An Intelligent Fused Approach for Face Recognition

3.1 Voronoi Diagram Content

VD, or Voronoi tessellation, is a well-known technique in computational geometry that generates clusters of intensity values using information from the vertices of the external boundary of DT. VD has been revived several times, and a comprehensive review of its variations and applications can be found in Ref. [18]. Furthermore, Blum and Nagel [2] proposed an algorithm for the computational analysis of the skeleton and the construction of VD/DT on the boundary of a shape image. It is presently used in many research areas; however, researchers primarily focus on its use in skeletonization and generation of Euclidean distances.

This research work exploits the triangulations (i.e., Delaunay) generated by the VD [17]. The VD set of “sites” (points) is a collection of regions that divide the plane. Each region corresponds to one of the sites, and all the points in one region are closer to the corresponding site than to any other site. Given a set of 2D points, the Voronoi region for a point p_i is defined as the set of all the points that are closer to p_i than to any other points. The intersections of the Voronoi regions for the set of points construct the Voronoi diagram. Additionally, it has geometric features such as Voronoi edges and Voronoi vertices. A Voronoi edge is a boundary line segment limiting its associated Voronoi region. A point on the Voronoi edge is associated with two input points such that each point on a Voronoi edge is equidistant from these two points. A Voronoi vertex is an intersection of Voronoi edges and is associated with three or more input points such that each Voronoi vertex is equidistant from these input points as shown in Figures 2 and 3, respectively [7].

Figure 2

(A) Set of Point, (B) VD, and (C) DT.

Figure 3

VD Component. V(S) = Voronoi Diagram (solid lines); DT(S) = Delaunay Triangulation (dashed lines); w = Voronoi Vertex; p, q, r, s = Co-circular Site Degree 4.

Let a set S = {p₁, p₂, …, p_n} of n distinct points in the plane. The Voronoi cell V(p_i) of a point p_i∈S is defined in the following:

Here, d(p, q) denotes the ordinary Euclidean distance between p and q:

The VD V(S) of S is the family of subset of R² that consists of the Voronoi cells and all of their intersections. The bound of a Voronoi cell consists of Voronoi edges and Voronoi vertices. A point q∈R² is on the Voronoi edge (p_i, p_j) if

3.2 Face Image Segmentation Phase

Image segmentation is a basic step in almost all image-processing applications [21]. In image analysis of face segmentation, identification and isolation into regions are mandatory in order to distinguish between the object image’s so-called foreground and the part of the non-object’s so-called background. However, before segmentation, preprocessing is carried out to enhance the quality of the original image such as lighting uneven effects, noise, and the impact background on the object. The proposed procedure used square morphological, Gaussian low-pass filter, median filter (to remove noise), and histogram equalization. Consequently, the grayscale values of the face images are reduced to 27.87%, which enhanced the speed and reduced memory usage. Additionally, the histogram equalization stage enhanced the image intensity contrast to generate a convex hull to be used in next stage. The convex hull of a set of featured points is the smallest convex set containing these points that have the outer boundary of VD. However, few selection points (fewer than 255) are selected [17]. The represented point sets can reflect dense point sets, and a set of unique dot patterns are attained. The two global maxima are obtained from the host image histogram, which obtains the minima between these two peaks. Finally, we set all points below the first peak and all points beyond the second peak to zeros, and then we set all points that are also equal to zeros to be equal to the argmax (peak1, peak2). Hence, it yields a local flip effect image histogram as shown in Figure 4. The new set points for the part of the convex hull corresponding with the DT were sorted in ascending order to form ranges to merge or split regions accordingly:

Figure 4

Global Maxima and Local Minima.

where Valnew(x) represents the highest frequency in the host image histogram.

To locate the face region, the authors have introduced distance transformation to separate the face region from the background, which used function operators on the Euclidean distance between two points (DisT ≥ threshold value). Next, a well-known strategy for face estimation and segmentation is used, which includes ellipse fitting, cross correlation, and the Euler number. From a previous step, the eye position in the original face image is detected, and finally, the arbitrary square angle (the so-called window), with a size of 200 × 200 pixels, is used to crop the face image automatically. The targets of this phase of facial image detection consist of the eyes, nose, and mouth as shown in Figures 5–7.

Figure 5

(A) DT, (B) Original Image, (C) Segmentation, and (D) Detection.

Figure 6

Facial Face (Automatic Crop).

Figure 7

Example Face Cropped Image from the BioID Data Set.

4.1 Face Extraction Using DWT

Wavelet transformation has been widely used in image-processing applications [25]. Mallat and Zhang [13, 14] presented the wavelet theory for signal processing. It defines an orthogonal multiresolution representation, the so-called “wavelet representation”. In the case of image, the wavelet representation differentiates several spatial orientations for data compression in image coding and texture discrimination. An image is repeatedly filtered and decimated into high and low spatial frequency bands, alternatively between the horizontal and vertical directions.

The 2D DWT is computed by applying a separable filter bank to the original image that is decomposed into four sets to represent wavelet coefficients, approximation, and details. At each step, the previous four sub-images of the wavelet coefficients are further decomposed into four new sub-images: approximation and detail [23]:

where A_n is the approximation at level n and A_o=I(x, y) (original image); D_ni is the level n details; parameter i stands for the direction of the details (i = 1, 2, 3 represents the vertical, horizontal, and diagonal directions, respectively); |2,1 and |1,2 are the image transformations performed in both the vertical and the horizontal directions, respectively; and H and L are the high- and low-pass filters, respectively.

In this research, the image is cropped with first-level Daubechies wavelet “db4” with a size of 128 × 128 pixels. The result of the extracted facial image is the part of sub-band HL, LH, and HH (Figure 8). Next, these sub-bands are selected to compute the wavelet feature that used the detail coefficient matrices of each sub-band:

Figure 8

Sub-band Type and First-level DWT.

where cH, cV, and cD are the detail coefficient matrices of horizontal, vertical, and diagonal directions, respectively.

4.2 Face Extraction Using Moment Invariants

Moment-based invariants are widely applicable in describing the features of moment invariants on 2D image and have been used for pattern feature extraction and object recognition [5, 15]. Initially, Hu [8] introduced a set of invariants based on non-linear combinations using regular moments. The significant central moments are invariant toward rotation, translation, and scale [10].

The 2D moment of the order (p+q) of a digital image f(x, y) is defined as

for p, q=0, 1, 2, …, where the summations are over the values of the spatial coordinates x and y spanning the image. The corresponding central moment is defined as

where

The normalized central moment of order (p+q) is defined as

for p, q=0, 1, 2,…, where

for p+q=2, 3, …. A set of seven 2D moment invariants that are insensitive to translation, scale change, mirroring, and rotation can be derived from these equations such as:

The central moment invariants are useful features for image description due to their independence and invariance to position, orientation, and size of image. In this article, we combine the absolute of the orthogonal moment invariants with the similitude moment invariants [7]. Thus, all fused feature vectors be composed of orthogonal moment invariants, similitude moment invariants, and moment invariants from both similitude and orthogonal transformations. The total of the feature vectors is 21, which was obtained from the combination of the seven features in each moment invariant.

5.1 Experiment of Face Segmentation Using VD/DT

After preprocessing, the proposed scheme uses VD and DT for segmentation and detection of the face image. All experiments are conducted on grayscale frontal face images, 3849 × 9286 pixels, obtained from the BioID face data set. There are 15 objects (people), and each object had 10 images. Additionally, each image had different illuminations and non-strict face expression. The target of this step is the detection of the eyes on original face image. Then we used the square angle (window) for automatic cropping of the face from its image, as shown in Figure 6. Our method sets the size of the facial face to 1289 × 9128 pixels, which is enough to include the eyes, nose, and mouth. The result of correct location rate with different lighting conditions is 90.7%, as shown in Table 1.

Only a few results are reported in the literature, but for the sake of comparison, Yi and Hong [27] claimed an accuracy rate of 89% and Lam and Yan [10] achieved an accuracy of 85%. In comparison, our proposed approach produced a better result [22].

5.2 Experiment of Face Classification Using Minimum Euclidean Distance

The BioID face benchmark database is composed of 10 different images of each of 15 people. These images are taken under different illuminations and without glasses. The experiments are carried out on nearest neighbor classifiers using minimum Euclidean distance. In our experiment, five images of each person are selected as training, and the rest of the 10 images are used for testing. The experiment results of the first-level discrete wavelet decomposition using db4 and the extraction of the feature using moment invariants are shown in Table 2.

Table 2 shows that the best recognition rate, 97.2%, is obtained for object 13. However, the lowest recognition rate is for object 11 (92.0%), where first-level db4 DWT and moment invariant extraction are used. Nonetheless, while the experimental setup and face data set are kept constant, the recognition rates are not the same. This is due to the arbitrary selection of training, testing data set, and different illuminations of objects 13 and 11. Therefore, the images for testing and training should be selected appropriately [20].