The dual channels selected for this study are the three primary color information
channel and the stroke information channel. This channel utilizes a grayscale co-occurrence
matrix to process the feature information extracted from the stroke channel, and inputs
the feature information extracted from the two channels into a dual path network for
processing; Then it combines support vector machines to classify feature data and
complete the task of classifying and recognizing art images in different styles and
genres.
3.1. Construction of a Dual Path Network Image Classification Model
The image classification technology for art drawing mainly operates by determining
the style and genre of the tested object, as well as the author's characteristics.
Common natural image classification technologies are mainly in view of DL networks.
This introduces the Dual Path Network (DPN) model, which, as a simple and efficient
model for image classification, can be considered as an integrated network model consisting
of DenseNet (DN) and ResNet (RN) through the HORNN framework. The mapping method of
RN is the difference between the actual observation values and the fitted values,
which can effectively transfer the learning objectives and ensure the accuracy of
the model. Fig. 1 illustrates the relevant schematic diagram.
Fig. 1. Schematic diagram of residual network structure.
Fig. 1 shows that in the RN model, the upper layer of the network will propagate the original
input information x forward together. This also means that no matter how poor the
performance of f (x) is, it is unlikely to affect the performance of the RN model.
DN network is a simple connection mode architecture that improves the short path model,
with fewer parameters and narrower network, with less than 100 convolutional layer
outputs in dense blocks. Therefore, the number of mapped features will also be small,
making it relatively easy to train the network. The DN network model is shown in Fig. 2.
Fig. 2. Schematic diagram of DN network structure.
Fig. 2 shows that the DN network model can directly connect all layers with matching features
and preserve information between layers in the order of mapping size. The nth layer
obtains additional information from the n-1 layer, and maps all the nth layer information
obtained to the n+1 layer. By gradually mapping and transmitting information, it ensures
that the feature mapping size in each structural block is consistent. This is to avoid
the problem of missing relevant information due to varying feature map sizes during
the information stitching process. The internal connection route of the DPN model's
neural network is a novel topology structure that mimics the dense DN and RN, and
the network structure of DPN is relatively similar to RN; The order of its network
structure is 7 * 7 convolutional layer, maximum pooling layer, and four stages; Each
stage includes UB Stage, which is then connected to the global average pooling layer
and fully connected layer, and finally to the Softmax layer. It can be considered
that DPN is a network model formed by integrating DN and RS. Fig. 3 demonstrates the details.
Fig. 3. DPN Schematic diagram of network structure.
Fig. 3 shows that the DPN model retains most of the structure of the RN model and integrates
some of the DN model, which can generate new features while ensuring low redundancy
of features. The formula involved in using RN networks to reduce complex data in the
DPN model is shown in Eq. (1).
In formula (1), $x^{k} $represents the information extracted in step $k$of a single path; $f(\cdot)$
is the dual path function; $f(\cdot)$ is the initial path; $h$ is the number of features.
It utilizes the DN network to generate new feature related formulas as shown in (2).
In formula (2), $v_{t} $is the feature learning function of the dual path function; $v_{t} $ represents
the generated new feature information. The entire function expression refers to the
remaining paths that support the reuse of common features. Integrate RN and DN to
obtain the functional expression of DPN, as shown in formula (3).
The current feature state of a single path is generated through the transformation
function of the DPN network, with the next mapping or prediction. The relevant function
expression is shown in formula (4).
In formula (4), $h^{k} $represents the current state; $g(\cdot)$is the conversion function.
3.2. Construction of a Dual Channel Dual Path Network Art Image Classification Model
Dual channels can enable the simultaneous dissemination of dual information and facilitate
cross-border flow of information, achieving two-way communication between different
locations; The dual path model can explain how information affects event processes
and outcomes from the dual path perspectives of the central and edge paths, providing
a very detailed and comprehensive framework. This study combines the advantages and
performance of both and proposes a fine art painting via two channel dual path networks
(FPTD) network model for the recognition and classification of art images. The structure
of the FPTD model constructed by the research institute is shown in Fig. 4.
Fig. 4. Structure diagram of RPTD network model.
Fig. 4 showcases that the dual channel of the FPTD model consists of two channels: the three
primary color channel (Red, Green, Blue, RGB) and the stroke information channel.
The RGB channel mainly extracts visual information of the image, including elements
such as graphics, lines, and colors, while the stroke information mainly extracts
information about the author's strength, speed, rhythm, and emotions when using the
pen. After extracting image features and author stroke related information through
dual channels, the FPRT model passes the channel information separately to the path
network for processing, and extracts image features through the DPN model. Then it
combines its features and uses support vector machine (SVM) for distinguishing the
extracted data information, achieving effective classification of feature images.
In the FPTD model constructed by the research institute, all original RGB information
of art images will be input into the DPN model for calculation; The information extracted
by the stroke channel will include the RGB channel information of the grayscale co-occurrence
matrix. By integrating the information of the two parts, they are jointly input into
the DPN model corresponding to the stroke channel for feature data extraction. The
mathematical relationships involved in processing stroke channel information using
the grayscale co-occurrence matrix (GLCM) include: let $G$ be a matrix containing
grayscale pixels $i$ and $j$; $g$ is the quantity of times pixels $i$ and $j$appear
at the specified position $I$; $L$ is the quantity of grayscale levels in the image
$I$ with size $M*N$. The functional expression of $G$ is formula (5).
The expression for the degree function of pixels $i$ and $j$ appearing simultaneously
in $I$ is Eq. (6).
After completion, in order to further improve the effectiveness and robustness of
information extraction, the study introduces support vector machine (SVM). SVM, as
a classical machine learning algorithm, has the advantages of handling high-dimensional
data and avoiding overfitting. Specifically, SVM is able to find the best classification
hyperplane in high-dimensional space, which improves the model's classification performance
and decision-making accuracy in complex traffic environments. By combining SVM and
DQN, the model not only learns more accurate state-action value functions, but also
improves the discriminative ability of the data and the generalization performance
of the model in the feature selection process. The relevant schematic diagram is showcased
in Fig. 5.
Fig. 5. Schematic diagram of SVM mathematical algorithm.
Fig. 5 shows that the core of SVM algorithm is to create curves or Hyperplane with the strongest
generalization and robustness to classify data sets. Linear and nonlinear data sets
can be fully classified in two-dimensional space. The classified data sets are generally
distributed next to the optimal classification curve or optimal Hyperplane, and the
vector data closest to the optimal Hyperplane becomes the support vector. The Hyperplane
function expression of two-dimensional linear data is expressed by formula (7).
In formula (7), $w$represents the sum of normal vectors that determine the direction of the Hyperplane;
$b$is the distance from the Hyperplane to the origin; $x$is the sample data. The distance
between Hyperplane of sample data bands can be expressed by formula (8).
The linear and nonlinear problems are transformed into the minimum problem with constrained
values for optimization, and the function expression of Quadratic programming is formula
(9).
In formula (9), $i=\{ 1$, $2$, ..., $l\} $, and $l$are sample functions; The value of $y{}_{i}
$ minimum constraint function is introduced into Lagrange multiplier $a_{i} $. The
decision function expression of SVM is shown in formula (10).
The introduction of KF enables the mapping of data from input space to feature space,
facilitating linear separation of data in higher dimensional spaces. The basic form
of SVM using KF is shown in formula (11).
In formula (11), $K(x_{i} *x)$ is the KF, and commonly used KF include linear KF, polynomial KF,
and Gaussian KF. Since the Gaussian KF can map the limited data into a higher dimensional
space with less computation, and is suitable for research background requirements,
it selects the Gauss sum KF as the KF of SVM to carry out experiments. The expression
of Gauss and functions is shown in formula (12).
In formula (12), $\sigma $is the parameter that determines the local range.