Dual-reference Face Retrieval

TL;DR

This paper introduces a dual reference face retrieval system that uses two images to retrieve faces matching a specific identity and age, addressing a novel challenge in face retrieval.

Contribution

It proposes a joint manifold and quartet-based model to effectively combine identity and age similarities for face retrieval.

Findings

Outperforms hierarchical methods in experiments.

Successfully retrieves faces at specific ages without explicit age labels.

Demonstrates the effectiveness of joint manifold and dual-reference approach.

Abstract

Face retrieval has received much attention over the past few decades, and many efforts have been made in retrieving face images against pose, illumination, and expression variations. However, the conventional works fail to meet the requirements of a potential and novel task --- retrieving a person's face image at a specific age, especially when the specific 'age' is not given as a numeral, i.e. 'retrieving someone's image at the similar age period shown by another person's image'. To tackle this problem, we propose a dual reference face retrieval framework in this paper, where the system takes two inputs: an identity reference image which indicates the target identity and an age reference image which reflects the target age. In our framework, the raw images are first projected on a joint manifold, which preserves both the age and identity locality. Then two similarity metrics of age and identity are exploited and optimized by utilizing our proposed quartet-based model. The experiments show promising results, outperforming hierarchical methods.

Tables

Table 1. Table 1: Statistics of the Datasets

Dataset	Images	Subjects	Images/sub.	Age gap
CACD	163446	2000	81.7	0-9
FGNet	1002	82	12.2	0-45
MORPH	55134	13618	4.1	0-5

Table 2. Table 2: Experimental results on CACD dataset.

Accuracy% @ top-$K$	$K$=1	$K$=2	$K$=3	$K$=4	$K$=5	$K$=8	$K$=10
eigenfaces+SVR	14.43	17.25	17.42	17.87	18.5	19.10	19.20
eigenfaces+CCA	14.97	17.73	18.21	18.53	18.71	19.24	19.35
LBP+SVR	17.58	20.32	20.86	21.52	21.85	23.45	24.53
LBP+CCA	17.98	21.44	22.13	22.13	22.22	24.78	25.71
CARC+SVR	18.34	22.45	23.02	23.64	24.30	25.70	26.20
CARC+CCA	18.57	22.25	23.50	23.85	24.50	26.12	26.42
FaceNet+SVR	19.76	23.20	23.33	23.77	23.64	24.70	26.33
FaceNet+CCA	19.63	23.48	24.12	24.37	24.54	25.38	26.40
DRFR(Ours)	20.67	23.75	24.33	24.87	24.90	25.80	26.23

Table 3. Table 3: Cross dataset validation on MORPH.

Acc% @ top-$K$	$K$=1	$K$=3	$K$=5	$K$=10
MORPH	18.26	20.81	22.99	23.17
CACD	20.67	24.33	24.90	26.23

Equations

$$S^{n}(x_{i}^{n},x_{j}^{n})=\begin{cases*}\exp\left(-\frac{\parallel x_{i}^{n}-x_{j}^{n}\parallel^{2}_{2}}{t}\right)&if $x_{j}^{n}\in\mathcal{N}(x_{i}^{n})$\text{,}\\ 0&otherwise\text{,}\end{cases*}$$

$$\underset{f}{\min }\sum _n\sum _{i,j}\parallel f(x_i^n)-f(x_j^n){\parallel }_2^2{S}^n(x_i^n,x_j^n)\text{.}$$

$$S_{i}(x_{i}^{n},x_{i}^{m})=\begin{cases*}\exp\left(-\frac{\parallel x_{i}^{n}-x_{i}^{m}\parallel^{2}_{2}}{t}\right)&if $|m-n|<\varepsilon$,\\ 0&otherwise.\end{cases*}$$

$$\underset{f}{\min }\sum _i\sum _{m,n}\parallel f(x_i^n)-f(x_i^m){\parallel }_2^2{S}_i(x_i^n,x_i^m)\text{.}$$

$$\begin{array}{rl}& {\Phi }_{ind}(f(x_i^m),f(x_i^n))<{\Phi }_{ind}(f(x_i^m),f(x_j^n))\\ & \forall (i,j,m,n)\text{,}\end{array}$$

$$\begin{array}{rl}& {\Phi }_{ind}(f(x_i^m),f(x_j^m))={\Phi }_{ind}(f(x_i^m),f(x_j^n))\\ & \forall (i,j,m,n)\text{,}\end{array}$$

$$\begin{array}{rl}& {\Phi }_{age}(f(x_i^m),f(x_j^m))<{\Phi }_{age}(f(x_i^m),f(x_j^n))\\ & \forall (i,j,m,n)\text{,}\end{array}$$

$$\begin{array}{rl}& {\Phi }_{age}(f(x_i^m),f(x_j^n))={\Phi }_{age}(f(x_i^m),f(x_i^n))\\ & \forall (i,j,m,n)\text{,}\end{array}$$

$$\begin{array}{rl}& {\Phi }_{age}(f(x_i^m),f(x_j^n))={d_{ij}^{mn}}^{\top }{\mathbf{M}}_{\text{age}}{d}_{ij}^{mn}\text{,}\\ & {\Phi }_{ind}(f(x_i^m),f(x_j^n))={d_{ij}^{mn}}^{\top }{\mathbf{M}}_{\text{ind}}{d}_{ij}^{mn}\text{,}\end{array}$$

$$H(y)=\max (0,\delta -y)$$

$${\mathcal{L}}_{ij}^{mn}=$$

$$+$$

$$\mathcal{L}=\sum _{i,j,m,n}{L}_{ij}^{mn}\text{.}$$

$$\begin{array}{rl}\mathcal{J}=\mathcal{L}+& \sum _n\sum _{i,j}\parallel d_{ij}^{nn}{\parallel }_2^2{S}^n(x_i^n,x_j^n)\\ +& \sum _i\sum _{m,n}\parallel d_{ii}^{mn}{\parallel }_2^2{S}_i(x_i^m,x_i^n)\text{,}\\ \text{s.t.}& {\mathbf{M}}_{\text{ind}}⪰0,{\mathbf{M}}_{\text{age}}⪰0\text{,}\end{array}$$

$$\begin{array}{rl}\Phi (f(x_i^m),f(x_j^n))& ={d_{ij}^{mn}}^{\top }\mathbf{M}{d}_{ij}^{mn}\\ & =||Lf(x_i^m)-Lf(x_j^n)|{|}_2^2\end{array}$$

Full text

Introduction

Over the past few decades, face retrieval has received great interest in the research community for its potential applications such as finding missing persons (?) and matching criminals with CCTV footage for law enforcement (?). Apart from a pinch of face retrieval works (?) that are text-based, most existing frameworks (?; ?) are based on the content, in which a target person’s image is required as the query input, and the system retrieves all the images belong to the target person in the database. Though these works in some kind improved the benchmark in the past, they fail to catch up with the pace of the new demands of the face retrieval in the age of big data. For example, rather than retrieving all the query identity’s images indiscriminately, we may prefer picking out the specific ones with some certain attribute, *e.g. *age. The huge volume of online images makes this kind of fine-grained face retrieval both feasible and indispensable. It is feasible as such large-scale dataset can contain many images taken from someone’s different age periods, thereby it is necessary to select them out in some potential applications.

Considering such a task – retrieving Emma Watson’s image at 23, although it is not absolutely impossible to be solved by the conventional face retrieval frameworks, for example, one can achieve it by concatenating an age estimation system at the end of the traditional face retrieval system to select the right images as illustrated in Figure. 1.(a), there exist many drawbacks in such a hierarchical framework. One of them is that using a single numeral is not capable to describe the human perceptions of the age, because the human performance on age estimation is with a large mean absolute error (MAE) as well as a large variance (?), which means generally a human prefers to guess the age within a range rather than a certain numeral. Also, for humans, it is easier to estimate someones’ age by comparing with age-known faces than directly assigning a facial image to a numeral(?). As the old saying goes, ‘One look is worth a thousand words’, the problem of retrieving Emma Watson’s images is better solved by inputting one Emma Watson’s picture and telling the machine: retrieving the images of the one shown in the input. Since a numeral is not representative enough to describe a person’s age, and in some scenarios, we do not even care about the certain age but the similarities in term of the age, what if we use an image to represent the target age? In this paper, we propose a novel face retrieval framework as shown in Figure. 1.(b), in which an age reference image besides the identity reference image is inputted to reflect the target age . We refer to the proposed framework as dual-reference face retrieval (DRFR). In the DRFR, the problem of retrieving Emma Watson’s image at 23 is turned into retrieving the images of the one shown in the first input, and in the similar age reflected in the second input.

In DRFR, the raw images are first projected onto a joint manifold, which preserves both the age and identity locality. Subsequently, as the age and identity are supposed to be measured differently on the joint manifold, a similarity metric for each is exploited and optimized via our proposed quartet-based model shown in Figure. 3. The final retrieval is conducted on the learned metric.

The contributions of this paper mainly lie in the following three aspects:

The task: retrieving someone’s image at some age is an emerging task as more and more precise retrieval is required due to the explosive web images. 2. 2)

The model: a joint manifold of identity and age is exploited in this paper, it simultaneously preserves the localities of these two aspects. Besides, a novel quartet-based model coordinated with two Mahalanobis distances is proposed to measure the similarities between the image pairs. 3. 3)

The framework: our proposed DRFR task can be abstracted into a high-level task — dual reference/query retrieval, which might lead to an emerging research direction. The existing retrieval methods generally take a single query or multiple queries indicating the same semantic information, while in our dual-reference framework, more than one semantic information can be taken into consideration.

The remainder of the paper is organized as follows: we review the works related to the proposed task in Section 2; our proposal is outlined in detail in Section 3; in Section 4, we discuss the experimental results, and we provide a short conclusion in Section 5.

Related Work

To the best of our knowledge, the task of the dual reference face retrieval has never been raised in the literature, and there are no similar existing works, thus we review related works in the areas of face retrieval and age estimation, focusing on those papers which explore facial feature representation, age variation capturing and similarity metric learning.

Facial Feature Representation A broad array of research (?; ?) has been completed on facial feature representation. As facial features extracting is not the core part of our framework, we just give a rough review here. For a comprehensive review, we refer our readers to (?). Early works mainly take heuristic features such as Gabor (?), HOG (?), LBP (?) or their extensions. However, designing hand-crafted features is a trial and error process which is less than adequate for our purpose. Another branch of research regarding facial features is based on utilizing deep learning. For example, (?) employed a nine-layer deep neural network to extract facial features for face verification and (?) proposed a precisely designed deep convolutional networks for joint face identification-Verification.

Age Variation Capturing Age variation capturing is rarely considered in conventional face retrieval approaches because in most works to date, features are required to be age-invariant. In contrast, we are seeking a facial representation that embeds both identity and age information. Approaches capturing age variation can primarily be found in age estimation literature. The earliest approach of age estimation based on facial images dates back to 1994, (?) uses geometric features, in which the ratios between different measurements of facial landmarks (e.g. eyes, chin, nose, mouth, etc.) are calculated to classify the individual into three age groups, namely infants, young adults and senior adults. Unfortunately, it suffers in distinguishing young and old adults as both the shape and texture of the face change during aging (?). To overcome the drawbacks of geometric features, the Active Appearance Model (AAM) is proposed in (?). AAM is able to simultaneously capture the shape and texture information of face images. Considering the temporal characteristics of human aging, Aging Pattern Subspace (?) treats a serial of a person’s images as an aging pattern thus the information during aging process is embedded.

Similarity Metric Learning Once the proper facial image representation is selected, the retrieval is conducted based on the similarity measurements. There are many works (?; ?; ?; ?) focusing on the similarity metric learning. (?) induced a contrastive loss to ensure that the neighbors are pulled together while the non-neighbors are pushed apart on the learned metric. Different with the contrastive loss that only considers pairwise examples at a time, (?) and (?) proposed the triplet loss, which minimizes the $L_{2}$-distance between an anchor and a positive sample, both of which belong to the same instance, and maximizes the distance between the anchor and a negative sample. However, the traditional triplet-loss may lead to a large intra-class variation during testing. (?) added a fourth sample in the triplet to enlarge the inter-class variation thus reducing the intra-class variation.

Dual-Reference Face Retrieval

For convenience, define $I_{i}^{m}$ as an image of the individual with identity $i$ at age $m$. Input an image pair $(I_{i}^{m},I_{j}^{n})$, where $i$ is the target identity and $n$ is the objective age, thus our required output is $I_{i}^{n}$. As discussed, DRFR consists of two stages. Firstly, a mapping function is learned to project the raw images onto a joint manifold. Subsequently, to measure the similarity between each pair of images, the two metrics are learned on the low-dimensional space, based on a quartet model. We devote the rest of this section to outlining these two stages.

Joint Manifold

A face image with $\mathcal{D}$-dimensional feature representation can be considered as a point in the $\mathcal{D}$-dimensional space containing rich information such as age, gender, race, identity. Manifold learning is first proposed in (?), in which they believe that the high-dimensional data is sampled from a smooth low-dimensional manifold. Thus it is natural that information from a facial image can be represented within low-dimensional manifolds embedded in a high-dimensional image space (?). Many applications (?; ?) already utilize low-dimensional manifolds to embed human face images, such as face recognition and age estimation. However, our proposed joint manifold as illustrated in Figure. 2 is very different; instead of treating the age and identity as two separate degrees of freedom in a single manifold, with the assumption that the age and identity are both manifolds sampled from a higher-dimensional manifold.

Let $\mathcal{X}$ be the original representation of the raw images and $\mathcal{Y}$ be the low-dimensional joint manifold, define the mapping function of the joint manifold to be $f:\mathcal{X}\rightarrow\mathcal{Y}$. Since both the locality of the age and identity can be represented as matrices, let $S$ denote the set of all such similarity matrices. Specifically, the matrix $S^{n}\in S$ reflects the similarity among all the individuals’ images at age $n$; similarly, $S_{i}$ denotes the similarity over those images belonging to an individual with identity $i$ across all ages. The desired properties of $f$ are discussed below.

Preserving Locality of Individual Space We first calculate the similarity matrix $S^{n}$. In detail, among all the images at age $n$, if two images are nearby in original feature space $\mathcal{X}$, we mark the similarity as $\exp\left(-\frac{\parallel x_{i}^{n}-x_{j}^{n}\parallel^{2}_{2}}{t}\right)$, where $x_{i}^{n}\in\mathcal{X}$ is the original feature representation of image $I_{i}^{n}$ and $\parallel\cdot\parallel^{2}_{2}$ is the $l2$-norm, otherwise their similarity is [math]. Thus the similarity matrix $S^{n}$ under age $n$ is calculated as:

[TABLE]

where $\mathcal{N}(x_{i}^{n})$ denotes the neighbors of $x_{i}^{n}$. To preserve the locality, we require the nearby points in $\mathcal{X}$ to remain close to each other after being embedded into $\mathcal{Y}=f(\mathcal{X})$, thus we optimize the function:

[TABLE]

Preserving Locality of Age Space Similarly, to calculate the age similarity matrix $S_{i}$, we gather all the images of the individual $i$, and assign $\exp\left(-\frac{\parallel x_{i}^{n}-x_{i}^{m}\parallel^{2}_{2}}{t}\right)$ as the similarity if $m-n$ is below a threshold $\varepsilon$, otherwise the similarity is [math]:

[TABLE]

To preserve the local smoothness, we optimize the function:

[TABLE]

Similarity Metric Learning Based on a Quartet Model

After both the original age and identity spaces are mapped onto a joint manifold, different measurements should be taken to obtain the similarity of the two aspects. In this paper, two similarity metrics are learned based on a novel quartet model, which is a graph with 4 vertices as shown in Figure. 3. The vertices sets $V=\{f(x_{i}^{m}),f(x_{i}^{n}),f(x_{j}^{m}),f(x_{j}^{n})\}$ are the embedded points of $\{(x_{i}^{m}),(x_{i}^{n}),(x_{j}^{m}),(x_{j}^{n})\}$, and the edges are defined as the distance between each embedded point. We use $\Phi(\cdot,\cdot)$ to denote the difference measurement function whereby the smaller $\Phi(\cdot,\cdot)$ is, the more similar the two images are. In the following of this subsection, the properties of the desired metrics are introduced.

Individual Metric Considering two image pairs $(x_{i}^{m},x_{i}^{n})$ and $(x_{j}^{m},x_{i}^{n})$, which are shown in the quartet model in Figure. 3, it is very clear that on the individual metric, the distance between $x_{i}^{m}$ and $x_{i}^{n}$ is smaller than that between $x_{i}^{m}$ and $x_{j}^{n}$, because these two pairs of images both have the age gap $m-n$ while the first image pair $(x_{i}^{m},x_{i}^{n})$ belongs to the same individual $i$. Mathematically, there is:

[TABLE]

where $\Phi_{ind}$ measures the individual difference between any pair of images.

Additionally, the distances between image pair $(x_{i}^{m},x_{j}^{m})$ and $(x_{i}^{m},x_{j}^{n})$ are supposed to be similar because the individual metric is uncorrelated with the age, which can be written as:

[TABLE]

Age Metric Similarly on the age metric, the distance between image pair $(x_{i}^{m},x_{j}^{m})$ is smaller than that between $(x_{i}^{m},x_{j}^{n})$, and the distances are close if the age gap within each image pair is same. Thus we have:

[TABLE]

[TABLE]

where $\Phi_{age}$ measures the age difference between any pair of images.

Quartet Loss To obtain the discussed characteristics of the individual and age metrics, a loss function which maximize the margin between the distances in Eq. 5 and Eq. 7, and meanwhile minimize the margin between the distances in Eq. 6 and Eq. 8 is designed. For convenience, we first define $d$ as the distance of two images embedded in the joint manifold $\mathcal{Y}$: $d_{ij}^{mn}=f(x_{i}^{m})-f(x_{j}^{n})$ and take the Mahalanobis distance as the distance measurement. Thus the $\Phi(\cdot,\cdot)$ can be written as:

[TABLE]

where $\mathbf{M}_{\text{age}}$ and $\mathbf{M}_{\text{ind}}$ are the Mahalanobis matrices. To maximize the margin, the hinge loss function:

[TABLE]

is employed.

Thereby for a quartet sample indexed by $(i,j,m,n)$, the loss $\mathcal{L}_{ij}^{mn}$ can be defined as:

[TABLE]

And the loss over the whole training set is

[TABLE]

Optimization

Considering the loss function $\mathcal{L}$ and the joint manifold as the regularization term, the overall objective function is:

[TABLE]

where $\mathbf{M}\succeq 0$ implies that $\mathbf{M}$ is a semi-definite positive matrix, thus pseudometrics are allowed.

As both the Mahalanobis matrices $\mathbf{M}_{\text{age}}$ and $\mathbf{M}_{\text{ind}}$ as well as the embedding function $f$ need to be learned in Eq. 12, we employ a deep network to optimize them jointly. The architecture of the proposed network is discussed in the following sections.

Deep Network Architecture Our quartet-based network architecture is shown in Figure. 4, which jointly optimizes the manifold embedding function $f$ and the two Mahalanobis matrices. The network takes quartet samples as input. Each quartet sample contains an image set $Q=\{x_{i}^{m},x_{i}^{n},x_{j}^{m},x_{j}^{n}\}$, which are the images of the person $i$ and $j$ at his $m$ and $n$ age stage. The images are firstly passed through a weight-shared convolutional layers, which can extract prolific and robust age and identity information from a facial image while preserving the locality. The deep convolutional network takes the joint manifold cost as the loss function. Subsequently, the distance between the outputs of the deep architecture, for example, $f(x_{i}^{m})$ and $f(x_{i}^{n})$ are measured via two independent metrics, which are namely, age metric and individual metric. With the distances between each image pairs, the quartet loss are thus optimized and the gradients are back-propagated to update the $\mathbf{M}$.

Deep Convolutional Layer In our model, the deep convolution layer is trained to explore the joint manifold of the age and identity. As discussed that the joint manifold is supposed to keep the locality structure, thus the Eq. 2 and Eq. 4 are taken as the joint manifold cost. In the experiment, we first compute the similarity matrix across the whole dataset while for each input batch, only the involved locality constraints need to be satisfied during training, which leads to a great computation saving. As a fact, the linear embedding can already reflect the joint manifold, however we employ the deep learning for a better performance.

Individual Metric and Age Metric Learning At the end of the deep architecture module, the facial images are represented by a $d$-dimensional feature. To measure the distances between each image, we introduce two Mahalanobis matrices $\mathbf{M}_{\text{age}}$ and $\mathbf{M}_{\text{ind}}$. Since Mahalanbis matrices are semi-definite positive, $\mathbf{M}$ can be factorized as $\mathbf{M}=L^{\top}L$. In other words, to learn the individual metric and age metric is equally to learn two projections $L_{\text{ind}}$ and $L_{\text{age}}$ as:

[TABLE]

In our architecture, the two metrics layer are inner product layers with independent weights. The eucledean distance in the projected space is the corresponding Mahalanbis distance. It is not hard to update the matrix $L$ via the loss function Eq. 12 while how to ensure $\mathbf{M}$ being semi-positive is a problem. Inspired by (?), we take a trick when updating on $L$ happens. After $L$ is updated by the network, we check all the eigenvalue of the matrix $L$ and change the most negative eigenvalue to zero and then update $L$ again to make it closer to a semi-positive matrix.

Experiment

As the dual-reference face retrieval is a newly explored task, there are few datasets where each individual’s images have a wide age range. However, we emphasize that the scarcity of suitable datasets does not mean the task is unnecessary. On the contrary, it reflects the fact that using dual reference images to indicate multiple semantic information is reasonable when merged by the huge volume of unlabelled online images.

In the experiment, we evaluate our DRFR on three face recognition and age estimation datasets: Cross-Age Celebrity Dataset(CACD) (?), FGNet (?), and MORPH (?). The statistics of these datasets are shown in Table. 1. As the CACD contains the most images among the three, we trained our deep neural network and conducted our main experiments on the CACD. Apart from that, we evaluated the robustness of our joint manifold model on FGNet and performed the cross-dataset validation on the MORPH.

Experiment on CACD

Settings The Cross-Age Celebrity Dataset is collected for the cross-age face retrieval task in (?), and it contains $163446$ images from $2000$ celebrities with the age ranging from $16$ to $62$. The large-scale data with high age variations provides the DRFR ideal experimental conditions. However, it is noteworthy that although the age ranges from $16$ to $62$, the maximum age gap for each celebrity is 9 years old, as all the collected images are taken from 2003 to 2014. In detail, the age gaps are stepping at 1 year old from $(14-23)$ to $(53-62)$, thus there are 40 age gaps in total. On average, each age gap contains $4000$ images of 50 celebrities. Following the settings in (?), we take $60\%$ data as training data and the remaining for the test. The training data is picked uniformly from each age gap to ensure all the age gaps are covered. For the test data, as there are $8$ different images for each celebrity at each age in average, we further split the test data into $8$ subsets for the following evaluation. To train our deep network on DRFR, the weights of two Mahalanobis matrices were initialized as identity matrices. For the hyper-parameters, we set the $\varepsilon$ in Eq. 11 as $5$ to calculate the similarity matrix set $S$, and the embeddings’ size on the joint manifold is set as $128$. The triplet selection scheme can heavily impact the convergence speed of the network training, so does the quartet samples selection. An effective triplet selection can avoid poor training and reduce the influences caused by the mislabelled data, we employed an online quartet selection protocol which is inspired by (?). During training, the images of an entire mini batch are firstly propagated forward to extract the embeddings with the current model, then those quartets which violate the average margin in this mini batch will be selected to train the network.

Evaluation Metrics and Comparison As DRFR can be regarded as a fine-grained retrieval, we use the top-$K$ retrieval accuracy(?) as the evaluation metric. Since there are no works on this task in the literature before, we combined the existing face retrieval approaches with the age estimation methods to form a hierarchical framework and made the comparison. In the combined hierarchical framework, the face retrieval was first conducted regarding the first reference image as the query. Subsequently, we estimated the age of the second reference image and the top 100 candidate images from the face retrieval session. Finally these 100 images are ranked according to the estimated ages. For the facial representation, we choose eigenfaces, LBP, CARC(?), which encodes the images with a set of celebrities, and the deep learning feature extracted from the FaceNet(?). In the following age estimation, we selected support vector regression (SVR) as well as canonical-correlation analysis (CCA). For the FaceNet feature, we used the same training data as our DRFR’s.

Results We conducted DRFR and the 8 hierarchical methods on the 8 testing subsets and compute the average top-$K$ retrieval accuracy. The results are shown in Table. 2. It shows that when the $K$ is small(less than 6), our proposed DRFR outperformed the other 4 three methods. It is interesting to note that when the allowed output image increases, the accuracy of CARC+CCA is slightly higher than ours. The reason is that CACD is the original dataset which CARC designed, and in our settings, each subset only contains approximately 10 images for each subject, it is reasonable for a high accuracy if the face retrieval system can retrieve all the images of the correct identity.

Experiment on FGNet

Settings FGNet dataset consists of 1002 images of 82 subjects in total. As it is tiny while has high age variations, we conducted experiments using different features on it to evaluate performance of the joint manifold embedding function $f$ of our proposed framework. Similar to the experiment setting on CACD, we split FGNet into training and test set, avoiding the situation that the same subject shows in both sets. The training set contains $60\%$ images while the rest is left for the testing.

Comparison with Linear Embedding Method To evaluate the robustness of our joint manifold embedding, we extracted the embeddings, which is shown as green stripes in Figure. 4, from the model trained in above CACD experiments. And we chose four other feature descriptors, which includes: LBP, BIF, SIFT and HDLBP, to make the comparison. To get the corresponding embeddings of these hand-crafted features, we employed PCA as the embedding technique, whose projection matrix is denoted as $W$. Subsequently, the age and individual metrics $\mathbf{M}_{\text{age}}$ and $\mathbf{M}_{\text{ind}}$ were trained for each embedding based on the quartet loss. And finally the retrieval was conducted on the learned metrics.

Results Figure. 6 shows the results of our experiments on FGNet. It can be seen that the CMC rank score of our joint manifold outperforms others. Since the $\mathbf{M}_{\text{age}}$ and $\mathbf{M}_{\text{ind}}$ are learned with respect to each embedding, we can draw the conclusion that: firstly, the joint manifold embedding function trained on CACD has a robust generalization. Secondly, the proposed joint manifold preserves more information of the age and identity locality.

Cross-Dataset Validation on MORPH

The MORPH dataset has 55134 images of 13618 subjects. Though both the images and subjects are in big amount, the number of images for each subject is only 4.1, which is not sufficient to compromise the quartet samples for training. Thereby instead of training a new model, we conduct a cross-validation on MORPH. We used the model trained on the CACD dataset directly on the MORPH dataset and the results are shown in Table. 3. It is shown that the results are very close to those on CACD. One reason of the minor backward can be the divergence of the age distribution between MORPH and CACD. Another reason is that the images in MORPH are over-cropped and some parts of the forehead and the chin in the image are absence, while the images are all of the full faces in CACD.

Conclusions and Future Work

In this paper, we proposed a dual-reference face retrieval framework, which tackles the problem of retrieving a person’s face image at a ‘given’ age. In the proposed framework, the retrieval is conducted on a joint manifold and based on two similarity metrics. We have systematically evaluated our approach on CACD, FGNet and MORPH, and the corresponding results show that the proposed approach achieves promising results on this new task and the framework is stable and robust.

For the future work, a larger dataset with wider age range can be collected to further improve our algorithm. Also, the dual-reference retrieval framework can be extended to other retrieval tasks besides the face.