Multi-scale elastic graph matching for face detection
© Sato and Kuriya; licensee Springer. 2013
Received: 5 July 2013
Accepted: 1 November 2013
Published: 21 November 2013
We propose a multi-scale elastic graph matching (MS-EGM) algorithm for face detection, in which the conventional EGM is improved with two simple image processing techniques of the Gabor wavelet-based pyramid and the weak Gabor feature elimination. It is expected to solve difficulties of the real-time process in the conventional EGM. The Gabor wavelet-based pyramid effectively reduces not only the computational cost of the Gabor filtering but also the computational complexity of feature representation of a model face, preserving the facial information. The elimination of the weak Gabor feature extracted from an input image facilitates an accuracy of the Gabor feature similarity computations as unexpected. We then test that the MS-EGM can be capable of rapid face detection processing while achieving a high correct detection rate, comparable to the AdaBoost Haar-like (HL) feature cascade. We also show that the MS-EGM has strong robustness to the image of a face occluded with sunglasses and scarfs because of topologically preserved feature representations.
Face detection is of importance in various research fields for computer vision technology. For example, in a security system, it is an important preprocessing for identifying or tracking moving persons on an image, taken with a surveillance camera in public places. It may also often be used for acquiring information about a person in order to make more sophisticated dialogs between persons and life support robots .
As referred to [2, 3], many different types of face detection algorithms have so far been suggested and developed progressively toward practical applications in industry. The algorithms are often classified into some approaches such as the knowledge-based , the feature-based [5, 6], and so forth. In particular, for the feature-based approach, finding faces using random labeled graph matching has been well known . Finding correct geometric arrangement of features for a face, the position of the face is effectively identified with random labeled graph matching. However, the deficit of the random labeled graph matching is extremely difficult detection of facial features in a complex background.
Such face detection algorithms have been comparatively tested thus far . One of them, remarkably exploited in recent computer vision, is a cascade of boosted classifiers with Haar-like (HL) features, proposed by Viola and Jones [8, 9]. In the Viola-Jones algorithm, a set of weak classifiers is used. A number of weak classifiers are singled out and then organized into a cascade. Viola and Jones then succeeded to realize rapid face detection. Nevertheless, there still remain challenging problems to solve, one of which is the low detection performance problem when lower resolution images  or occluded facial images are used.
In face recognition processing, not only a face detector as the preprocess of the face recognition but also the face recognition itself is strongly significant. Many different algorithms for face recognition were developed, some of which must be well known as face recognition literature, called the elastic graph matching (EGM) [11–13] or the elastic bunch graph matching (EBGM) [14–16]. Their essential concept for effective facial identification is the so-called dynamic link architecture [17, 18] where Gabor feature detectors establish dynamic projections of an undistorted graph to the elastic one. In the algorithm, there seem to exist several demerits as follows: (1) topological feature-based representations’ complexity and (2) the still difficult real-time process.
For the former, facial images are conventionally expressed with full Gabor feature representations encompassing many different orientations and many different spatial frequencies of the Gabor wavelet kernel . This can easily be expected to cause consuming time increments and high computational complexity, which make the real-time process difficult. Many researchers have been trying to solve such problems by using complex wavelets , weighted sub-Gabor  wavelets, and simplified Gabor wavelets . However, most of the problems have not been solved. It is still questionable what effective and efficient Gabor feature representations are.
Wolfrum et al. suggested a recurrent network model for processing of both detection and identification of a face on an input image . The network model may be very interesting, whose technical improvements are furthermore requested toward practical applications. The Viola-Jones algorithm for face detection is integrated with the EGM algorithm for convenience [23, 24]. Such an integrated system may be good. However, it is better that a face detection algorithm is established in the same concept for the face recognition algorithm of the EGM.
For this purpose, the current urgent task is to progressively develop an EGM-based face detection algorithm, which has rapid and high correct detection abilities, comparable to the AdaBoost of the HL cascade type. The final goal is to realize the real-time EGM. The achievement of the real-time EGM has so far been regarded to be extremely difficult. In this work, we discuss how the real-time process can be achieved, by using the simple image processing technologies of the Gabor pyramid and weak Gabor feature elimination.
In Section 1.3, we test the capability of face detection for the MS-EGM, in comparison with the one for the Viola-Jones algorithm. At least, four datasets of BioID , FERET , Caltech Faces , and AR Faces  are employed. Finally, discussion and conclusion will be given in Sections 1.4 and 2, respectively.
1.2 System design for face detection
1.2.1 Weak Gabor feature elimination
1.2.2 Gabor wavelet-based pyramid
A square graph of (n×n−4) nodes without any vertexes is set on each resolution image M s , letting the position of each node be p s . Here n (=5) is the number of full nodes on a row and a column of the square graph. The graph is depicted in Figure 5. The reason why we removed these vertexes is that the MS-EGM has a risk that a correct detection rate declines with unnecessary Gabor feature for the vertex.
Let us briefly discuss the advantages of the use of the GWP, in comparison with the Gaussian pyramid employed in scale invariant feature transform (SIFT) [33, 34], because there are two common points between the utilities of the GWP and Gaussian pyramid. One is the reduction of computational cost for the filters with sub-sampling images while the other is scale invariance.
The remarkable difference is the feature representation for a face. Because there is no orientation parameter on the Gaussian feature representation, the SIFT must be incorporated with additional representations such as histogram-of-oriented gradient (HoG) features [35, 36]. Such duplicate feature representations for an image give rise to extremely high computational complexity and cost, although the SIFT with the HoG feature may be a logically sophisticate algorithm.
The multi-scaled Gabor feature is more abundant in facial representations, compared to the Gaussian feature. This indicates that such abundant facial representations on the Gabor feature can easily identify a location of the face on image I, which takes the highest similarity to feature representations of image M. This is shown in the next section, by creating a similarity map of image M for each size onto image I. One can see that higher similarity areas are predicted to correspond to locations of the face meanwhile the low similarities are regarded as the background. In any case, we herein address that an additional merit in the Gabor wavelet-based pyramid is the less computational complexity for an image information preserved in feature representations.
1.2.3 Face detection process
where represents summation of the similarities of the Gabor feature at x I on image I to the one at node p s . In Equation 7, let us assume that the similarity is 0 when the norm equals 0 with the weak Gabor response elimination. G s is a set of nodes on the graph. represents the elasticity of the graph on image I. λ d is a constant parameter for the graph elasticity. λ d =0.05, except for obtaining a similarity map E s (x I) when λ d =0. is a set of nearest neighbor nodes for p s . and are the Euclidean distance between nodes p s (or x I) and on the graph of image M s (or I). and take one vector form consisting of four elements. Each element is an angle between two nearest neighbors on each quadrant, centered at p s .
This face detection process is also split into two sub-processes: The first sub-process is undistorted graph matching with λ d =0, in which each node p s links to full pixels on I to produce a similarity map of J I to at each scale s. The local maximum positions on the map are then picked up as candidate locations of a face on I, whose feature representations closely resemble the M s feature representations. The second is the real EGM with a finite λ d to find the position taking the highest similarity in the candidates and, at the same time, to choose the most likely relative size of I to M.
22.214.171.124 Select candidate positions
We herein notice that the candidate confinement is naturally done for the sake of achievements of the rapid face detection processing. One can see that computational cost for the following EGM is increased with the increment of the candidate number.
126.96.36.199 Find the most likely position
Here let C be a set of candidates .
1.3 Face detection ability tests
We test a face detection ability of the MS-EGM, using four different databases of BioID , FERET , Caltech Faces , and AR Faces , compared to an AdaBoost type of the HL cascade face detector mentioned in Section 1.1. Both face detectors can process on the following computer configuration: Intel Core i5-2410M Processor (2.30 GHz ×2, TurboBoost 2.90 GHz, hyper-threading, TDP 35W), RAM 4 GB, Windows 7 Home Premium SP1 64 bit.
Comparative performance evaluation for face detection
We notice that we employ only one competing method of the AdaBoost type of the HL cascade. This is because there remain a lot of improvements such as Gabor feature extraction with fast Fourier transform (FFT). Thus, we decided that after improving more the MS-EGM, we should test the detection ability, using the other databases that were not employed in this work.
1.3.1 Weak Gabor response elimination
Face detection performance for different thresholds
1.3.2 Requirement of EGM
Effects of EGM on correct face detection
We test detection abilities with other databases of the FERET and Caltech Faces. For the FERET, we have found that our system is almost comparable to the AdaBoost HL cascade. In the Caltech Faces, the AdaBoost HL cascade shows higher detection performance than our MS-EGM, which wins against the AdaBoost HL cascade, in terms of process speed. In the Caltech Faces, there are also some occluded face images. The AdaBoost HL cascade could not correctly detect the occluded faces whereas our MS-EGM did it very well.
Then, we tested the detection ability with the use of the AR Faces database. The AR Faces database was made by Computer Vision Center at Universitat Autonoma de Barcelona (UAB). It contains the images of 126 people (70 men and 56 women), where there are frontal faces with different facial expressions, illumination conditions, and occlusions (sunglasses and scarfs).
In Table 1, the AdaBoost HL cascade obtained 90% while our MS-EGM achieved a higher performance, 97%. For the average consuming time with the AR Faces database, the HL cascade costs less consuming time than our MS-EGM. The reason that the HL cascade can cost less consuming time is that the background of the occluded images is blank.
In this work, we have proposed the MS-EGM that should be worthy of comparison to the detection ability of the AdaBoost HL cascade. However, we still have to improve more the MS-EGM to integrate multi-face detection because the AdaBoost HL cascade could detect multi-objects. Also, the MS-EGM may still be requested for higher performance for the sake of its effective works in the real world. So, it would be necessary for us to inspect the causes of false detection in the experiments or drawbacks in our system.
The false detection was done mostly by detecting backgrounds. One reason for background detections is the square graph-based feature representation. As shown in Figure 1, most of the grids are located around fiducial points on the face, like eyebrows, eyes, lips, and facial edge. Such square graph-based feature representations are significantly sensitive to linear edges in the backgrounds. Indeed, they take higher similarities to representations for linear edges, compared to the facials. The square graph-based feature representations also induce misrecognition in that that our system recognizes the round necks and lips as the lips and eyes, respectively. In order to solve such misrecognition problems, it is better to use a face graph, instead of a square graph. This is because face graph-based feature representations can be distinguished against the background and may reduce misrecognition.
The other cause for misdetection is that the size of the input face cannot be identified because it is unfitted to any sizes of down-sampling model faces. So, if another size of the model face is additionally prepared, our system can more easily detect the suitable size of the input face. It can thus expect to increase the detection rate. However, we have to be aware of the trade-off between computational costs and the number of the model face size to be prepared because an increase of face size number causes to take a longer process time. Then, we will have to find the optimal parameter such as the number of sizes and so on.
In order to increase the correct detection rate, it would be beneficial to employ not only the eyes but also other fiducial points such as the nose. As mentioned above, our face detection system with the square graph tends to misrecognize the lip to be the eyes. This indicates that the obtained square for face detection tends to be positioned below the eyes. The correct detection can be defined again if a silhouette part in the obtained square involves both the eyes and nose or only the nose. Since, in this redefinition, the nose in the silhouette part compensates for incorrect detection even though the eyes are out of the silhouette part, it can be expected to reduce misrecognition and then further increase the correct detection rate.
In this work, we employed only one competing method of the AdaBoost type of the HL cascade. We suppose that it is interesting to compare our MS-EGM with other methods of face detection such as SIFT. In the SIFT, the main functionalities are thought as follows: (1) to find key points to create features invariant to scale and rotation and (2) to create HoG feature representations from the key points. Such functionalities are preprocesses for face/object detection. So, in order to compare the SIFT with our MS-EGM, we will have to more actively discuss the following: (1) how to make feature representations for a model face and (2) how to establish the matching process for detection with SIFT-based feature representations. Such discussions will give us insights into improvements of our MS-EGM.
In addition, the model image in our MS-EGM algorithm was down-sampled, in a different way from the SIFT. This can be predicted to cause more efficient scale invariance. When the optimal scale correspondence is to be considered in a Gabor pyramid in the MS-EGM, thus, it can expect to highly identify the size of a face on image I. At least, in the real-time face detection demonstration (not shown here), the MS-EGM is robust to illumination and distortion. In the future, introducing the rotation invariance [37, 38] into our MS-EGM, we develop a more accurate face detection system that can easily detect the face when putting the head on one side. Also, it is interesting to use the face graph, instead of the square graph.
The deficits in our current algorithm are constraints to the down-sampled size of a model face and the incorrect detection on much lower resolution images. These are closely related to the Gabor kernel size of 25 ×25 pixels employed in our system. In the current algorithm for convolution with the Gabor filter, if we use images smaller than 25 ×25 pixels, we will need to implement extrapolation methods such as the replicated border and the constant one to cover additional pixels outside the images. However, even if such extrapolation methods are implemented into our current algorithm, it is still unclear whether or not our system can have better detection performance. This is because we do not ensure whether or not appropriately desired convoluted values are computed.
The MS-EGM face detector developed in this work saves a critical amount of information for a face but succeeds to remove the complexity of feature representation as possible as we can. The HoG features, which are, in recent years, used frequently for being incorporated with the SIFT, encompass all information around the local, which most probably contains the undesired information. Such information causes increments of computational cost. After all, computational costs increased by dealing with the undesired information have to be reduced.
However, our system has realized rapid and high face detection performance without easygoing supports of the CPU power, taking into account the following points: improvements of Gabor feature representation, namely removals of complexity and noise on the representations. In particular, removing the weak Gabor responses has almost never been done as far as we know. It was shown that weak Gabor responses in high-resolution satellite images were removed with Otsu’s thresholding method  in order to find edges of buildings . Effects of such removals on detection or on recognition were not yet discussed. Meanwhile, we have found that it is a significantly effective technique for increasing the probability of correct detection. In the future, it may be more interesting to apply the weak Gabor feature elimination into the EGM or EBGM algorithm for visual object/face recognition.
It is also interesting for us to implement MS-EGM into a digital hardware circuit. This is because the EGM in our face detection algorithm is developed by modifying the EGM for face recognition improved into the digital hardware . It can also expect that the EGM-specific integrated circuit will be developed for parallel processing for detection and recognition of a face. Such a system must be definitely compact and simplified, compared to the system integrated with several individual functions.
In this work, image I was resampled to 60 ×60 pixels because of reduction of computational cost of the Gabor filter for the original size. The resampling to 64 ×64 pixels would be better rather than that to 60 ×60 pixels if we consider the extraction of GW features using the FFT. However, taking current computer performances into account, it can be expected that both cases of 64 ×64 pixels and 60 ×60 pixels obtain almost the same speed such that both cases can realize real-time performance of EGM.
Rather, we have to be aware that there is still one problem about a down-sampled scaling factor in the Gabor pyramid. One of the merits to use the Gabor pyramid is the optimal scale correspondence, which provides us the best trade-off between spatial resolution and frequency resolution. Nevertheless, we did not care of the optimal scale correspondence but only how the EGM is realized in the real-time process. As the next step, we will have to reconsider the correct scale for finding the best trade-off. This allows us to realize the additional functionality of the scale invariance. We can establish the EGM system for face detection, independent of facial sizes of the input.
Finally, we discuss the reason to employ an image of the average face for German. We will have to be aware that the core target in our work is to develop the algorithm for parallel processing for detection and recognition of a face within the framework of the EBGM. In the EBGM, topologically the same face graphs are prepared for different identities in the M domain. Such different face graphs stored in the M domain recognize or identify the corresponding face on image I. Assuming that such an EBGM-based algorithm for face recognition is integrated with our algorithm for face detection in the future, an average face image must be better to use, rather than using several different face graphs or one identifiable face image. In this work, using an average face image for German men, we have found extra tasks, one of which is how racial and gender differences affect the face detection ability of our MS-EGM. This also implies that our MS-EGM algorithm proposed here is expected to further develop.
In this work, we have proposed the MS-EGM as a face detector, improving two following formulae in the conventional EGM: The first is to use a Gabor wavelet-based pyramid. This effectively reduces not only computational costs for Gabor filtering but also computational complexity for feature representation, preserving the image information about the model face. The second is elimination of the weak Gabor feature extracted for image I. This facilitates an accuracy of the Gabor feature similarity computations as unexpected. The MS-EGM can thus be capable of rapid face detection processing while achieving a high rate, comparable to the AdaBoost HL feature cascade. We have shown that the MS-EGM has strong robustness to the image of a face occluded with sunglasses and scarfs because of topologically preserved feature representations.
The authors thank C. von der Malsburg at FIAS, C. Weber, S. Wermeter at the University of Hamburg, K. Horio, and H. Miyamoto at Kyushu Institute of Technology for the fruitful and active discussion. This work was partially supported by the Grant-in-Aid for Challenging Exploratory Research (to Y.D.S.) (no. 25540110) from MEXT.
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