As an efficient technique for anticounterfeiting, holographic diffraction labels has been widely applied to various fields. Due to their unique feature, traditional image recognition algorithms are not ideal for the holographic diffraction label recognition. Since a tensor preserves the spatiotemporal features of an original sample in the process of feature extraction, in this paper we propose a new holographic diffraction label recognition algorithm that combines two tensor features. The HSV (Hue Saturation Value) tensor and the HOG (Histogram of Oriented Gradient) tensor are used to represent the color information and gradient information of holographic diffraction label, respectively. Meanwhile, the tensor decomposition is performed by high order singular value decomposition, and tensor decomposition matrices are obtained. Taking into consideration of the different recognition capabilities of decomposition matrices, we design a decomposition matrix similarity fusion strategy using a typical correlation analysis algorithm and projection from similarity vectors of different decomposition matrices to the PCA (Principal Component Analysis) subspace , then, the subspace performs KNN (KNearest Neighbors) classification is performed. The effectiveness of our fusion strategy is verified by experiments. Our double tensor recognition algorithm complements the recognition capability of different tensors to produce better recognition performance for the holographic diffraction label system.
With the rapid development of printing technology, new types of product labels are used. Holographic diffraction labels have been chosen by many manufacturers due to their unique anticounterfeiting feature. With the popularity of smartphones, there is an increasing demand for image recognition using mobile phones. Different image features are shown in different illumination environments due to the unique physical feature of holographic diffraction labels. Traditional image recognition algorithms are not ideal for holographic diffraction label recognition.
In this study, tensor is used to represent data to preserve the optically variable data of a diffraction image. Tensor has been widely used in signal and image processing [
Lowdimension subspace learning methods have been expanded to tensor representation, such as tensor principal component analysis [
Information from changing illumination of holographic diffractive labels is lost if it is represented using matrix [
A color image has three channels of RGB and can be represented as a tensor intrinsically. A holographic label has different color information for different illuminations because of its lightvarying feature. In order to preserve the color information of an image, the holographic image is converted from the RGB to the HSV color space and is further represented as an HSV tensor [
The tilt and rotation of an image taken by a mobile phone always causes incorrect recognition. In order to ensure the accuracy of the classification, rotation correction using edge detection and the Hough transformation are performed for all input images.
In order to remove interference from the background in a label image, the grayscale image is converted into a binary image using the maximum OTSU. Then Canny edge detection is performed on the binary image. The traditional Canny operator performs Gaussian smoothing on the original image in the process of edge detection. However, the influence of noise is related to the distance of the noise point from the center after Gaussian smoothing. It causes image edge blurring [
After the rotation correction, the original RGB color space is converted into a HSV space and normalized into a thirdorder HSV tensor
Image features are extracted using HOG descriptors. In contrast to traditional HOG feature extraction algorithms, a faster HOG feature extraction method [
The size of a normalized image is given as
where
Each block yields four different normalization results,
A thirdorder tensor
The obtained HOG tensor and HSV tensor are the primary features of an image. These primary features are decomposed into orthogonal matrices using HOSVD algorithm. The similarity between the decomposition matrices of the test sample and the training sample are measured using CCA [
A tensor is decomposed into decomposition matrices using HOSVD. First, a highorder tensor is expanded into a twodimensional matrix. An
HOSVD decomposition of an expanded matrix is represented as follows:
where
CCA is used to measure the similarity between tensor decomposition matrices. For random vector
where
Six decomposition matrices
Six typical correlations are obtained based on calculating the similarity of holographic labels described in the previous sections. The summation of all six typical correlations may be simply used as the similarity between the samples. However, different decomposition matrices of a tensor contain different information and have different distinctive capabilities. Therefore, each decomposition matrix serves as an independent unit, and an effective method is proposed to fuse these similarities. The process is shown in
The similarity vectors between the test sample and the training samples are represented as
The scatter matrix is calculated using
The scatter matrix is decomposed using
The diagonal matrix
where
The dataset used in this study contains 200 holographic diffraction labels with an image size of
The advantages of the similarity algorithm of the fusion decomposition matrix are analyzed in this study. First, a classification experiment is performed using the decomposition matrices for the HSV tensor, and the recognition results are shown in
Recognition algorithm  Recognition rate 

The recognition abilities of different decomposition matrices are not the same but it was not considered in their study. Our strategy overcomes this shortcoming. As shown in
Calculating the typical correlation between the test sample and the training samples, we obtain five threedimensional similarity vectors
The complementarity of the double tensor is tested. First, only the HSV tensors of the original data are used for holographic image recognition in the dataset. The confusion matrix of the HSV tensor recognition is shown in
The typical correlation coefficients of the HSV tensor and the HOG tensor are combined based on the above experiment. A confusion matrix is obtained using this double tensor, as shown in
Method  Recognition rate 

Our algorithm is compared with the algorithm proposed in [
50%  70%  90%  130%  

10%  20%  50%  

0 
45 
90 
135 


An algorithm for holographic diffraction label recognition using a complementary double tensor is proposed. First, an approach is proposed to generate the HOG feature tensor that combines the HSV tensor of the original data to obtain the double tensor. Then, the double tensor is decomposed using HOSVD to obtain the double tensor decomposition matrix. Finally, typical correlation analysis is used to calculate the similarity between the decomposition matrices. The similarity of the decomposition matrix is fused according to different recognition capabilities, and the similarity vectors are projected to a PCA subspace for classification. The algorithm makes up for the deficiency of the original data tensor, improves recognition rate, does not require advanced training process, and has high computational efficiency. The experimental results have shown that the double tensor fusion algorithm is capable of performing efficient recognition for holographic diffraction labels.
We thank the anonymous reviewers and editors for their very constructive comments.