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Face recognition using histograms of fuzzy oriented gradients
Salhi, Abdel Ilah; Kardouchi, Mustapha; Belacel, Nabil
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https://nrc-publications.canada.ca/eng/view/object/?id=f6594e0d-b5cd-4ad8-b034-89b43bde732f https://publications-cnrc.canada.ca/fra/voir/objet/?id=f6594e0d-b5cd-4ad8-b034-89b43bde732fFace Recognition using Histograms of Fuzzy
Oriented Gradients
Abdel Ilah Salhi and Mustapha Kardouchi
Computer Science Department Université de Moncton Moncton NB Canada E1A 3A9
abdel.ilah.salhi@umoncton.ca mustapha.kardouchi@umoncton.ca
Nabil Belacel
Information and Communications Technologies National research Council of Canada
Moncton NB Canada E1A 7R1 nabil.belacel@nrc-cnrc.gc.ca
Abstract
— Efficient face descriptors require a carefulequilibration between accuracy and feature dimension. In recent years Histogram of Oriented Gradient (HOG) starts to be used in the face recognition task. However the best recognition rate for HOG requires a high dimensional feature. In this paper, we will incorporate fuzzy concept to HOG aiming to achieve a good recognition rate with a low feature vector dimension. The proposed Histogram of Fuzzy Oriented Gradient will be applied to the face recognition task. Experimental results on ORL database show that HFOG outperforms the standard HOG in terms of recognition rate with a lower dimensional vector.
Keywords : Fuzzy sets; HOG; HFOG; Face recognition;
Feature dimension.
I. INTRODUCTION
Biometric systems are increasingly developed in recent years due to their widespread application in video surveillance, human-machine interaction and virtual reality. The face recognition is one of the most famous biometrics, which has attracted the attention of both industrial and academic communities in the past decades. The main elements of a face recognition system are the feature extraction [1][3] and the classification method [2][4]. However, the feature extractor is of great importance to the extent that if this feature is not efficient even the best classifier will not provide good recognition rate
.
Several feature extraction techniques havebeen proposed for deal face recognition, among them we can cite: LBP [5], HOG [6][7], Gabor [8], EBGM [9]. HOG is a descriptor based on gradient measurement which has been used in different areas such as the pedestrian detection [11], and the hand gesture recognition [10]. Recently some researchers adopted HOG to face recognition task [6] [7]. In this paper we propose to improve the HOG descriptor by introducing fuzzy concept [12]. The improved HOG reduces the dimension of features and in some cases gives a higher recognition rate than HOG.
The following section of the paper explains the standard HOG descriptor with its drawbacks. Section 3 presents the proposed approach based on Fuzzy HOG. Experimental results are presented in section 4 and conclusions are given in the final section.
II. RELATED WORK
A. Histogram of oriented gradient
The HOG descriptor is a local statistic of the image gradients. It counts the occurrences of edge orientations in a local neighbourhood of the image. This descriptor is characterized by its invariance against rotation and illumination. Moreover; its simplicity makes it among the fastest state-of-the-art descriptors. The HOG descriptor is built with combination of some partial histograms which represent occurrences counters of pixels orientations in partial blocks of the image.
The whole process of HOG computing can be summarized into three major steps:
Image derivative computing.
Magnitude and Gradient Orientation computing Histogram building
1) Image derivative Computing
In a first step, the derivative of the image in the horizontal and vertical directions are calculated by convolving the image with the 1-D centered kernel filter [-1 0 1]. The kernels are applied separately in each pixel of the input image to produce separate measurements of the gradient components in the vertical and horizontal orientations. We call Gx and Gy the output images.
2) Magnitude and Gradient Orientation computing
The second step of the HOG computing is to calculate for each image pixel I(x,y) its magnitude and its gradient
The magnitude is given by:
= (1) While gradient is given by:
(2)
Where is a function that returns the direction of the vector [Gx , Gy] in the range [0 , 2π] by taking into account .
3) Histogram building
Once magnitude and gradient are computed, we start building the histogram. In this order, the image is divided into N cells
and the gradient angles in each cell are quantized into a number of bins B of regularly spaced orientations in the range [0, 2π]. In each one of these cells, a partial histogram is computed by adding the magnitude of each pixel to the closest bin to its orientation. We get thus N partial histograms; each one is composed of B bins. Aiming to get invariance against illumination and contrast, a local l-2 Euclidian normalization is performed into each partial histogram.
(3)
where v is the vector to be normalized and ε is a small positive value needed when evaluating empty gradients.
Once normalized, the partial histograms will be concatenated altogether in a single feature vector which represents the final descriptor of the image.
B. Drawback of HOG
An empirical study of the impact of increasing bins number in the HOG descriptor concluded that more large the number is more accurate the descriptor is. In fact this is due to the reduction of orientations range that each bin covers. As a result of the former, two pixels belonging to the same range in an 8-bins HOG representation can belong each to a distinct range in a 12-bins HOG representation. Therefore the vote of each pixel will be more accurate and the face description will also be. From Fig.1 we can see the impact of the bins number increasing on the distribution of the histogram.
Despite the efficiency of augmenting the bins number, this technique has limited spatial support as the augmentation of the number of bins used leads to increase the histogram dimension.
In this context, we propose in this paper to introduce the fuzzy concept to the HOG descriptor. By applying fuzzy sets, the pixel membership to a bin will be relative and can belong, then, to several bins at the same time with different degrees. As advantage of applying fuzzy concept we will simulate a high dimension HOG descriptor with a lower feature vector. The HFOG should reflect a more objective description of content than the conventional HOG features. Results in experimental section show its superiority.
III. PROPOSED METHOD HFOG
As mentioned above, we propose into this paper to incorporate fuzzy set concepts into HOG features. This does not result in too much modifications compared to the standard HOG as the main steps stay the same. First, the image derivative in the horizontal and vertical directions are calculated, the next step consists in computing the gradient and the magnitude of each pixel in the image. Then, contrarily to the standard HOG when each one of these pixels votes for a unique bin by adding its magnitude, we suppose, in the proposed HFOG that the belonging of a pixel to a bin is not obsolete. In this context, we will associate to each pixel a fuzzy description considering more than one bin; this represents the contribution of the pixel into each one of these bins. Let I(x,y) be a pixel with a
magnitude M(x,y) and a gradient θ(x,y). In the original HOG, I(x,y) will belong only to the range
where k is a positive integer belonging to and n is the number of bins considered. In another words, the whole magnitude of the pixel I(x,y) will be added only to the range
. However, in the proposed HFOG, based on the idea that a pixel gradient can belong to several bins at the same time, the magnitude of I(x,y) will be added to all these bins with a degree
specified by membership grades between o et 1. For this purpose, a membership degree is defined using the Fuzzy membership function of Fuzzy-C-Means algorithm [12]:
(4)
Where is the contribution of the pixel in the value of the bin , and m is a parameter which controls the degree of fuzziness in the distribution of pixels (1<m<∞). Empirically, we found that m=1.1 is the best setting. Once the degree of voting of a pixel on each bin is calculated, the magnitude of this pixel will be added to the bins, depending to the membership degree.
IV. EXPERIMENTS
In this section, some experiment results will be given to evaluate the proposed method. The ORL face database has been used to this purpose. This database contains 40 distinct subjects where 10 images were taken for each subject. These images were taken at different times with different facial expressions, as (opened/closed eyes, smiling/non-smiling…). Moreover, light variation and pose changes have been taken into account add to some facial details as putting glasses or not. Figure 3 shows some sample images extracted from ORL Face database. As regarding the classification method, we used into this paper the Nearest-Neighbor Classifier [13] due to its simplicity. We also used 280 images for the training step and the remaining images for the testing.
Next, we proceeded to evaluate the proposed HFOG and compare it to other methods. In fact HOG descriptor involves many parameters concerning the overlapping or not of the blocks, the sign of the gradient or the number of bins used. All of these parameters were investigated in our last publication Figure 1.Histogram of oriented Gradient with 6, 9, 18 bins.
Figure3. Recognition rate Versus feature dimension Figure 2. Sample of Images in ORL face database
[15] and we concluded that overlapping the blocks and using a signed gradient leads to a better performance in the face recognition task. Regarding the number of bins, we investigated this setting into this work aiming to show the impact of increasing the number of bins in the vector dimension and the accuracy of the descriptor. We showed by result how, by incorporating the fuzzy concept in HOG, we can get the accuracy of a high dimension HOG descriptor with a smaller number of bins.
A. Effect of increasing the number of bins
The orientation bins are evenly spaced over [0, 2π]; each of them represents the number of edges that have orientations within a certain angular range. Thus, each pixel votes on a specific orientation based on its gradient orientation and accumulates its magnitudes into the corresponding bin. We can see from Table 1 that increasing the number of bins provides best recognition rate. However, when reaching a certain level -which corresponds to 24 in our case- the recognition rates will no longer increase.
TABLE1.EFFECT OF INCREASING THE NUMBER OF BINS
Number of Bins Recognition rate (%)
4 76.5
8 82.9
12 92.6
16 92.6
20 92.6
B. Comparison of different features
In this section we will compare the proposed HFOG with original HOG as well as Local Binary Pattern (LBP) and Gabor descriptor which are widely used in the face recognition task. This description will take into account the dimension of the feature vector aiming to bring out the quotient recognition rate/dimension. Concerning LBP, it is a local approach which computes a histogram by taking into account each pixel in the image and considering the values of its neighbourhoods. In fact, the dimension of the vector computed will depend basically on the number of neighbors chosen. If p is the total number of neighboring pixels, LBP operator will be 2p dimensional histogram. As regards Gabor features, it is computed after convolving a face image with a family of Gabor kernels at different scales and orientations. Despite its success, this descriptor is characterized by its high feature dimension which depends essentially on the number of kernels used.
From Fig.3 we can see that the proposed HFOG descriptor outperforms all the other descriptors in terms of recognition rate while the feature vector’s dimension does not exceed 128. However, we can also see that the Gabor descriptor reaches the best recognition rate, but only if the vector dimension is too high. It has to be noted that we considered in this experiment the highest recognition rates.
V. CONCLUSION
The Histogram of Oriented Gradient is a powerful descriptor which became used recently in the face recognition task. This descriptor leads to a better performance the higher the number of bins increases. In this paper we incorporated the fuzzy concept to this descriptor. The ORL face database was used to show the power of the proposed Fuzzy-HOG when compared to other widely used methods in face recognition task. The experimental results have shown that the proposed HFOG outperforms the others methods in terms of balance between accuracy and feature dimension. Our future research will be focused on integrating color information into the proposed descriptor and applying it to different computer vision problems such as Medical image processing and object tracking.
ACKNOWLEDGMENT
We gratefully acknowledge the support from NSERC’s Discovery Award (RGPIN293261-05) granted to Dr. Nabil Belacel. Authors would like also to thank University of Cambridge for providing the ORL face database.
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