Ratios Between Facial Features Points

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The ratios between facial features points are the third type of features, which their effects on family likeness are evaluated. These 9 ratios are calculated from the distances between facial feature points. In order to eliminate the dependency of the proposed algorithm to image scale, this set of ratios is utilized instead of distances between the facial feature points. These ratios are as follows:

Eleven distances use to calculate the above ratios are illustrated in Figure 6.

Locating the exact coordinates of the facial features points are crucial for calculating the ratios. As is evident from Figure5, the hair line, chin, and sides of face are points that form the face boundaries. These points are simultaneously localized while face is detected and cropped from the image. In order to extract other facial feature points two types of geometric feature-based methods are used. First, Linear Principal Transformation (LPT), which is proposed by Dehshibi et al [Deh10], is performed to locate the eyebrows, eyes, nose tip and center line of lips in frontal view of face. Then, an extended version of LPT, which we called it LPT2 are used to locate these points in profile view.

Linear Principal Transformation (LPT) is a one to one transformation, which has three key features, including "accuracy," "power," and "simplicity." The main goal of LPT is to identify the most meaningful basis, which contains the features of interest. It will reveal the hidden structure of data. LPT assumes that an m×n image consists of m observation sets in an n-dimensional vector space. Among these vectors, the vector which has the highest variance corresponds to the feature of interest. To obtain a feature, first, the covariance matrix of image is calc...

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...ing images is calculated. Then, based on the calculated weight half of the training data is eliminated. In the second stage filtering the database is done using the "eye region". In the last stage of recognition the "Frontal face" is used to find three images, which have the minimum Euclidean distance with the input image.

In order to rate the efficiency of the proposed algorithm, a structure for the family should be considered. With respect to the images in the FFIDB, a structure with three levels is defined. As is evident from Figure 11 each level has an impact factor. The efficiency rate of proposed method is equal to(sum of each level impact factor)/(sum of maximum impact factor). For example, if the selected images in recognition phase have the "mother", "sister", and "cousin" relation with the input image, then the accuracy of the algorithm is 77.77 percent.

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