3D martial arts image classification algorithm based on symmetry theory

Abstract

Aiming at the problems of large error and poor robustness of traditional image classification methods, a three-dimensional martial arts image classification algorithm based on symmetry theory is proposed. According to the preprocessed 3D martial arts image, the classification algorithm based on symmetric neural network is used to realize the classification of 3D martial arts image. The experimental results show that the minimum error rate of this algorithm is 6.1%, which is far lower than the traditional algorithm, it is shows that the improved algorithm has higher definition, better robustness, and the test results of different topological nodes on the test solution show that the average error rate of the algorithm is lower. Compared with the same type of algorithm, the application value of the proposed algorithm is significant.

Keywords

Denoising sharpening SDBN network mean filtering gray uniformity

1 Introduction

When people recognize an object or image, the first or deepest impression is their shape and outline, so they can be quickly judged whether they are symmetrical or not. Of course, there is no very accurate symmetry in nature, so this kind of judgment is not a strict mathematical judgment. It’s just that people’s initial intuitive understanding of an object, even because each person’s observation angle is different, the conclusion will be different [7 , 23]. However, through preliminary analysis, we can get the approximate symmetry axis of this object or image, so as to facilitate the later work of image recognition and positioning [16, 17].

With the advent of the information age, the visual tasks of machines in various fields also need to deal with a large number of image information. When processing and analyzing these information, in order to save time and storage space, we need to acquire and locate image feature points as quickly and accurately as possible [14]. According to the different characteristics of different types of images, we can design symmetry feature detection operators that are suitable for this kind of image, and preprocess the image with translation, scaling, filtering, denoising and so on. According to the symmetry of the object, the image compression and coding technology is used to simplify the feature information of the image, realize the fast storage of the image, record the overall features of the target image to be studied, recover some important information lost in the image preprocessing stage, and obtain the orientation and attitude of the object in the 3D space, so as to facilitate the later detection and recognition development of 3D model work [3, 4]. In order to make more achievements in this field and get everyone’s recognition, many companies, universities and scientific research institutions at home and abroad have carried out relevant researches and committed to this emerging field, and even the government has set up exclusive departments, invested a lot of human and material resources and financial resources to study the digital information of 3D model and plane image. After unremitting efforts, many valuable results have been achieved. Under the guidance of this trend, more and more people begin to have a great interest in image symmetry and have carried out a lot of theoretical research and experiments, so the research and application of various symmetry detection algorithms for image has become a hot research direction of computer vision [19]. In reference [10], an algorithm of fog image classification based on SVM and hybrid features is proposed to meet the requirement of automatic recognition of fog concentration in adaptive defogging system. Combined with the characteristics of fog images, the mixed feature vector is composed of dark channel features, wavelet features and mean value normalization features, which is used to describe the characteristics of different fog concentrations. The SVM algorithm is used to supervise and learn the mixed eigenvectors, and finally realize the automatic recognition and classification of fog images. Experimental results show that the algorithm can effectively identify and distinguish non fog, light fog and dense fog images, which provides a good classification reference for the defog system to adaptively select defog parameters according to the fog concentration, but the algorithm has a high error rate. In reference [13], an image classification algorithm based on data mining is proposed to solve the classification accuracy problem of traditional image methods. Firstly, the channel model of image retrieval in multimedia database is constructed, and vector quantization coding is carried out, then Harris corner detection algorithm is used to extract image feature points, and fuzzy c-means clustering algorithm is used to realize image classification [20, 21]. The experimental results show that the algorithm can accurately express the image content information, improve the accuracy of image classification, and has strong robustness. However, the algorithm does not enhance the image, resulting in low definition and poor robustness.

Based on the above background, in order to solve the problems of traditional methods, this paper proposes a 3D martial arts image classification algorithm based on symmetry theory, and classifies 3D martial arts image according to the symmetry of 3D martial arts image.

2 Definition of the algorithm

2.1 Preprocessing method of 3D martial arts image

2.1.1 Denoising

In real life, when collecting 3D martial arts images, generally because of one or several factors, the images formed by 3D martial arts image acquisition equipment contain certain noise, which affects the quality of images, increases the area of insignificant areas, and reduces the image quality. Therefore, it is necessary to denoise the 3D martial arts image. In the image space domain, the mean filtering method is used to denoise.

Supposing that x and y are objects in d-dimensional feature space F^d, and the influence function of data object y on x is a function $f_{B}^{y} : F^{d} \to R_{0}^{+}$ , which is defined according to a basic influence function f_Gauss (i, j). The expression is as follows: $f_{Gauss} (i, j) = e^{- \frac{d {(X_{i}, X_{j})}^{2}}{2 σ^{2}}}$ (1) where d (X_i, X_j) ² is the distance between object i and object j; σ is the density adjustment coefficient and e is the derivation coefficient.

Two dimensional windowed Fourier transform is used to extract the spectrum information W of each part of infrared image. The definition of transform can be expressed as follows:

$\begin{matrix} F (i, j, u, v) = \int_{- \infty}^{+ \infty} f (x, y) W (x - i, y - j) \\ e^{- j (ux, vy)} dxdy \end{matrix}$ (2) where, F represents the transformed image vector, (i, j) is the central coordinate of the sub block of infrared image, (x, y) is the spatial coordinate, and (u, v) is the frequency coordinate.

Assuming that the image is I (x, y), it is composed of 3D martial arts image and reflection image, which are represented by L (x, y) and R (x, y) respectively. The output image is obtained by single-scale Retinex algorithm, and the expression is as follows: $R (x, y) = log I (x, y) - log [L (x, y) * I (x, y)]$ (3)

The average filtering method is used to filter the 3D martial arts image. The average filtering formula is: $g (x, y) = \frac{1}{M} \sum_{(i, j) \in s} f (i, j)$ (4) where, g (x, y) is the gray value of the processed 3D martial arts image at this point; s is the neighborhood set centered on (x, y); M is the total number of pixels in s.

After filtering, the infrared image spectrum needs to be inverse Fourier transformed to obtain the spatial data of infrared image, further reducing the impact of noise on the 3D martial arts image [9]. If f′ (x, y) is the infrared image after inverse transformation, the inverse transformation is expressed as follows: $f^{'} (x, y) = \sum_{u = 0}^{N} F^{'} (u, v) \times exp {j \frac{2 π}{N} (xu + yu)}$ (5) where, N represents the vector, N = 1, 2, . . . , n.

2.1.2 Sharpening

In the application of image enhancement, bilateral filter is a kind of nonlinear filter, which is mainly used to smooth the image [11, 15]. Due to the more comprehensive factors considered in bilateral filtering, bilateral filtering can remove the residual noise of the image while retaining the edge information of the image. The expression is as follows: $R_{s} = \frac{1}{k (s)} \sum_{p \in Ω} f (p - s) g (I_{p} - I_{s}) I_{p}$ (6)

In the formula, R_s is the filtering result; Ω is all pixels of 3D martial arts image; f and g are Gaussian functions; I_p is the pixel value of p; k (s) is the standardization factor. s and p represent the left and right sides of 3D martial arts image; I_s represents the pixel value of s.

The gradient vector which can reflect the 3D martial arts image is obtained by gradient operator, and the expression is as follows:

$\begin{matrix} s_{k}^{g} = \sum_{j = 0}^{k} P_{r} (r_{j}^{g}) = \sum_{j = 0}^{k} \frac{nj}{n}, \\ k = 0, 1, 2, . . ., {| \nabla u_{0} |}_{max} - 1 \end{matrix}$ (7) where, $s_{k}^{g}$ is the mapping probability of the gradient value k; n is the total number of pixels in the 3D martial arts image; | ∇ u₀|_max is the maximum gradient value; nj is the number of pixels with the gradient value j; $\sum_{j = 0}^{k} P_{r} (r_{j}^{g})$ is the probability of the gradient value j.

Since minimizing the overall variation of 3D martial arts image can suppress noise, in order to enhance the details of insignificant area of 3D martial arts image and suppress noise, TV model is used to enhance the insignificant area of 3D martial arts image, and the following energy pan function is constructed:

$\begin{matrix} E (u) = min {χ \iint_{Ω} | \nabla u | dxdy \\ + δ \iint_{Ω} | \nabla u - E^{'} | dxdy} \end{matrix}$ (8)

In the formula, u is the enhanced 3D martial arts image; parameters χ and δ are used to balance the enhancement and denoising of 3D martial arts image.

For any object x and distance R in 3D martial arts image space, with x as the center and R as the circular area, the gradient image expression is: $R = \frac{mean (D)}{n^{coefR}}$ (9) where mean (D) is the average distance between the center and all objects; n^coefR is the adjustment coefficient of domain radius. Then the balanced gradient field of 3D martial arts image is expressed as: $E = \frac{\nabla u_{0}}{| \nabla u_{0} |} \cdot E^{g} [| \nabla u_{0} |]$ (10)

In the formula, E is the balanced gradient field; u₀ is the original 3D martial arts image; E^g [| ∇ u₀|] is the equalization of 3D martial arts image; $\frac{\nabla u_{0}}{| \nabla u_{0} |}$ is the unchanged gradient field direction of 3D martial arts image.

To sum up, on the basis of filtering 3D martial arts image with mean filtering method, the 3D martial arts image is sharpened with differential operator in the spatial domain of the image [8].

2.1.3 Image enhancement

Based on the 3D martial arts image sharpened by the above summary, the enhancement image processing effect method based on gray level uniformity is adopted to enhance it, and the steps are as follows:

Calculate the nonuniformity ψ_ij of 3D martial arts image’s feature information, whose expression is: ${psi}_{ij} = 1 - β_{ij}$ (11) where, β_ij represents the regularization coefficient of the sharpened 3D martial arts image.

Calculate the average nonuniformity value of special diagnosis information of 3D martial arts image for w_ij, the formula is as follows:

${\begin{matrix} δ_{ij} = \frac{\sum_{p - i - (d - 1) / 2}^{i + (d - 1) / 2} \sum_{q - j - (d - 1) / 2}^{j + (d - 1) / 2} (g_{pq} - ψ_{ij})}{\sum_{p - i - (d - 1) / 2}^{i + (d - 1) / 2} \sum_{q - j - (d - 1) / 2}^{j + (d - 1) / 2} ψ_{pq}} \\ i \geq 0, j \geq 0, p \geq M - 1, q \geq N - 1 \end{matrix}$ (12) where, w_ij represents the d × d window centered on the pixel (i, j); g_pq represents the gray value of the feature information pixel (p, q); d represents the weight of the feature information of the 3D martial arts image.

Calculate the contrast C_ij of the feature information pixel p (i, j) of 3D martial arts image and convert it to obtain: $C_{ij} = | \frac{g_{ij} - δ_{ij}}{g_{ij} + δ_{ij}} | = C_{ij}^{ξ ij}$ (13)

In the formula, ξ_ij represents the contrast magnification factor of 3D martial arts image’s feature information; δ_ij represents the brightness similarity of 3D martial arts image’s feature information; g_ij represents the gray value of 3D Martial arts image’s feature information pixel.

Change the gray value of the feature information pixel of 3D martial arts image, its expression is: $g_{ij} = δ_{ij} + \frac{1 - C_{ij}}{1 + C_{ij}}$ (14)

Repeat the above steps for all pixels of 3D martial arts image’s feature information.

Assuming that the gray level of the given 3D martial arts image’s feature information is from g_min to g_max, the determination process for the minimum magnification factor of the contrast of the 3D martial arts image’s feature information is as follows:

Step 1: calculate the histogram H (g) of 3D martial arts image’s feature information, and find all peaks of the 3D martial arts image’s feature information histogram as follows: $H_{max} (g 1), H_{max} (g 2), . . ., H_{max} (gn)$ (15)

Step 2: calculate the average value ${\bar{H}}_{max}$ of all peaks of the 3D martial arts image’s feature information histogram in step 1, and the calculation formula is as follows: ${\bar{H}}_{max} = \frac{\sum_{i = 1}^{n^{'}} H_{max} (g_{i})}{n^{'}}$ (16)

Step 3: find out the peak value of the feature information histogram of 3D martial arts image which is greater than ${\bar{H}}_{max}$ ;

Step 4: calculate the first and last peaks of the feature information histogram of 3D martial arts image obtained in step 3, and their corresponding gray values g1 and gn′;

Step 5: calculate the minimum contrast magnification factor ξ_min of 3D martial arts image’s feature information according to the following formula: $ξ_{min} = \frac{{gn}^{'} - g 1}{g_{max} - g 1}$ (17)

According to the calculation results of the above formula, the contrast magnification factor ξ_ij of 3D martial arts image’s feature information is calculated by the following formula: $ξ_{ij} = ξ_{min} + \frac{ξ_{max} - ξ_{min}}{β_{max} - β_{min}} \times (β_{ij} - β_{min})$ (18)

According to the above calculation process, the enhancement processing of 3D martial arts image is completed [18].

2.2 Image classification algorithm based on symmetric neural network

Based on the 3D martial arts image processed in Section 2.1, the image classification algorithm based on symmetrical neural network is used to classify it.

In this paper, the method of network combination is applied to deep belief network (DBN) and convolutional neural network (CNN), respectively integrating symmetric deep belief network (SDBN) and symmetric convolutional neural network (SCNN) [5, 16].

2.2.1 Structure of SDBN network

– Pre-training

Network training makes the initial weight of the network closer to the global optimum. When training the SDBN network of 3D martial arts image after preprocessing, i.e. training the RBM in the left and right subnetworks, since the RBM hidden layer of the restricted Boltzmann machine is used to reconstruct the visible layer of 3D martial arts image after preprocessing, the approximate calculation method of contrast divergence (CD) is used, which is one of the sources of differences between different networks [12].

In the left and right sub-network of SDBN of 3D martial arts image, any two adjacent layers, except the category layer, constitute an RBM, which is defined as visible layer and hidden layer. There is full connection between the hidden layer and visible layer of 3D martial arts image, and there is no connection between nodes in visible layer and nodes in hidden layer of 3D martial arts image. The node in visible layer of 3D martial arts image is v∈ { 0, 1 }, and the node in hidden layer of 3D martial arts image is h ∈ { 0, 1 } ^p. In 1982, Hopfield et al. proposed that the joint configuration {v, h} between hidden layer and visible layer nodes has joint energy.

$E (v, h; θ) = - \sum b_{i} v_{i} - \sum b_{j} v_{j} - \sum v_{i} h_{j} w_{ij}$ (19) where, E represents the joint energy factor, and the algorithm parameters are θ ={ w, b }. v_i and h_j are the offsets between the visible layer and the hidden layer corresponding to the binary states b_i and b_j of the node i in visible layer and the node j in hidden layer respectively. w_ij is the connection weight between them. Based on the 3D martial arts image processed in Section 2.1, it is set as a training image. The probability that the binary state of hidden layer feature detection node is 1 is set as follows: $p (h_{i} = 1 | v) = δ (b_{j} + \sum v_{i} w_{ij})$ (20) where, δ (x) = 1/(1 + e^-x) is sigmoid or ReLU function. Once the state of hidden node is selected, the 3D martial arts image can be reconstructed. By setting the probability that each pixel value is 1: $p (v_{i} = 1 | h) = δ (b_{i} + \sum h_{i} w_{ij})$ (21)

The principle of conditional probability is similar on the left and right sides of SDBN network. It should be noted that SDBN is designed for classification. The logistic regression network composed of joint layer and category layer is not in the process of pre training, and its processing mode is just random initialization. Traditionally, the parameter value of RBM is solved by maximizing the likelihood function of the gradient rising process. The logarithm of the gradient likelihood function based on the energy model is:

$\frac{\partial}{\partial θ} L (θ) = - {[\frac{\partial E (v; θ)}{\partial θ}]}_{data} + {[\frac{\partial E (v; θ)}{\partial θ}]}_{model}$ (22) where, ∂ represents the likelihood function, E (v ; θ) belongs to the free energy of v, ${[\frac{\partial E (v; θ)}{\partial θ}]}_{data}$ and ${[\frac{\partial E (v; θ)}{\partial θ}]}_{model}$ represent the expected values relative to all values of data and driving nodes in visible layer respectively. The parameter needs to perform the logarithmic likelihood function of gradient rise. For an RBM, updating the parameter w_ij is equivalent to expressing as follows: $Δ w_{ij} = ɛ ({[v_{i}^{0} h_{i}^{0}]}_{data} - {[v_{i}^{\infty} h_{i}^{\infty}]}_{mod el})$ (23) where, ɛ is the learning rate, ${[v_{i}^{0} h_{i}^{0}]}_{data}$ is the expected value of configuration when the hidden layer of 3D martial arts image is driven by data, ${[v_{i}^{\infty} h_{i}^{\infty}]}_{mod el}$ is the expected value of configuration when the hidden layer of 3D martial arts image is driven by algorithm.

– Fine adjustment of SDBN

After the DBN is pre trained, the joint layer of 3D martial arts image is combined with the two networks. Finally, the joint layer of 3D martial arts image is fully connected with the category layer, and the better network of 3D martial arts image is obtained by fine adjustment the network connection weight through the back propagation algorithm.

After the combination of subnetworks, the SDBN network difference is captured by measuring the angle between the corresponding output vectors of the joint layer subnetwork, and then the difference value is taken as the penalty term of the loss function in the fine adjustment stage. The loss function of our model is: $Γ_{w} (p) = | - \sum p_{i} log p_{i}^{⌢} - β^{*} 〈 q_{L}, q_{R} 〉 |$ (24)

In the formula, $p_{i}^{⌢}$ is the output of node i in the category layer of 3D martial arts image, p_i is the label corresponding to $\overset{⌢}{q}$ , q_L and q_R are the output probability of left and right sides of joint layer respectively, and the number of nodes on left and right sides should be consistent, where 〈 · 〉 = 1 - cos(q_L, q_R). The cosine value is used to reflect the similarity of vector through the angle between vectors. β is the correlation rate, usually it is a small constant.

In SDBN network, the state values of all nodes in 3D martial arts image network are calculated by forward propagation, including the assumed loss function Γ_w (p), in which the activation function of RBM is sigmoid or ReLU function. Ghe category layer is linear node, and their activation function is soft-max function. The purpose of fine adjustment is to use gradient descent algorithm to make formula (24) reach the minimum value for model parameter w, then the weight updating formula is: $w_{ij}^{(l)} = w_{ij}^{(l)} - \frac{\partial}{\partial w_{ij}^{(l)}} Γ_{w} (p)$ (25) where, $w_{ij}^{(l)}$ represents the connection weight of layer l. In order to explain the error back propagation algorithm in SDBN conveniently, it is assumed that the corresponding residual of node i in layer l is $δ_{i}^{(l)}$ , which indicates how about the node affects the residual of the final output value in 3D martial arts image. For network output nodes, we can directly measure the gap between the network activation value and the actual value. The gap is defined as $δ_{i}^{(nl)}$ (where nl represents the output layer). For the hidden layer unit of 3D martial arts image, $δ_{i}^{(l)}$ will be calculated based on the weighted average of several residuals. These nodes take $a_{i}^{(l)}$ as the input, and $z_{i}^{(nl)}$ means the total input of the output layer nodes. The back propagation algorithm is as follows:

$\begin{matrix} δ_{i}^{(nl)} = \frac{\partial}{\partial} Γ_{w} (p) = (p_{i} - p_{i}^{⌢}) \\ * (z_{i}^{(nl)}) i \in {1, . . ., s_{nl}} \end{matrix}$ (26) $w_{class} = w_{class} - a^{(nl - 1)} * δ^{(nl)}$ (27) where, s_nl represents the number of nodes in the category layer of 3D martial arts image, and a^(nl-1) is the state of the joint layer of 3D martial arts image. For l = n_l - 1, the residual formula of each node i of layer j is: $δ_{i}^{(l)} = (\sum_{j = 1}^{s_{n_{l}}} w_{class}^{(l)} δ_{j}^{(l + 1)} * (z_{i}^{(nl)}))$ (28) where, if i = 1, . . . , s_{n
_l}, the symmetry characteristics of 3D martial arts image are as follows: $δ_{L}^{(l)} = β * \frac{\partial, 〈 q_{L}, q_{R} 〉}{\partial z_{L}^{l}}$ (29) $δ_{R}^{(l)} = β * \frac{\partial, 〈 q_{L}, q_{R} 〉}{\partial z_{R}^{l}}$ (30) The updating formula of connection weight is: $w_{L} = w_{L} + a_{L}^{(l - 1)} * δ_{L}^{(l)}$ (31) $w_{R} = w_{R} + a_{R}^{(l - 1)} * δ_{R}^{(l)}$ (32) where L and R represent left and right directions respectively. Other connection weights and offset update methods correspond to DBN, which will not be described in detail.

2.2.2 3D martial arts image classification based on feature and depth neural network

Based on the symmetry feature extracted from the upper section, a method combining feature with deep neural network is proposed. CNN can be used as the left and right subnetworks of symmetrical deep neural network of 3D martial arts image to form SCNN, and the structure is shown in Fig. 1:

Fig. 1

The method of combining feature with depth neural network.

The left and right sides of SCNN are composed of CNN with the same dimension of output 3D martial arts image, and the output of SCNN is the category layer of 3D martial arts image. Different from SDBN training mode, SCNN randomly initializes the weights, alternately performs convolution and sampling operations, and then fine adjusts the network connection weights through supervised learning. Its loss function of back propagation is as follows:

$\begin{matrix} Γ_{w} (x) = - \sum_{ij} (x_{ijc} - log \sum_{d = 1}^{D} w_{L} w_{R}) \\ - β * cos (q_{L}, q_{R}) \end{matrix}$ (33) where, x_ijc represents the category of 3D martial arts image output from the category layer of 3D martial arts image, and q_L and q_R are the corresponding output values of the left and right sub networks in the joint layer of the 3D martial arts image.

3 Results

3.1 Experimental data source

Two datasets, MNIST and CIFAR-10 are selected to test the performance of SDBN and SCNN. Among them, the MNIST digital set contains 60000 3D martial arts test images, 10000 test images from 0 to 9 in 10 categories of digital handwriting data set. Cifar-10 data set contains 60000 3D martial arts images, which are divided into 50000 training samples and 10000 test samples. The training batch is a random division of the original data set, and data processing is carried out through the data processing software MOA (an experimental tool for massive online analysis).

3.2 Enhancement effect test

In order to verify the effectiveness and feasibility of the algorithm in 3D martial arts image enhancement, a comparative experiment is designed and analyzed. The algorithm in this paper, image classification algorithm based on SVM and image classification algorithm based on data mining are compared and analyzed. The results are shown in Fig. 2:

Fig. 2

Comparison of three algorithms for 3D martial arts image enhancement.

According to Fig. 2, when the algorithm in this paper is used to enhance the 3D martial arts image, the processing effect of the adaptive enhancement is better than that of the other two algorithms, and the 3D martial arts image enhanced by the other two algorithms is distorted. The 3D martial arts image enhanced by the algorithm in this paper is more natural, the details are clearer, and has more advantages.

3.3 Robustness effect test

Because the 3D martial arts image has certain noise, the experiment takes the noise level as the benchmark to test. Under different noise levels, the experiment compares the algorithm in this paper, the image classification algorithm based on SVM and the image classification algorithm based on data mining [1 , 6]. The comparison indexes of classification performance take PSNR and MSSIM as examples, and the comparison curves of the three algorithms are shown in Figs. 3 and 4.

Fig. 3

PSNR index of image enhancement processing under different noise levels.

Fig. 4

MSSIM index of image enhancement processing under different noise levels.

It can be seen from Figs. 3 and 4 that, compared with the image classification algorithm based on SVM and the image classification algorithm based on data mining, the algorithm in this paper has higher PSNR and MSSIM values at any noise level, and with the increase of noise level, the advantages are more obvious, and the PSNR index remains above 34 dB. Compared with the best of the other comparison methods, the algorithm in this paper has an average increase of 5% in PSNR index and 4% in MSSIM index. This shows that the algorithm has better robustness.

3.4 Classification effect test

In order to verify the effectiveness of the algorithm, MNIST and CIFAR-10 are used to test the performance of SDBN and SCNN.

MNIST digital set: it contains 600003D martial arts images for test, 10000 test images are 10 types of digital handwriting data sets from 0 to 9.

CIFAR-10 data set: it contains 60000 3D martial arts images. The data set is divided into 50000 training samples and 10000 test samples. Training batch is a random division of the original data set.

3.4.1 Experiment and verification of MNIST data set

In the experiment, the DBNs on both sides are trained, different topological network structures are designed to verify the performance of SDBN in this algorithm, and the relationship between the classification performance of the proposed algorithm and the number of network nodes is verified. The 10 nodes in category layer of 3D martial arts image represent 10 categories from 0 to 9, and the joint layer is fully connected with the category layer. Finally, all the nodes except that in the class layer of 3D martial arts image are of logistic type. At the same time, different CNN are designed to test the performance of SCNN network. In order to verify the relationship between the performance improvement of SDBN network and the increase of network nodes, a group of comparative experiments are designed. The number in the table is the number of network nodes. The experimental results are shown in Table 1:

Table 1
Mnist dataset classification accuracy table

Method Accuracy

SVM 98.70%

DBN[501-501-2001]-11 98.80%

DBN[501-501-851]-11 98.80%

Symmetric DBN (SDBN) [L:501-501-1001]& [501-501-1001]-11 99.10%

Symmetric DBN (SDBN) [L:501-501-2001]& [501-501-2001]-11 99.10%

Symmetric DBN (SDBN) [L:201-201-856]& [201-201-851]-11 99.10%

CNN [input-C-S-C-S-label] 99.20%

Symmetric CNN(SCNN) 99.30%

Method	Accuracy
SVM	98.70%
DBN[501-501-2001]-11	98.80%
DBN[501-501-851]-11	98.80%
Symmetric DBN (SDBN) [L:501-501-1001]& [501-501-1001]-11	99.10%
Symmetric DBN (SDBN) [L:501-501-2001]& [501-501-2001]-11	99.10%
Symmetric DBN (SDBN) [L:201-201-856]& [201-201-851]-11	99.10%
CNN [input-C-S-C-S-label]	99.20%
Symmetric CNN(SCNN)	99.30%

As shown in Table 1, the topological structure of DBN is 501-501-20001-11, and the topological structure of SDBN of the algorithm in this paper is 501-501-851 for the left sub network node, 501-501-851 for the right sub network node, and 11 nodes for the classification layer. The number of experimental nodes is consistent. It can be seen from the results that the SDBN performance of the algorithm in this paper is slightly better than that of Hinton’s DBN and SVM performance when classifying 3D martial arts images. In the second group of experiments, Hinton’s DBN structure is 501-501-851-11, and SDBN contains 11 categories. The left sub network topology is 201-201-851, the right sub network topology is 201-201-851, and the left and right sub network nodes are less than half of DBN. The experimental results show that the SDBN of the algorithm in this paper is still better than DBN. Two corresponding experiments exclude that the increase of the number of nodes dominates the SDBN performance of the algorithm in this paper. Table 1 shows the test results of different topological nodes in the test solution. The performance of the algorithm in this paper is better than other deep network algorithms in the set of test, which shows the effectiveness of the algorithm in MNIST.

3.4.2 Experiment and analysis of CIFAR-10 data set

CIFAR-10 dataset is used to test the performance of the algorithm in this paper. The data set is divided into 5 training batches and 1 test batch, each batch contains 10000 3D martial arts images. The test batch contains 1000 3D martial arts images randomly selected from each category. The training batch contains the random arrangement of the remaining images, but some of the training batch images need more than other categories, and the training data of each batch contains 5000 images of each category. The topology and results of the network are shown in Table 2: where, the DBN node excitation function is sigmoid function, while CNN excitation function is ReLUc. The SDBN of the algorithm in this paper takes the corresponding deep structure as the sub network.

Table 2 shows that the minimum error rate of this algorithm is 6.1%, compared with CNN and DNB, this algorithm has the minimum error rate.

Table 2
Cifar-10 data set classification accuracy table

Method Misclassification rate

DBN 10.10%

Symmetric DBN (SDBN) 6.10%

CNN 14.50%

Method	Misclassification rate
DBN	10.10%
Symmetric DBN (SDBN)	6.10%
CNN	14.50%

4 Discussion

Inspired by the human vision system, many image processing models are designed as multi-layer structure, and the way to establish multi-layer structure features for target detection is deeply rooted in the computer vision art. In 2006, Hinton et al proposed a greedy layer by layer processing method for training the deep belief network (DBN). Simulating the human visual cortex, each layer of the network was trained from the bottom to the top by an approximate algorithm. Each upper and lower structure was regarded as a restricted Boltzmann machine (RBM). This model creatively proposed a pre training processing method. Krizhevsky A expanded the structure of the convolutional neural network (CNN) in 2012, and improved the network structure. The biggest feature of Krizhevsky A was sparse connection and weight sharing, and the model achieved good test results in MNIST data set. In this paper, this algorithm is based on the deep theory, the essential difference is to introduce symmetry structure. The sub networks on both sides of SDNN are made up of DNN, feature difference is introduced, and sample classification is decided jointly, so the classification result of the algorithm in this paper is more accurate.

5 Conclusions

It is difficult for objects in nature to satisfy the strict symmetry, so it is far from enough to rely solely on the precise mathematical definition of symmetry to detect symmetry. In addition, due to the transformation of the object angle, the noise caused by the figure digitization and other reasons, the processed figure loses the original symmetrical features, resulting in the inaccurate detection results. Symmetry detection plays an important role not only in locating and recognizing plane objects, but also in 3D object reconstruction. With the wide application of intelligent robots, symmetry plays an important role in texture detection and guiding machines to grasp objects. So it is very important for pattern recognition and image classification to extract symmetry from complex images. In this paper, a 3D martial arts image classification algorithm based on symmetry theory is proposed, and its credibility is verified in the experiment. The average error rate of this algorithm is 6%. Compared with the same algorithm, the classification accuracy is the highest, which can be used in the research of 3D martial arts image classification. However, this paper does not take into account the large amount of data and the lack of classification efficiency. Next, we will take classification efficiency as the main goal for in-depth study.

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3D martial arts image classification algorithm based on symmetry theory

Abstract

Keywords

1 Introduction

2 Definition of the algorithm

2.1 Preprocessing method of 3D martial arts image

2.1.1 Denoising

2.2.1 Structure of SDBN network

3.1 Experimental data source

3.2 Enhancement effect test

3.4.1 Experiment and verification of MNIST data set

Table 2 Cifar-10 data set classification accuracy table Method Misclassification rate DBN 10.10% Symmetric DBN (SDBN) 6.10% CNN 14.50%

5 Conclusions

References

Table 2
Cifar-10 data set classification accuracy table

Method Misclassification rate

DBN 10.10%

Symmetric DBN (SDBN) 6.10%

CNN 14.50%