The basic idea of automatic kinship verification using facial images is to check if a given two facial images input have pertinence from the same family or not. Several applications can be useful under automatic kinship verification e.g. for forensics, finding missing children, social media comprehension and image annotation. Thus, a DNA test is the most reliable source for kinship verification, it unfortunately cannot be utilized in many situations such as in video surveillance.
Many authors feed their method by different features or multiple features (multi-view data) to represent facial images for kinship verification. Lu et al. used the Multiview neighborhood repulsed metric learning (MNRML)  method to train four multi-view features, Local Binary Patterns (LBP), Learning-based descriptor (LE), SIFT and Three-patch LBP (TPLBP). Yan et al.  employed three different feature descriptors including Local Binary Patterns(LBP), Spatial Pyramid LEarning (SPLE) and Scale-Invariant Feature Transform (SIFT) to extract different and complementary information from each face image through DMML method. Yan et al.  applied three dif-ferent feature descriptors including LBP, spatial pyramid lEarning (SPLE), and SIFT to extract different and complementary information from each face image to train the MPDFL method. Lu et al.  used four features as it; Local Binary Patterns (LBP), Dense SIFT (DSIFT), the histogram of oriented gradients (HOG) and LPQ for train DDMML method. Lu et al.  used MvDML to train four multi-view features, Local Binary Patterns (LBP), Learning-based descriptor (LE), SIFT and Three-patch LBP (TPLBP). Laiadi et al.  used three features LPQ, BSIF and CoALBP to train SIEDA method. Dornaika et al. used MNRML to train the two features, FC7 layers of VGG-F and VGG-Face for the purpose of kinship verification. Laiadi et al. proposed TXQDA  method to train LPQ and BSIF features using ten scales.
In this work, we propose a new framework to kinship verification from facial images using eight deep features based on four pre-trained deep learning networks. For this reason, we extract FC6 and FC7 layers from VGG-F, VGG-M, VGG-S and VGG-Face models to train the proposed Multilinear Side-Information based Discriminant Analysis integrating Within Class Covariance Normalization (MSIDA+WCCN) method. We report our preliminary experimental investigations on the KinFaceW-I and KinFaceW-II benchmarks using four relations, Father-Son, Father-Daughter, Mother-Son and Mother-Daughter face subsets showing very high performance compared to state-of-the-art methods.
Ii Proposed Framework
Figure 1 depicts an overview of our proposed framework. The input is a pair of two face images e.g. a Parent and a Child. We extract features from these images into eight deep features of the input test pair. We compute the cosine similarity between the two facial images to encode the final metric. The cosine similarity is fed to the ROC curve for the performance evaluation.
Ii-a Extracting Multi-view Deep Features
Many methods suggested in the literature on automatic verification of kinship have focused mainly on analyzing deep features trained on facial images (i.e. VGG-Face), thus ignoring deep features trained on object images (i.e. VGG-F, VGG-M and VGG-S). Recently, deep facial features have shown great performance than their shallow counterparts to verify kinship relation (e.g. ). When considering the facial deep information, the problem usually consists in learning a discriminating metric where the classification (e.g. kinship verification in our case) becomes more affordable when combined to the object deep features. As suggested in , we consider the object deep features for kinship verification. Facial and object features show a complementarity which extracted by MSIDA+WCCN method. This is in contrast to use facial deep features or object deep features information separately. Therefore, we extract the facial deep features using VGG-Face  method and object deep features  (VGG-F, VGG-M and VGG-S methods) using MSIDA+WCCN method. Figure 2
depicts multi-view deep features extraction (Mv-VGG) and tensor design. From this figure, the different colors of block architecture represent the difference in each architecture type. For deep object features, VGG-Fast is an architecture contains number of parameters smaller than VGG-Medium, and this latter is an architecture contains number of parameters smaller than VGG-Slow and these three architectures were trained on the object recognition ILSVRC-2012 database. For deep face features, the VGG-Face architecture was trained on VGG Face database  which contains 2.6M facial images from 2,622 identities. Furthermore, in the tensor representation, the length of each data stacked in a tensor mode must be the same, and this property was saved by the four pre-trained models with 4096 neurons in each of the eight used fully connected layers (i.e the FC6 and FC7 layers of the four pre-trained models have the same length).
Iii Multilinear Side-Information based Discriminant Analysis integrating Within Class Covariance Normalization (MSIDA+WCCN)
Iii-a Side-Information based Linear Discriminant analysis (SILD)
The positive classes pair images are directly utilized to calculate the within class scatter matrix and the negative classes pair images are used to compute the between class scatter matrix. Let us refer that as the collection of positive-class image pairs and
as the collection of negative-class image pairs, where the image is represented by the class label . Here, the within-class and between-class scatter matrices of Side-Information based Linear Discriminant analysis  (SILD) method can be represented by:
The target function for SILD is:
Secondly, is also diagonalized:
Finally, the projection matrix can be computed as:
where H and Z are orthogonal matrices and and E are diagonal matrices.
Iii-B Proposed Multilinear Side-Information based Discriminant Analysis integrating Within Class Covariance Normalization
Let a Tensor training set of classes, where: contains samples of Parents samples and contains samples of Children samples. The goal of MSIDA  is the calculation of projection matrices (). Thus, we calculate one projection matrix for each tensor mode. The objective function of MSIDA method is defined as follow:
We calculate the two covariance matrices and for each mode by:
S_w = ∑_p=1^∏_o≠kI_o S_w^p, S_w^p = ∑_i=1^C_1((ˇξ_i^1)^k,p-(^ξ_i^1)^k,p)((ˇξ_i^1)^k,p-(^ξ_i^1)^k,p)^T
S_b = ∑_p=1^∏_o≠kI_o S_b^p, S_b^p = ∑_i=1^C_0((ˇξ_i^0)^k,p-(^ξ_i^0)^k,p)((ˇξ_i^0)^k,p-(^ξ_i^0)^k,p)^T
Now that the solution for one mode is known, the optimization problem in equation 10 can be solved iteratively. The projection matrices are first initialized to identity. At each iteration are hypothetical known and
is estimated. Set:and are replaced in equation 10 by X and Z. The new equation can be solved by the generalized eigenvalue decomposition problem:
Where, is the eigenvectors matrix and the eigenvalues matrix.
The iterative process of MSIDA breaks up on the recognition of one of the following situations: i) The number of iterations reaches a predefined maximum; or ii) the difference of the estimated projection between two consecutive iterations is less than a threshold, where is the mode dimension of . As depicted in Fig. 1, the block diagram of the proposed approach consists of three essential components: feature extraction, tensor subspace transformation and comparison. We focus in this work on subspace transformation and the feature extraction based multiple scales local descriptor.
Iii-C Within-Class Covariance Normalization
The first use of the Within-Class Covariance Normalization (WCCN) is in the community of speaker recognition. While Dehak et al. 
founded that it is the best technique to project the reduced-vectors of LDA method to a new subspace determined by the square-root of the inverse of the within-class covariance matrix. We propose a new variant of MSIDA by integrating WCCN:
G = ∑_p=1^∏_o≠kI_o G^p, G^p =∑_i=1^C_1 (Wk)T(ˇξi1)k,p-(Wk)T(^ξi1)k,p(Wk)T(ˇξi1)k,p-(Wk)T(^ξi1)k,p
where, is the MSIDA projection matrix found in Eq.11. The WCCN projection matrix is obtained by Cholesky decomposition [11, 28] of the inverse of : . Where the new projection matrix is obtained by: . By imposing upper bounds on the classification error metric , WCCN decreases the within-class variations effect by reducing the expected classification error on the training step.
Iv Experimental Analysis
For experimental evaluation, we considered the KinFaceW-I and KinFaceW-II databases are gathered through Internet research, including some public figures with their parents and/or children. In the KinFaceWI dataset, there are 156, 134, 116, and 127 pairs corresponding to the F-S, F-D, M-S, and M-D relations, respectively. For the KinFaceW-II dataset, each kin relation type contains 250 pairs. In total KinFaceW-I count 1066 face images and 2000 face images for KinFaceW-II.
|ResNet + CF ||78.00||83.70||87.00||80.80||82.40||87.70||86.00||86.70||87.40||86.60|
Iv-a Experimental Setup
The number of the positive and negative pairs used in the experiments is the same for each relation on the four subsets. We use five-fold cross validation strategy for the evaluation. We report the mean accuracy over the five folds. The negative pairs and folds are predefined for the all four relations. For the facial deep features and object deep features, we extracted VGG-Face, VGG-F, VGG-M and VGG-S as this has shown to perform better than shallow methods [30, 7]. The tensor features are performs by the proposed MSIDA+WCCN method.
Iv-B Results and Analysis
Iv-B1 Results on RFIW’20 Challenge
For RFIW’20 Challenge [20, 24, 22, 21], we used the eight fully connected layers of the four pre-trained models (facial and object models). For this reason, we used the Simple Scoring Cosine similarity (SSC) method by concatenating the eight deep features to form a vector of features for each pair facial images. Then, we compute the cosine similarity metric between the two vectors. This method show and prove how can a raw weights of deep features perform in kinship verification as an excellent features of facial images without using any application of learning methods.
Iv-B2 Results on KinFaceW databases
We run the experiments on the four relations of the two databases, KinFaceW-I and KinFaceW-II, using SSC, SILD, MSIDA, SILD+WCCN and MSIDA+WCCN methods. The results of these experiments are reported in Table I. The ROC curves comparing SSC, SILD, MSIDA, SILD+WCCN and MSIDA+WCCN are provided in Figures 7 and 12 for the four relation of KinFaceW-I and KinFaceW-II databases, respectively. As can be noticed from the figure, the performance of MSIDA+WCCN is much better than that the other methods in all cases.
Our proposed method is compared against some recent state-of-the-art methods in Table I. Note that some of these methods, such as MvDML, DDMML, ResNet+CF, MNRML+SVM, use combination of different features to describe a face image. Some other methods are based on deep learning. On the four relations of KinFaceW-I and KinFaceW-II databases, our approach yields in the best results for the mean of all the four kinship subsets of the two databases. These results are promising and demonstrate that our proposed approach is performs better than the recent methods for kinship verification. Furthermore, MSIDA+WCCN and SILD+WCCN improve the performances of their counterparts (i.e. MSIDA and SILD) with large margin. Besides, for linear (vector-based) methods, SILD+WCCN improves SILD method with about 2.47% and 4.30% for KinFaceW-I and KinFaceW-II databases, respectively. Also, for multilinear (tensor-based) methods, MSIDA+WCCN improves MSIDA method with about 12.08% and 13.05% for KinFaceW-I and KinFaceW-II databases, respectively. Thus, the integration of WCCN shows stable and robust performances on the metric learning methods for kinship verification.
In this paper, we presented an effective approach based on multi-view deep features (facial and object) features to the problem of kinship verification. To achieve a low dimensional and discriminative subspace, we proposed the MSIDA+WCCN method. Also, we studied the effect of WCCN on different metric learning methods showing that the within-class intra-variability introduced by the training data (multi-view deep features in our case) can be reduced to a large extent. Thus, we see that the performances was improved and the metric learning methods can learn good metrics through WCCN integration. The obtained results by MSIDA+WCCN method outperform the state of the art on four Parent-Child relations on two databases, KinFaceW-I and KinFaceW-II.
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