 Research
 Open Access
Local dominant orientation feature histograms (LDOFH) for face recognition
 Xinfang Cui^{1, 2},
 Peng Zhou^{1, 2} and
 Wankou Yang^{1, 2}Email author
 Received: 1 September 2017
 Accepted: 5 November 2017
 Published: 17 November 2017
Abstract
This paper presents a simple and robust feature descriptor method, namely local dominant orientation feature histogram (LDOFH). In this method, the discriminant histogram contains dominant orientation, and the corresponding relative energy value is obtained by calculating the direction and the amplitude of the gradient of each pixel over a local patch. The LMNNDA (Yang et al. in Pattern Recognit 44:1387–1402, 2011) method based on the principal component analysis (PCA) method is finally employed to reduce the redundancy information and get the lowdimensional and discriminative features. We apply this descriptor on AR, IMM face image databases. Experimental results demonstrate the effectiveness of the proposed LDOFH method.
Keywords
 Feature extraction
 LDOFH
 LMNNDA
 PCA
 Histogram
Introduction
With the development of pattern recognition, many researchers focus on the topic of face recognition. Feature extraction is an important factor influencing the final classification results. The identitypreserving features are extracted through hierarchical nonlinear mappings. Good image representation features are expected to have high discriminative ability and robustness. During the recent decades, there have been a large amount of literature on developing traditional image featureextraction methods, such as local binary patterns (LBPs) (Huang et al. 2011), LTP (Tan and Triggs 2010), scaleinvariant feature transform (SIFT) (Lowe 2004), speededup robust features (SURF) (Bay et al. 2006), and histogram of oriented gradient (HOG) (Dalal and Triggs 2005). Recently deep learningbased methods have shown great success in face recognition (Zhu et al. 2013; Wen et al. 2016), but the complexity of deep learningbased methods is very high. Here, we mainly focus on handcrafted feature descriptors, since these kinds of methods are very effective and efficient.
The remainder of this paper is organized as follows. “Related work” briefly introduces the image featureextraction method, DHLDO, proposed by Qian; “LDOFH for feature extraction” develops our proposed image featureextraction method, LDOFH and describes its merits. “Experiments” shows the experimental methodology and the results. “Conclusions and future work” offers the conclusions drawn and scope for future work.
Related work
The related work from Qian is introduced in this part. In DHLDO method, the dominant orientation and the corresponding energy values are acquired by PCA.
Principal component analysis for local orientation and energy
In this section, we mainly introduce the PCAbased method to estimate the local gradient orientation. PCA is a special case of KL transform (Deprettere 1988). It minimizes the meansquare approximation error to get a set of optimal basis vectors. This can represent the given data with lower dimension. PCA can be achieved by eigenvalue decomposition of the data covariance matrix or singular value decomposition (SVD) of the data matrix. Here, we introduce the method SVD.
Specifically, the gradient matrix over a P × P window (w _{ i }) around the interesting point (x, y) of an image is defined as
The resulting matrix \(O = \left[ {\left( {\theta_{1} ,e_{1} } \right), \ldots \left( {\theta_{i} ,e_{i} } \right), \ldots \left( {\theta_{N} ,e_{N} } \right)} \right]^{\text{T}}\) contains dominant orientation and energy information of an image, and there are N pixels in the image.
Constructing histogram of local dominant orientation
LDOFH for feature extraction
Feature extraction plays an important role in exploring data by mapping the input data onto a space which reflects the inherent structure of the original data. In the mapped space, distinctive features are extracted from source data to represent the source data. In general, feature extraction is always considered as the preprocessing step which offers distinctive features for the following learning. An efficient featureextracted method is proposed as followes.
The dominant orientation map and the energy map
We define the angle θ(x, y) (gradient direction) as the dominant orientation of the pixel, and the amplitude m(x, y) of the gradient is defined as the corresponding energy value of the point. Thus, one can get the orientation map and the corresponding energy map through this operation covering the whole image.
Constructing dense histogram as the extracted feature
Obtaining the lowdimensional feature
The dimension of the histogram features extracted from the above method is very high because some redundant information is introduced, while rich structural features are obtained. This section introduces a LMNNDA method to obtain a more efficient lowdimensional feature with more discriminative ability.
At last, we choose the nearestneighbor classifier to achieve the face recognition, and LDOFH uses the cosine distance.
The algorithm of LDOFH
 Step 1.:

Calculate the gradient amplitude m(x, y) and the gradient direction θ(x, y) of each pixel using Eqs. (8) and (9);
 Step 2.:

Divide the dominant orientation map and the corresponding relative energy map into a series of overlapping local regions;
 Step 3.:

Construct the histogram on each local region;
 Step 4.:

Concatenate the histograms of all overlapping local regions to obtain the total histogram; and
 Step 5.:

Reduce the dimension of the total histogram by LMNNDA to get the final features.
Merits of LDOFH
First, LDOFH calculates the local dominant orientation of each pixel over local patches to obtain the structure information of the image. The information can describe the local shape feature of the image well. Second, the change in light has little effect on the LDOFH recognition performance, because the change in light causes weak change in the dominant orientation over a local region. Third, the LDOFH is much faster than DHLDO, because DHLDO uses SVD to obtain the dominant orientation and energy value of each pixel, but this operation consumes more time. The following experiments show that our proposed LDOFH method is nearly three times faster than DHLDO method. Given that the image resolution is w × h, the time complexities of Step 1, Step 2, Step 3, Step 4, Step 5 are O(w × h), O(1), O(w × h), O(1), O((b × L) ^{ 3 } ), respectively. Therefore, the total time complexity of our LDOFH is O((b × L) ^{ 3 } ).
Experiments
In this section, we will evaluate the effectiveness of LDOFH and compare it with the DHLDO algorithm on two large available face image databases (AR, IMM). There are three parameters in our method: the number of orientation bins (here we set bin = 9) over 0–180^{°}, Gaussian smoothing parameter σ (σ = 0.3), block size bsize (we construct histogram on a bsize block). Here, we compare the results including face recognition rate and cost time in different bsize values and the number of training samples. The experiment is done on DELL computer (CPU i53470, 3.20 GHZ, 8G, win 64) with matlab 2016a.
Experiment on AR database
The recognition rates (%) of PCA, FLDA, LBP, LTP, DHLDO, and LDOFH with the NN classifier on the AR database
PCA  FLDA  LBP  LTP  DHLDO  LDOFH  

Recognition rate  0.833  0.976  0.953  0.964  0.978  0.986 
The time cost results of LBP, DHLDO, and LDOFH on the AR database
LBP  DHLDO  LDOFH  

Time cost(s)  77.254  121.432  51.410 
Experiment on IMM database
IMM is a database consisting of 240 annotated monocular images of 40 different human faces. Points of correspondence are placed on each image so the dataset can be readily used for building statistical models of shape.
It can be seen from the above experimental results that on the IMM database, LDOFH has lower recognition rate than DHLDO under the same conditions. However, the cost time of the DHLDO method is nearly three times greater than the cost time found from the LDOFH method.
Integrating the results from the two databases, the LDOFH method is shown to be more effective than the DHLDO method.
Conclusions and future works
In our work, a novel image featureextraction method—local dominant orientation feature histograms (LDOFH)—is proposed. LDOFH obtains the dominant orientation and the relative energy value of each pixel by calculating the gradient direction and the gradient amplitude in a local patch around the pixel. The feature histogram is constructed by accumulating the relative energies of the dominant orientations in the rectangular region. All the histograms are concatenated into a highdimensional feature vector. LMNNDA is finally adopted to reduce the dimension of the feature to obtain the more discriminative feature. LDOFH is compared with the DHLDO method on two different image databases, AR and IMM. The results demonstrate the effectiveness of the presented method.
In the future, we will find an algorithm to achieve feature fusion to improve the recognition rate of the proposed method.
Declarations
Authors’ contributions
The authors discussed the problem and the solutions proposed all together. All the authors participated in drafting and revising the final manuscript. All authors read and approved the final manuscript.
Acknowledgements
This project is partly supported by the NSF of China (61473086), partly supported by the Fundamental Research Funds for the Central Universities (2242017K40124).
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
Not applicable.
Consent for publication
We agree.
Ethics approval and consent to participate
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