embroidery is applied directly to the skirts, representing geometric and floral elements. For the bodices, embroidery with yellow thread is mainly used. Decorations with other colors of the textile thread are less common. Aprons are characterized by a pattern of weaving directions. In this process, decorations are created using the technique of weaving. When using complex embroidery, the base is not always of a complex structure. Shirts are woven from thinner threads as the warp and thicker threads, mainly cotton, as the weft. With these, the emphasis is on the monochromatic embroidery on the sleeves and less often on their bodices.

An analysis of the structure of the textile fabrics of costumes was made. The structures of textile fabrics vary considerably, depending on the composition and properties of the textile fibers and the technology by which they are made. The comfort and aesthetic appearance of costumes depend on both their design and the materials used. The main materials used in costumes are wool, cotton, and, in rarer cases, silk. The textile fabrics of the costumes are produced on looms by passing the fiber threads lengthwise and crosswise over one another. Longitudinal threads are warp, and transverse threads are weft. The sequence in which they intertwine is the structure of the textile fabric. The longitudinal ends of the woven textile fabric have hard terminating edges that stop the fabric from unraveling.

Figure 12 shows the main structures used in costume textile fabrics. Figure 12a is a basic litho structure. It is used for cloth and skirts, as it is much more densely woven for cloth. Figure 12b has the same litho structure, but the main threads are thinner and the weft has thicker textile threads. This structure is characteristic of shirts. Figure 12c is a twill-type structure. It is characteristic of the belts and aprons of costumes. The following structures are combined: They are also characteristic of the belts and shirts of the costumes and are also used to obtain decorations on other parts of the costume, such as the skirt, shirt, bodice, and skirts.

Table 6. Color indices (c_x) values for folk costume textile fabrics. The values are significantly different at p < 0.05.

FCP	Brim	Bodice	Apron	Shirt	FCP	Brim	Bodice	Apron	Shirt
cx					cx
c1	42.76 ± 20.9	44.98 ± 19.62	42.84 ± 19.35	44.86 ± 19.28	c9	16.89 ± 19.67	20.96 ± 20.97	39.44 ± 27.12	23.02 ± 26.72
c2	7.97 ± 13.01	7.63 ± 6.16	22.25 ± 22.67	14.62 ± 19.77	c10	0 ± 0	5.05 ± 5.62	4.84 ± 3.62	5.01 ± 5.2
c3	13.31 ± 16.21	17.38 ± 21.94	29 ± 21.06	16.08 ± 19.53	c11	0 ± 0	108.18 ± 111.86	182.96 ± 148.81	168.96 ± 207.76
c4	3.45 ± 2.66	4.29 ± 2.47	5.64 ± 2.79	4.14 ± 3.2	c12	0 ± 0	8.51 ± 41.75	0.97 ± 1.31	3.42 ± 22.83
c5	0 ± 0	0.84 ± 0.52	1.01 ± 0.42	0.87 ± 0.39	c13	0 ± 0	8.71 ± 41.69	1.34 ± 1.59	3.73 ± 22.82
c6	49.1 ± 48.7	61.27 ± 67.28	104.4 ± 74.05	52.75 ± 55.46	c14	29.68 ± 22.14	28.88 ± 25.88	38.28 ± 35.36	32.79 ± 22.92
c7	37.08 ± 20.47	37.5 ± 19.48	25.62 ± 18.25	35 ± 20.02	c15	0 ± 0	60.86 ± 244.78	2.92 ± 3.75	36.86 ± 245.64
c8	120.22 ± 113.38	52.05 ± 45.74	58.33 ± 95.43	101.98 ± 337.71	c16	0 ± 0	212.63 ± 230.01	565.17 ± 515.36	362.35 ± 439.41

FCP—Folk costume part; c_x—color index.

shows the values of the calculated color indices. The largest differences in color index values are observed for the textile fabrics of the shirts. The bodice and the apron have close values of the color components. The textile fabrics of the skirts also differ in values of this type of indices from the other parts of the costume.

Table 7. Texture features (t_x) values for folk costume textile fabrics. The values are significantly different at p < 0.05.

FCP	Brim	Bodice	Apron	Shirt	FCP	Brim	Bodice	Apron	Shirt
tx					tx
t1	15.32 ± 2.7	13.94 ± 2.16	12.09 ± 0.88	13.94 ± 1.59	t12	0.31 ± 0.1	0.27 ± 0.07	0.29 ± 0.09	0.31 ± 0.11
t2	0.19 ± 0.07	0.54 ± 0.31	0.41 ± 0.22	0.33 ± 0.45	t13	15.29 ± 2.72	14.09 ± 2.09	12.19 ± 0.88	13.99 ± 1.58
t3	0.93 ± 0.05	0.81 ± 0.11	0.85 ± 0.08	0.9 ± 0.1	t14	7.2 ± 0.53	7.11 ± 0.47	6.43 ± 0.39	7.03 ± 0.44
t4	0.93 ± 0.05	0.81 ± 0.11	0.85 ± 0.08	0.9 ± 0.1	t15	37.46 ± 6.66	31.29 ± 5.7	27.61 ± 3.72	33.7 ± 5.32
t5	237.34 ± 223.89	98.76 ± 53.71	232.88 ± 279.46	140.33 ± 119.12	t16	1.93 ± 0.38	2.05 ± 0.17	1.97 ± 0.32	1.86 ± 0.42
t6	8.31 ± 15.51	3.37 ± 6.43	20.06 ± 27.58	8.08 ± 8.19	t17	0.19 ± 0.07	0.54 ± 0.31	0.41 ± 0.22	0.33 ± 0.45
t7	0.18 ± 0.05	0.38 ± 0.16	0.33 ± 0.14	0.23 ± 0.23	t18	0.48 ± 0.09	0.75 ± 0.22	0.68 ± 0.19	0.51 ± 0.28
t8	0.2 ± 0.09	0.14 ± 0.05	0.17 ± 0.08	0.21 ± 0.1	t19	−0.63 ± 0.06	−0.42 ± 0.17	−0.46 ± 0.13	−0.61 ± 0.17
t9	2.08 ± 0.43	2.42 ± 0.29	2.28 ± 0.45	2.07 ± 0.6	t20	0.91 ± 0.05	0.82 ± 0.09	0.84 ± 0.06	0.89 ± 0.08
t10	0.91 ± 0.02	0.83 ± 0.06	0.85 ± 0.06	0.9 ± 0.08	t21	0.98 ± 0.01	0.96 ± 0.02	0.96 ± 0.01	0.98 ± 0.02
t11	0.91 ± 0.02	0.83 ± 0.07	0.85 ± 0.06	0.89 ± 0.09	t22	1 ± 0	0.99 ± 0	0.99 ± 0	1 ± 0.01

FCP—Folk costume part; t_x—texture feature.

shows the values of the calculated textural features. Similar values are observed for bodices and shirts, while those for skirts are significantly different from the others. For aprons, the textural feature values are slightly higher than for shirts and bodices, but lower than for skirts.

A selection of informative color and texture indices for the costume fabrics was made. The results of this selection are shown in Figure 13. The indices that had weight coefficient values above 0.6 were taken into account. As can be seen in the figure, a total of 14 features were selected, which changed according to the part from which the image was obtained and which also had no correlation with each other. It can be seen that the textural features had higher values of the weight coefficients compared to the color ones.

The vector of the selected features consisted of seven color and seven texture indices. It has the following form:

FV = [c₁ c₃ c₅ c₇ c₉ c₁₄ t₅ t₆ t₈ t₁₂ t₁₄ t₁₆ t₁₉]

(77)

Figure 14 shows a representation of the reduced data in the resulting feature vector by the kPCA method. The greatest overlap of the data was observed after reducing them with kPCA with a Gaussian kernel, followed by those with simple and polynomial kernels. For the data reduced with kPCA with a simple kernel, the data overlapped less compared to the other two methods.

The following data classes were defined: c1—brim; c2—bodice; c3—apron; c4—shirt. These were used to denote the groups of textile fabrics in classification.

Table 8. Classification results from Naïve Bayesian classifier (e, %).

kPCA	Simple			Polynomial			Gaussian
Error	ei	gi	e0	ei	gi	e0	ei	gi	e0
Class
c1-c2	0%	17%	11%	4%	29%	23%	95%	55%	71%
c1-c3	14%	2%	8%	58%	25%	37%	4%	50%	50%
c1-c4	0%	25%	18%	6%	35%	28%	4%	50%	50%
c2-c3	21%	4%	12%	25%	0%	14%	4%	50%	50%
c2-c4	21%	0%	11%	40%	6%	23%	4%	50%	51%
c3-c4	0%	9%	5%	4%	37%	31%	96%	50%	59%

shows the classification results with a naïve Bayesian classifier. It can be seen that the highest error rates (over 60%) were observed when using a Gaussian kernel, followed by a polynomial kernel. The lowest error values compared to the other two methods are obtained when using a simple kernel.

Using the data reduced by the three variants of kPCA, it can be seen that the lowest values (0–37%) were obtained for the actual classification error. This is indicative that the data from the second class were referred to in the first. High levels of actual and total classification errors indicate that data from the second class were misclassified into the first, which in turn, increased the total classification error values.

From the obtained results, it can be seen that the classification accuracy depended both on the data volume reduction method and on the separability of the data classes. A reason for the high classification errors is that the classification algorithm set spherical boundaries among the classes. Boundaries among the data classes were linear or non-linear but different from a circle. This caused some of the data to fall into a class to which they did not belong. Using kPCA with polynomial and Gaussian kernels resulted in relatively high levels of classification errors. Therefore, these methods were not used in the following analyses.

Table 9. Classification results from discriminant analysis (e, %).

Discriminant Analysis	LDA			QDA
Error	ei	gi	e0	ei	gi	e0
Class
c1-c2	0%	15%	9%	0%	18%	9%
c1-c3	18%	0%	23%	13%	0%	19%
c1-c4	0%	34%	3%	0%	33%	4%
c2-c3	36%	12%	37%	20%	3%	19%
c2-c4	11%	7%	18%	20%	0%	24%
c3-c4	0%	18%	8%	0%	12%	8%

shows classification results with discriminant analysis. Reduced feature vector data with the simple kPCA method were used. In LDA, high levels of actual classification errors indicate that part of the data from the second class were misclassified into the first, which in turn increased the overall classification error. The same trend was observed when using QDA to separate the classes, but the fundamental and total errors were at levels lower than 10%. This shows that the separability of the data did not depend on the partition function used.

Table 10. Classification results using the support vector machines method (e, %).

Separation Function	Linear			Polynomial			RBF
Error	ei	gi	e0	ei	gi	e0	ei	gi	e0
Class
c1-c2	0%	9%	9%	0%	9%	9%	0%	9%	9%
c1-c3	0%	9%	9%	0%	9%	9%	0%	9%	9%
c1-c4	0%	7%	4%	0%	7%	4%	0%	8%	4%
c2-c3	10%	10%	10%	12%	10%	11%	10%	10%	10%
c2-c4	4%	9%	4%	6%	10%	9%	2%	9%	8%
c3-c4	4%	5%	10%	4%	6%	9%	4%	6%	9%

shows the classification results using the support vector method. Data from the selected feature vector reduced with the simple kPCA method were used. The trend in classification error values was similar to that of the previous two cases. When using a linear partition function, high levels of actual classification error indicate that some of the data from the second class were misclassified into the first, which in turn increased the overall classification error. On the other hand, when using a single SVM, zero basic classification error rates were observed, and when using non-linear discriminant functions, the overall classification error was below 10%. As with DA, in the case of kSVM, the separability of the data did not depend on the partition function used.

From the analyses made and the classifiers used, it can be summarized that the data for the textile fabrics from the costume parts did not have a linear separability among them. The resulting error when using linear discriminant functions was e = 3–37% for both DA and SVM. With the lowest values of the total classification error, the support vector method works (e₀ = 4–11%). The separation of the groups of textile fabrics from costumes, depending on their color and textural features, did not depend on the type of separation function. It can be summarized that the data reduction method had the greatest influence on the separability of the data from the textile fabrics of costumes.

4.3. Creation of Modern Cross-Stitch Patterns with Embroidered Folk Costume Elements

The embroidery images can be converted into a cross-stitch pattern. For this purpose, the online tool Pic2Pat (https://www.pic2pat.com, accessed on 22 February 2023) was used. The results of this conversion are shown in Figure 15. Once an embroidery photo is selected, the tool converts it into appropriate colors and skeins. Finally, a *.PDF file is generated with the necessary data for making the embroidery.

4.4. Creation of Modern Textile Patterns with Folk Costume Elements

In this part of the work, an example of creating modern textile patterns with costume elements is presented. A floral motif from a costume apron from the Yambol region of Bulgaria was used. The element represents stylized flowers with leaves shaped like floral fragments.

Figure 16 shows a developed pattern and an example of its application in creating clothing accessories. In the creation of the pattern and its visualization, the following software products were used: Inkscape (https://inkscape.org, accessed 12 September 2022). The software product is convenient for working with vector and raster images. Through the following application, a repeat and a pattern were created: Vida Studio (https://studio.shopvida.com, accessed 12 September 2022). This tool is suitable for creating visualizations of textiles, clothing, and accessories. The online tool was used to create visualizations of the created patterns on textile fabrics and garments. The motifs were alternated in a full-drop repeat. A scarf was used to visualize the pattern because it is a simple form of decoration and an accessory to clothing. For this reason, a scarf is a universal accessory for clothing. It can be worn wrapped around the neck or head. The resulting scarf was rectangular in shape, allowing it to be worn in many different ways. It can be combined with suitable clothes and worn on suitable occasions. For example, with a casual elegant dress or suit, this is a wonderful suggestion for a complete woman’s look. The scarf fits tightly, is soft, and is gentle on the other garments. It turns into a colorful flag with every gust of wind.

4.5. Creation of Contemporary Clothes with Folk Costume Elements

In Figure 17a, an ensemble design of a women’s jacket in combination with trousers is presented. The jacket was designed with a straight silhouette and length to the waistline; the sleeves are single-stitched, ending with a wide cuff to match the belt of the jacket. The highlights of the model’s design are the fringes that surround the edges of the lapels, the belt, and the cuffs. This element was borrowed from costume aprons, and it gives character and a beautiful finish to the piece. Fringes are a current fashion element in modern clothing and accessories that are present in designers’ collections. The design of the jacket also uses a twill weave structure, which is very characteristic of belts and aprons, for the fabric. Combinations of pastel colors are used, which are most common in costumes of orange and green. This harmony of colors is borrowed from nature, a source of inspiration for costume designers.

In Figure 17b, a model of a women’s dress in an A-shaped silhouette is presented using sets and a wide frill. The neckline design of the dress was borrowed from the bodices of costume cloths, being designed with a deep-hole pleat embellished with embroidery of stylized floral elements. Basic details are attached to the richly set placket, with the lengthwise dress ending in a wide asymmetric flounce. The main decorative element and accent of the model is the embroidery located on all the details decorating the cloths of the costumes. The combinations of colors used in the costumes have been preserved, which shows that they can also be successfully applied to modern urban clothing. The fringe, a decorative element used in aprons, also gives a beautiful finish to the frill of the dress.

Figure 17c shows a classic knee-length women’s dress pattern in an A-line silhouette achieved by cut-out frills and 3/4-length sleeves. Decorative elements of the model are the embroidery and lace, with emphasis on the color combinations in the embroidery, preserved as they were used in the costume aprons. The application of several shades of green, pink, and blue makes the colors sparkling and lively, which gives a lot of freshness and vitality to the model.

Figure 18 shows models of women’s clothing with elements of Bulgarian folk costumes. The design of the women’s jacket was inspired by the throne woman’s costume. The compositional center is the embroidered quadrangular neckline and the embroidered quadrangular bodice. The embroidered rectangular bodice, called the “gazé”, is the most distinctive decoration of the throne women’s costume. The ornaments on the gauze neckline are floral, zoomorphic, and geometric. Sometimes “magical” symbols, such as crosses, swastikas, and octagonal stars, are embroidered. Gazé cloth is multicolored, with yellow being the most commonly used color. The main idea of the four variants of the presented design is the harmonious relationship between the shape of the neckline and the shape of the sleeves. In the figures, it can be seen that the square neckline is harmoniously combined with kimono sleeves and off-the-shoulder sleeves, as well as with raglan and wedged sleeves, formed with straight and smooth lines that close the corners.

5. Discussion

The results obtained in the present work complement those of [1]. The relationships among the research, sustainability, and related cultural heritage conservation activities are proven with data from elements of Bulgarian national costumes.

Digitizing the elements of Bulgarian folk costumes, as well as the proposed methods of obtaining data about them, in order to organize data sets, is a solution to the priority task of ensuring the sustainability of the use of cultural heritage. This can be achieved by reducing and even eliminating the costs of this activity, where possible, thereby improving the results of Gorofyanyuk [3].

The offer of modern embroidery patterns, textile patterns, and clothing allows for the creation of products with a minimum residue in their production. This complements the guidelines set forth by Ilieș et al. [4].

The detailed numerical analysis of elements of Bulgarian costumes improves upon the results presented by Kuo et al. [7], which only extracted data for similar elements, in order to obtain patterns.

The methods proposed in the work of Shih et al. [8] have been refined through geometric, textural, and topological descriptions of the elements of Bulgarian folk costumes.

The proposed modern solutions with the application of the elements of Bulgarian costumes in bodices, textile patterns, and clothing, remove some of the main shortcomings of the works by Elnashar and Boneva [9], Florea-Burduja et al. [12], and Indrie et al. [13], who only presented data on the elements of Egyptian folklore without presenting options for their modern application.

The automated algorithms and procedures chosen in the present work facilitate the process of collecting and systematizing the captured images of folklore elements, thus improving the work of Arora et al. [10].

The works by Baeva and Baev [11] and Baeva [5] have been supplemented. Practical methods for obtaining, processing, and analyzing numerical data of the elements of Bulgarian costumes, instead of their textual descriptions, are proposed.

To complete the work, and following the recommendations of Kalita et al. [14], more research has been done related to the traditional textile fabrics used, which will enrich the knowledge of folk dances and costumes.

This research has improved upon the work of Elnashar et al. [15]. The indices of Bulgarian folklore elements were formed into a vector containing the most informative of them. This improved and refined the data analysis, rather than relying on only one type of feature, such as textural ones.

The methods and tools proposed in the work help to refine, improve, and complement the previous developments in the field of the fourth pillar of sustainability [24], namely the preservation of cultural heritage and its application in modern fashion and textile design. The results obtained in this work can be a driver for the environmental, social, and economic aspects of sustainable development.

6. Conclusions

The results of this research make a valuable contribution to the preservation, digitization, and promotion of Bulgarian cultural heritage. The successful application of digital color imaging and non-destructive testing has contributed to the appreciation and understanding of Bulgarian cultural values and history, ensuring that this rich heritage endures and remains relevant for generations to come. In addition, the incorporation of traditional elements into contemporary textiles broadens the cultural impact, making the research contribution even more profound and impactful for both local communities and a wider global audience.

Non-destructive tests of textile fabrics and elements of Bulgarian costumes were carried out. Contemporary textile patterns and garments with elements of Bulgarian costumes are offered.

It was established that in the analysis of decorative elements from Bulgarian costumes, the accuracy of classification depends both on the method for reducing the volume of data and on the separability of the classes of data, depending on the classifier used.

It was established that in the analysis of microscopic images of textile fabrics from Bulgarian costumes, the accuracy of the classification for the studied objects depended both on the method for reducing the volume of data and on the used classifier. In the considered cases, a classification error below 10% was obtained using a non-linear kPCA kernel and SVM with a non-linear separation function.

The link to sustainability in this research lies in its commitment to protecting cultural heritage in a responsible and sustainable way. By using digitization techniques, non-destructive testing, and encouraging community engagement, the research ensures that the beauty, wisdom, and creativity of Bulgarian costume embroidery can flourish sustainably for generations to come.

The results of this research can be used by various stakeholders in the field of cultural heritage and beyond. First of all, cultural heritage institutions can benefit from the digitization and preservation of embroideries from Bulgarian costumes. Using digital color images, these institutions can create comprehensive and accessible archives, preserving priceless cultural artifacts for posterity. Researchers can delve into these digitized records to conduct in-depth studies of embroidery techniques, patterns, and historical context, contributing to a deeper understanding of Bulgaria’s cultural heritage.

This research can be extended in several directions. Expanding the scope and scale of digitization efforts to include a more diverse range of Bulgarian costumes and needlework styles would provide a more comprehensive and representative depiction of the country’s cultural heritage. This may involve collaboration with regional experts and communities to ensure inclusiveness and accuracy in capturing diverse traditions.

The limitations of this work include the focus on a specific aspect of Bulgarian cultural heritage, namely, costume embroidery elements, which may not fully encompass the entirety of the country’s rich cultural values and history. Additionally, while the research presents successful classification results using certain methods, the classification accuracy may vary depending on the dataset and classifier used, suggesting the need for further exploration and validation on a wider scale. Moreover, this research primarily focused on digitization and classification techniques, and additional studies might be required to address broader sustainability aspects related to the preservation and cultural impact of traditional elements in contemporary textiles.