Journal of Control Science and Engineering

Volume 2018, Article ID 9061796, 7 pages

https://doi.org/10.1155/2018/9061796

## Image Recognition Based on Two-Dimensional Principal Component Analysis Combining with Wavelet Theory and Frame Theory

^{1}College of Electrical Engineering, Henan University of Technology, Zhengzhou, China^{2}School of Automation, Hangzhou Dianzi University, Hangzhou, China

Correspondence should be addressed to Chenglin Wen; nc.ude.udh@lcnew

Received 19 April 2018; Revised 6 August 2018; Accepted 27 August 2018; Published 19 September 2018

Academic Editor: Daniel Morinigo-Sotelo

Copyright © 2018 Pingping Tao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

The key to improve the image recognition rate lies in the extraction of image features. In this paper, a feature extraction method is proposed for the images with similar feature in the strong noise background, which is two-dimensional principal component analysis combined with wavelet theory and frame theory. Considering that the image will be influenced by man-made and environmental noises, the algorithm of this paper considers the improvement of many algorithms. Firstly, the images are preprocessed by images enhancement based on feature enhancement. The images are processed by wavelet transform. Then, the preprocessed image matrices are used to obtain the eigenvectors, and the eigenvectors are interpolated with frame, which makes more sufficient information in the frame theory and better extracts the features on the image. Finally, this algorithm is compared other algorithms in the standard ORL face recognition database. The comparison of recognition rate and recognition time by simulation experiment is carried out in order to obtain the validity of the proposed algorithm.

#### 1. Introduction

Image recognition is an important area of artificial intelligence, and the accuracy of image recognition is getting higher and higher. Principal component analysis (PCA) is a common linear transformation method for extracting features in image recognition. This algorithm has been developed very well. However, the calculation of this algorithm is large. In the face recognition technology, one-dimensional PCA algorithm needs to transform the two-dimensional image matrix into one-dimensional vector. The dimension of the image vector is as high as 10304, if the resolution of the image is 112 92. And the larger the data set is, the higher the dimension of the image vector will be. When the data set of image class is 100000 and the image matrix is 10304 100000, the calculation of one-dimensional PCA directly calculating the image matrix is large. This makes the calculation of the entire feature extraction process very large and leads to a high dimensional space and the relative increase of computational complexity. This requires large calculation of the entire feature extraction process. The computational complexity of the large dimension of the small sample, which also makes the image lose the structure information, is not conducive to accurate detection and recognition. For the defects of one-dimensional PCA, [1] proposes a face recognition algorithm based on 2DPCA, which is a linear unsupervised statistical method. In general, the dimension of face image is large, while the calculation of face image processing is very large. The use of one-dimensional PCA algorithm leads to the increase in computational complexity and time-consuming, so 2DPCA is introduced to deal with the images [2]. 2DPCA algorithm is a feature extraction method that directly deals with the image matrix and overcomes the problem of converting a two-dimensional image matrix into a one-dimensional vector by using the one-dimensional PCA extracts feature. To a great extent, the amount of calculations is reduced. 2DPCA also makes use of the differences between samples, effectively preserves the sample structure information, adds the identification information, and becomes a new research hot spot [3]. Reference [4] explains the application of linear transformation in matrix theory. It uses 2DPCA to find out the feature vectors and uses the classical one-dimensional PCA technology to make further compression, so that the dimension is reduced. The result shows that the direct covariance matrix can be obtained directly for the image, which is more effective in recognition rate. In [5–9], the classical 2DPCA algorithm has been improved, but the intra-class feature vectors are not considered fully. The image recognition algorithms are constantly updated and optimized, the classical PCA algorithm, the improved PCA algorithm and improved 2DPCA algorithm, the SVM algorithm, and the convolutional neural network algorithm can be used for face recognition. References [10–12] first block the image and then use the 2DPCA algorithm to extract features for each block, at last, use the information fusion method to complete feature extraction. These algorithms use only local information, they lost information between blocks on the original face image easily. As a result, the information extracted is not complete enough. In [13], a face recognition method is proposed based on the average partition of 2DPCA. In this method, the image matrix is first divided into blocks, the intraclass normalized blocks are used to construct the overall distribution matrix; then the projection is carried out, which can reduce the dimension of the feature and avoid the use of singular value decomposition and reduce the recognition distance of the samples in the class. The experimental result shows that the recognition rate of this method is higher than 2DPCA algorithm. The above algorithms are not processed by wavelet transform, and they are processed directly by 2DPCA algorithm on the image processing, they cannot solve the external influence effectively (such as the changes of expressions and posture on the ORL face database). So the accuracy of the extracted features is not high. In [14], by combining the advantages of WT and 2DPCA, a face recognition algorithm is presented. First, in this algorithm, the firstorder wavelet transform is used to decompose the image, reduce the noise and increase the feature information, and solve the external influence (such as the changes of the expression and posture on the ORL face database). Then the 2DPCA algorithm is used to reduce the images dimensions extract the features. The result shows that the image recognition rate is improved after using the wavelet transform. After the image is processed by the wavelet, the unimproved 2DPCA algorithm does not use the redundant information between the eigenvectors. It is difficult to obtain the maximum projection value. The extracted information is not accurate enough. Therefore, this paper proposes an image recognition method based on 2DPCA combining wavelet theory and frame theory, which can fully consider the feature information and improve the recognition rate.

In summary, although the recognition rate of these improved algorithms are slightly higher than the classical 2DPCA face recognition algorithm, the recognition effect is still not very good for similar features. The analysis shows that none of these algorithms use the redundant information between the feature vectors and it is difficult to obtain the maximum projection value. Therefore, the extracted information is not accurate enough. This project is based on the wavelet decomposing and denoising, and adopts improved 2DPCA dimensionality reduction. This project expands the orthogonal principal element space into the (nonorthogonal) principal element space of the frame, so as to obtain more sufficient information in the frame principal element space. This algorithm is compared with other algorithms in the standard ORL face recognition database. The recognition rate and recognition time are compared through simulation experiments, so as to obtain the effective results of image recognition of two-dimensional principal component analysis combined with wavelet theory and frame theory.

#### 2. Image Preprocessing Based on Feature Enhancement

For detecting and recognizing small-target images in the background of strong noise, directly processing the original image will affect the detection results. Therefore, the preprocessing of the image will help to extract the features of the image, and then improve the detection accuracy and recognition rate. In ORL face database, the image is affected by the similarity of features such as attitude, so the feature information can be enhanced by wavelet transform to improve the recognition rate.

This section reviews the idea of one-dimensional wavelet transform. Figure 1 introduces the basic idea of one-dimensional wavelet transform. After the image is processed by the wavelet, the image information is decomposed into many different spatial resolutions, frequency characteristics, and the characteristics of the direction of suband image signal. In this way, wavelet decomposition can provide good local information. And in each level of wavelet transform, image is divided into one low frequency information and three high frequencies information (respectively corresponding to hori-zontal, vertical and diagonal detail components) [15].