Triangle Method for Fast Face Detection on the Wild

For detection of face, facial features are used three kinds of features. The value of a two-rectangle feature is the difference between the sum of the pixels within two rectangular regions. The regions have the same size and shape and are horizontally or vertically adjacent (see Figure. 1). A three-rectangle feature computes the sum within two outside rectangles subtracted from the sum in a center rectangle. Finally a four-rectangle feature computes the difference between diagonal pairs of rectangles. All features must be gray color and rectangle features can be changed.

Fig. 1. Rectangle features (two, three and four rectangle features).

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Image is divided into 12x12, 24x24, 48x48 windows by 12-net, 24-net, 48-net and compare based on features. Rectangle features can be computed very rapidly using an intermediate representation for the image which we call the integral image. The integral image at location x, y contains the sum [4] of the pixels above and to the left of x, y, inclusive:

where ii(x, y) is the integral image and i(x, y) is the original image. Using the following pair of recurrences:

where s(x, y) is the cumulative row sum.

Once computed, any one of these Haar-like features can be computed at any scale or location in constant time. In the domain of face detection it is possible to achieve fewer than 1% false negatives and 40% false positives [5] using a classifier constructed from two Haar-like features. As a result each stage of the boosting process, which selects a new weak classifier, can be viewed as a feature selection process. Our first task is minimizing false negative rates and we triangle method using capsule and convolutional neuron networks (section proposed method).

By using HOG [6], we can find face features easily. To find faces in an image, we’ll start by making our image gray (value of gray color 0-255) because we don’t need color data to find faces. Then we’ll look at every single pixel in given image one at a time. For every single pixel, we want to look at the pixels that directly surrounding it. Our goal is to figure out how dark the current pixel is compared to the pixels directly surrounding it. Then we want to draw an arrow showing in which direction the image is getting darker. If we repeat that process for every single pixel in the image, we end up with every pixel being replaced by an arrow. These arrows are called gradients and they show the flow from light to dark across the entire image (see Figure. 2).

Fig. 2. Detection eye by HOG.

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This might seem like a random thing to do, but there’s a really good reason for replacing the pixels with gradients. If we analyze pixels directly, current dark images and current light images of the same person will have totally different pixel values. But by only considering the direction that brightness changes, both really dark images and really bright images will end up with the same exact representation.

For faster and efficiency, detection and boosting the classification performance of a simple learning algorithm is used AdaBoost learning algorithm [3]. AdaBoost takes weak classification functions from stronger, because strong features are used for detection easily, but we need to work with weak features. For learning weak functions we use capsule neuron networks in our triangle method.

The conventional AdaBoost procedure can be easily interpreted as a greedy feature selection process. Input part has several values and it helps to separate weak and strong features.

For construction strongly and efficiency face detection system, Li and others [7] proposed using cascaded convolutional neuron network (CNN). Face detection by cascaded CNNs requires bounding box calibration from face detection with extra computational expense and ignores the inherent correlation between facial landmarks localization and bounding box regression. We know that in one frame will be one or a lot of faces. Also, by scanning a window we can see that there are strong and weak face windows. Zhang and others [8] used multi-task CNN to improve the accuracy of multi-view face detection, but the detection recall is limited by the initial detection window produced by a weak face detector. By multi-task cascaded face detection uses fourteen different face features such as a Figure 3. Also, Jeffry Hinton has introduced a newer, capsular neuron network [9] identification system, which has a more detailed face identification approach. By Hinton’s capsules we can detect and find facial features from low resolution images.

Fig. 3. Different face characters.

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Zhang’s method proposed a new framework to integrate these tasks using unified cascaded CNNs by multi-task learning. This method consists of three stages. In the first stage, it produces candidate windows quickly through a shallow CNN. Then, it refines the windows by rejecting a large number of non-faces windows through a more complex CNN. Finally, it uses a more powerful CNN to refine the result again and output five facial landmarks positions.

If we return to the neuron networks it studies every point of research area weak or strong results of function. Using neuron networks for face detection is realized problems with pose, expression, and lighting. For protection from these problems are used CNNs and it gives high quality performance. This CNN cascade operates at multiple resolutions, quickly rejects the background regions in the fast low resolution stages, and carefully evaluates a small number of challenging candidates in the last high resolution stage. Also, CNN is used to improve localization effectiveness, and reduce the number of candidates at later stages. Kaipeng Zhang and others said that deep CNNs [10] achieve substantial improvements and increase of detection rate in face identification in the wild. Classical CNN-based face detection methods simply stack successive layers of filters where an input sample should pass through all layers before reaching a face/non-face decision. Inspired by the fact that for face detection, filters in deeper layers can discriminate between difficult face/nonface samples contextual CNN (see Figure.3). In deep learning CNN differ with traditional CNN which enables different layers to be trained by different types of samples, and can focus on handling more difficult samples. Also, Kaipeng Zhang and his commands used Body Part Sensitive Learning.

But, Jeffry Hinton developer of “Deep learning” said that there is a problem with CNN which it works by accumulating a variety of features at each level. It begins with finding edges, then shapes, and then actual objects. However, information about the spatial relationships of all functions is lost. We can explain the principle of the CNN in the following way:

It is not true, because in this code doesn’t attend to the real face rules (see Figure. 4). In Figure 4.a is shown real face, but in Figure 4.b not face. Our function is solving this problem. For solving this problem, we propose using triangle method for detection faces by facial features easily, faster and without negatives.

Fig. 4. Face or not face pose.

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Ref. [11] is given recommendations and optimizing ways of collecting face databases for face detection and recognition. By these databases, we are trained faces and face features. For searching facial features, we scan the image or video frame by 12, 24, 48-net (see Figure. 5) [12] and send to the neuron network (see Figure. 7).

Fig. 5. Scan image by 12, 24, 48-net window.

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Fig. 6. Face poses and features.

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Fig. 7. Neuron network.

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12-net. 12-net refers to the first CNN in the test pipeline. 12-net is a very shallow binary classification NN to quickly scan the testing image. Densely scanning an image of size WxH with 4-pixel spacing for 12x12 detection windows is equivalent to apply the 12-net to the whole image to obtain a $\left(\left[\frac{w-12}{4}\right]+1\right)*\left(\left[\frac{H-12}{4}\right]+1\right)$ map of confidence scores. Each point on the confidence map refers to a 12x12 detection window on the testing image.

24-net. 24-net is an intermediate binary classification CNN to further reduce the number of detection windows. Remaining detection windows from the 12-net are cropped out and resized into 24x24 images and evaluated by the 24-net. A similar shallow structure is chosen for time efficiency. With this multi-resolution structure, the 24-net is supplemented by the information at 12x12 resolution which helps detect the small faces.

48-net. 48-net is the last binary classification CNN. At this stage of the cascade, it is feasible to apply a more powerful but slower CNN. Similar to the 24-net, we adopt the multi-resolution design in 48-net with additional input copy in 24x24 and a sub-structure the same as the 24-net. Or we can window size as a 48x48.

If we analyze all of the nets, 12-net gives best result for detect facial features but it detects slowly.

Triangle method. Finding faces by facial features is big problem. By our triangle method, we can solve this problem. Triangle method is used to sort facial and no facial images by calculating dependencies between key-points. This method consists of following steps (see Figure. 6.A):

If face pose is left side or right side (see Figure. 6.B and 6.B.1), than we can implement fallowing methods:

Here, m=size of the mouth,

e – size of the eye,

a – distance between left eye and nose,

b – distance between two eyes,

c – distance between right eye and nose,

d – distance between nose and mouth,

α, β, γ – corners (see Figure. 6.A).