1 Introduction
Deep learning models have attracted significant attention thanks to their powerful regression capacity in a spectrum of applications from speech recognition to natural language processing and computer vision. It is recognized that training of deep neural networks requires a large corpus of labeled data to attain generality of the learned models and robustness of the feature maps. Such networks seem less useful for oneshot learning tasks where the objective is to learn a model, often in an online fashion, from a single exemplar (or a few). One exemption is the embedding with Siamese networks [1, 2, 3] since it is not necessary to retrain the deep model for a newly given object or class. Siamese architectures can identify other instances of the target class from its original exemplar using a fixed model.
Conventional Siamese networks use tuples of two labeled instances for training [1, 7, 8, 2, 3]. They are sensitive to calibration and the adopted notion of similarity vs. dissimilarity depending on the given context [9]. The requirement of calibration can be removed by applying triplets for training with a contrastive loss, which favors a small distance between pairs of exemplars labeled as similar, and a large distance for pairs labeled dissimilar [9]. At the same time, using triplets enables utilization of the underlying connections among more than two instances. Our intuition is that more instances (larger tuples) lead to better performance in the learning process. Therefore, we design a new network structure adding as many instances into a tuple as possible (including a triplet and multiple pairs) and connect them with a novel loss combining a pairloss and a triplet based contractiveloss. Existing Siamese [3] or triplet networks [9] do not use the full potential of the training instances since they take randomly sampled pairs or triplets to construct the training batches. In contrast, our framework aims to select the triplets that would lead to a powerful representation for a stronger deep network.
In this paper, we introduce a novel quadruplet network for oneshot learning. Our quadruplet network is a discriminative model to oneshot learning. Given a single exemplar of a new object class, its learned model can recognize objects of the same class. To capture the underlying relationships of data samples, we design four branch networks with shared weights for different inputs such as instances, exemplar, positive and negative branches. We randomly sample a set of positive and negative instances as inputs of instances branch. A pair of loss function is designed to connect the exemplar and instances branch to utilize the underlying relationships of pairs. To achieve the triplet of representation, we select the positive instance that is most similar to the exemplar and the negative instance that is most dissimilar as the inputs of positive and negative branches, respectively. Then, we use a contractive loss function to measure the similarity of this triplet. Finally, the weighted average of the pair loss and the contractive loss is assigned as the final loss.
The triplet loss is the key to utilize the underlying connections among instances to achieve improved performance. To combine it and pair loss, a simple solution is to apply a weighted average with prior weights between these two losses. However, directly applying prior weights maybe not improve even reduce performance. For example, we test our approach with prior weights for visual object tracking on OTB2013 benchmark [4] while the distance precision is reduced from 0.809 to 0.800. Thus, we propose a weight layer to automatically choose suitable combination weights during training to solve this problem. We evaluate the quadruplet network with oneshot learning for visual object tracking. SiamFc3s [3] is our baseline tracker. We apply our quadruplet network instead of its Siamese network to train the shared net and adapt the same mechanism for online tracking. As shown in Fig. 1, our training method achieves better tracking accuracy, which demonstrates the more powerful representation of our framework. In several popular tracking benchmarks, our experimental results show that the tracker runs at high realtime speed (78 framespersecond on OTB2013) and achieves excellent results compared with recent stateoftheart realtime trackers.
The main contributions of this work are summarized as:

We propose a novel quadruplet network for oneshot learning that utilizes the inherent connections among multiple instances and apply it to visual tracking. To the best of our knowledge, we are the first to introduce quadruplet network into single object tracking.

A weight layer is proposed for selecting suitable combination weights between triplet and pair loss. It may take a lot of time to manually choose appropriate combination weights while our weight layer is able to automatically adjust these weights during each training iteration to achieve powerful features.

By applying the proposed quadruplet network on training to get more representable features, our detectionbytracking method can achieve stateoftheart results even without online updating during tracking. Furthermore, our tracker runs beyond realtime with high speed of 78 fps.
2 Related Work
Our work is related to a wide array of literature, in particular, oneshot learning with generative models, learning an embedding space for oneshot learning, and visual object tracking.
Many previous studies focus on the context of the generative models for oneshot learning, which is different from our formulation of the problem as a discriminative task. One early approach [10] uses probabilistic generative models to present object categories and applies a variational Bayesian framework for learning useful information from a handful of training samples. In [11]
, a recurrent spatial attention generative model is proposed to generate images using a variational Bayesian inference. Having seen samples once, this method generates a set of diverse samples.
The most common discriminative approach to oneshot learning is embedding learning, where the goal is to learn an embedding space and then perform classification by applying a simple rule in the embedding space such as finding the nearestneighbor of an exemplar of a novel category. Learning embeddings of objects is to represent each object as a lowdimensional vector. It is essential in unsupervised learning and in data preprocessing of supervised learning. A typical model for embedding learning is Siamese networks
[1]. Recently, several techniques [2, 3, 9] are presented to improve the embedding performance. In [2] a learningtolearn approach is proposed to determine the shared weights of Siamese network. It applies a number of factorizations of the parameters to make the construction feasible. In [3], a fully convolutional Siamese network is designed for visual object tracking. As an alternative to using pairs in Siamese network, [9] employs triplets for training by distance comparisons. In comparison, our method combines the pairs and triplets for training to take the advantage of the underlying useful connections (e.g. the manifold structure) among samples.The task of visual object tracking can be viewed as an application of oneshot learning [2]. We only provide a brief introduction of recent object tracking methods such as correlation filter based trackers and deep neural networks based solutions. After Kernelized Correlation Filters [12] had reported stateoftheart performance at hundreds of framepersecond speed, more investigation focused on correlation filters [13, 14, 15, 16, 5, 17, 18, 19, 20, 21]. The tracking performance improved consistently, and DSST [13] and CCOT [17] obtained the top ranks at the VOT 2014 [22] and the VOT 2016 challenges [23], respectively. However, the speed became lower and lower, i.e. the speed of CCOT is only 1 fps. The computational load remains as the same problem in deep neural networks for tracking. The online learning network [24] provided superior tracking performance, albeit its prohibitive load (near 1 fps on GPU) limits its practicality. To accelerate deep network for tracking, some studies proposed offline training of models, such as DeepTrack [25], GOTURN [26] and SiamFc3s [3], and directly applied them for online tracking to avoid the cost of online retraining. All of these achieve a speed of more than realtime (30 fps) with a comparable performance. Our work is similar to SiamFc3s, while we focus on improving offline training phase to obtain more robust feature representation. Thus, our method runs at a comparable speed with SiamFc3s yet achieves better performance.
3 Siamese Networks for Tracking
Here, we briefly review recent work on Siamese networks for object tracking [3]. When applying oneshot learning scheme for visual tracking, the object patch in the first frame is used as an exemplar, and the patches in the search regions within the consecutive frames are employed as the candidate instances. The aim is to find the most similar instance from each frame in an embedding space, where the object is represented as a lowdimensional vector. Learning an embedding function with a powerful and discriminative representation is a critical step in this task.
To this end, Bertinetto et al. [3] apply a deep learning method to learn the embedding function and design a fully convolution Siamese network to reduce computation for realtime speed. This network includes two network branches processing different inputs. One is the exemplar branch used to receive the object bounding box in the first frame. The other is the instances branch applied to process the patches in searching regions of the following frames. These two network branches share the parameters; thus they can be seen as an identical transformation for different inputs. Accordingly, the similar function for an exemplar and an instance is defined as , where is a simple similarity metric such as vectorial angle and crosscorrelation. In [3], they use the crosscorrelation for , and the formulation of function is transferred as follows:
(1) 
using the convolution operator. Then, a logistical loss is applied to the pairwise loss function, which is formulated as follows:
(2) 
where is the set of inputs for instances branch, is the groundtruth label of a single exemplarinstance pair , is the similarity score of i.e. .
4 Quadruplet Network
A quadruplet network (inspired by Siamese networks [1, 3] and triplet networks [9]) contains four branches of the same network with shared parameters, while building a direct connection between them through a common loss function. Our proposed quadruplet network structure is shown in Fig. 2.
4.1 Network branches
These four network branches are respectively named as exemplar, instances, positive, and negative branches according to their inputs. We first introduce the input of exemplar branch since other inputs are depended on it. An instance is randomly chosen as an exemplar . Then the instances with the same class are denoted as positive instances and the others are denoted as negative instances. The inputs of instances branches (denoted as a set ) consist of some positive instances and negative instances, which are used for two aspects.
Firstly, these instances are used to learn an function of similarity metric that compares an exemplar to an instance and returns a high score with a positive instance and a low score with a negative instance. Secondly, according to these scores, we select the instance with lowest score from positive instances as the input of positive branch and select the one with highest score from negative instances as the input of negative branch . and have the strongest representation among the inputs of instances branch, since they are on the boundaries of classification in current small sample space (defined on the set ). If we decrease the distance between and , and increase it between and , the corresponding positive boundary will be closer to and negative one will keep away from . In other words, the margin between boundaries of classification will be increased and it will reduce the error of classification. To achieve this purpose, we design a new loss function for these three branches. More details are shown in the next subsection.
4.2 Loss function
The loss function of a quadruplet network consists of two kinds of loss function. The first one is constructed between the outputs of exemplar branch and instances branch, and the second one connects positive, negative and exemplar branches. To give the definition of these two loss functions, we first simplify the notation of branches. In fact, these 4 branches are an identical transformation to different inputs. Thus, we denote them as a transformation function . Then the function is transfered as , where is a simple similarity metric such as vectorial angle and cross correlation. In this paper, we use the cross correlation for as the same as Siamese network [3]. And the formulation of function is defined as the same as the function in Eq. (1).
Then, we apply a weighted averaged logistical loss to the first pairwise loss function, which is formulated as follows:
(3) 
where is the set of inputs for instances branch, is the groundtruth label of a single exemplarinstance pair , is the similarity score of i.e. , is the weight for an instance , and . is a dynamic weight that is changed during the training process. Different to general training method for deep learning, we first do forward computation once to get the similarity score of each exemplar instance. If the similarity score of a negative instance is larger than the minimum score of positive instances, it will violate the assumption of similarity, i.e. the score of the positive instance should be larger than the negative instance. Thus, we amplify the penalty for this situation by increasing the corresponding weights. In this work, we set for the cases violating the assumption, and then normalize the weights by dividing their summation. These adapted weights are applied for forward computation and backward computation to finish a training process.
Inspired by the triplet network [9], the second loss function is constructed by a mean square error on the softmax results of similarity scores between different branches. Comparing softmax results to vector, we can get the triplet loss function:
(4) 
where
(5) 
and
(6) 
The final loss function is the weighted sum of these two loss functions:
(7) 
where are the weights to balance the loss and . They are not prior constants but learned during training. The parameters of branch network and the weights of loss
are obtained by applying Stochastic Gradient Descent (SGD) to the problem:
(8) 
For our neural networks, we propose three new layers using , and losses. The backward computation of loss is similar to the logistic loss since the weights are fixed during backward computing. We only need to add the weights into the derivatives of logistical loss. The other two are not similar to the common loss. Thus, we give the gradients of these two losses for backward computation. loss layer can be decomposed as a square error layer (Eq. 4) and a softmax layer (Eq. 5, 6). We get the derivatives of the square error as:
(9) 
To avoid big gradients in the softmax layer, we reformulate Eq. 5 as follows:
(10) 
Similarly, the reformulation of Eq. 6 becomes
(11) 
Where and are similarity scores and , is the maximal between and i.e. . Then we can get Jacobian matrix :
(12) 
According to the chain rule, we can get the partial derivatives as follows:
(13) 
The loss layer contains two inputs ( and ) and two parameters ( and ), which partial derivatives are formulated as:
(14) 
where and . In practice, we set a small threshold , such as 0.01, for to insure by imposing .
4.3 Framework of our tracker
We apply the proposed Quadruplet network on an oneshot learning problem in visual object tracking. Given an object of interest on the first video frame, the task of single object tracking is to find the object on the following frames. In the opinion of oneshot learning, a subwindow enclosing the object is seen as an exemplar and the subwindows of each frame are viewed as a candidate of instances. The goal is to find the most similar one with exemplar in each frame. Our tracking method consists of offline training and online testing stages using different network structures.
In offline training, we use quadruplet network to achieve powerful embedding representation. The architecture of shared convolutional network is the same as SiamFc3s [3], which is a variation of the network of Krizhevsky et al. [27].
As shown in Fig. 3, we simplify the quadruplet network by selecting powerful feature patches at the last convolutional layer of instances branch instead of positive and negative branch. Pairs of an exemplar image and a larger search image are applied to inputs of exemplar and instances branch, where each subwindow of the same size with the exemplar image is an candidate instance. The scores in equation (3) will become a score map as shown in Fig. 3. It’s label map is designed according the location i.e. we set positive label to points in the central area within radius ( in our experiments), which is denoted as positive area , and ones in other area (negative area ) are set as . Before each iteration training, we first precompute the score map, and respectively select the instance in the center and the one with highest score in negative area as the powerful positive and negative instance. Their last convolutional features are set as the inputs of triplet loss. Otherwise, the precomputed score map is also used to construct the weighted pair loss. The initial weights are defined as balance weights to balancing the number of positive and negative instances. The formulation is defined as:
(15) 
If a negative score is more than the minimal of positive scores, we increase the weight as and then normalize all weights as . After precomputation, we do forward and backward computation to finish a training iteration.
In online testing (tracking) phase, only the exemplar branch and the instances branch are used. We crop an exemplar image in the first frame and also larger search images (search region) in the consecutive frames. The search images center on the location of the object in the previous frames. The exemplar and the search images are resized to and , respectively. Using these inputs, our tracking network calculates a score map as shown in Fig. 4
. Then, the score map is upsampled by bicubic interpolation from
to to achieve a higher location accuracy. The location of the object is determined by the maximum score in the upsampled map.5 Experimental Results
5.1 Implementation details
Training. We use MatConvNet [28] to train the parameters of the shared network and the weights of loss by minimizing Eq. (8) with SGD. The initial values of the shared network are copied from the trained model in SiamFc3s [3] and the weights are set as . We use the same training and validation sets with [3]
. They are randomly sampled from the ‘new object detection from video challenge’ in the 2015 edition of the ImageNet Large Scale Visual Recognition Challenge [10] (ILSVRC). The dataset contains almost 4500 videos with 30 different classes of animals and vehicles. Training is performed over 10 epochs, each consisting of 53,200 sampled pairs. We randomly select
pairs as the validation set at each epoch, and the final network used for testing is determined by the minimal mean error of distance (presented in [3]) on the validation set. The gradients for each iteration are estimated using minibatches of size 8, and the learning rate is decayed geometrically after epoch from
to . To handle the gray videos in benchmarks, of the pairs are converted to grayscale during training.Tracking. As mentioned before, only the initial object is selected as the exemplar image. Thus, we compute the embedding feature once and compare it with the searching images of the subsequent frames. To handle scale variations, three scales are searched for the object, and the scale is updated by linear interpolation with a factor of 0.59 to avoid huge variation of scale. Our Intel Core i76700 at 3.4 GHz machine is equipped with a single NVIDIA GeForce 1080, and our online tracking method runs at 78 framespersecond.
5.2 Benchmarks and evaluation metric
We evaluate our tracking method, which we call as ‘Quad’ with the recent stateoftheart trackers in popular benchmarks including OTB2013 [4], OTB50, OTB100 [29], and VOT2015 [30].
The OTB2013 benchmark contains 50 challenging sequences and uses different metrics to evaluate tracking methods. The authors expand the OTB2013 to OTB100 including 100 sequences and select 50 more challenging sequences denoted OTB50 as a small benchmark. In this paper, we use the overlap success rate and distance precision metrics [4] to evaluate trackers on OTB2013, OTB50, and OTB100. Overlap success rate measures the intersectionoverunion (IoU) of groundtruth and predicted bounding boxes. The success plot shows the rate of bounding boxes whose IoU score is larger than a given threshold. We apply the overlap success rate in terms of threshold 0.5 to rank the trackers. The precision metric means the percentage of frame locations within a certain threshold distance from those of the ground truth. The threshold distance is set as 20 for all trackers. The VOT2015 benchmark is a challenging dataset to evaluate the shortterm tracking performance since in VOT2015, a tracker is restarted in the case of a failure, where there is no overlap between the predicted bounding box and ground truth. It contains 60 sequences collected from some previous tracking benchmarks (356 sequences in total). For this dataset, we evaluated tracking performance in terms of accuracy (overlap with the groundtruth), robustness (failure rate), and Expected Average Overlap (EAO which is principled combination of accuracy and robustness) [30].
5.3 Ablation study
To evaluate the effect of different components in our method, we compare the tracker SiamFc3s [3] against different variants of our tracker: SiamInit, SiamAt, QuadC, and Quad. SiamFc3s3s can be seen as the baseline of our method. Since our online tracking method is the same with it. The difference is the training model. SiamInit is the variant of SiamFc3s, which is initialized with the final network parameters in SiamFc3s and trained again over 10 epochs. SiamAt is also a Siamese network but trained with the proposed adapt weighted pairs loss. QuadC is the version that combines the weighted pairs loss and the triplet loss with constant weights , and Quad is the final version with the learned weights.
We evaluate these trackers with onepass evaluation (OPE) while running them throughout a test sequence with an initialization from the groundtruth position in the first frame. As shown in Fig. 5, directly training more epochs (SiamInit) will improve precision but reduce overlap success rate compared with the baseline SiamFc3s. This indicates that representation power of the original network was close to its limit. More training may not improve more performance. Thus, we seek for an alternative solution for improvement. Firstly, we try an adapt weighted pairs loss and achieve slightly overall improvement with increasing overlap while slightly reducing precision compared with SiamInit. Secondly, we want to add triplet loss to mine the potential relationships among samples further. However, directly adding triplet loss into a Siamese net with prior weights may reduce the performance (see QuadC in Fig. 5) since the prior weights may not be optimal for the combination of triplet loss and pair loss. To solve this problem, we design a weight layer to choose suitable combination weights during training and achieve better precision and overlap success rate as shown with Quad in Fig. 5.
5.4 Results on OTB2013 benchmark
On OTB2013 benchmark, we compare our Quad tracker against several stateoftheart trackers that can operate in realtime: CFnetconv2 [6], SiamFc3s [3], Staple [5], CN [13], and KCF [12]. For reference, we also compare with recent trackers: DSST [13], MEEM [31], SAMF [32], DLSSVM [33].
Overall comparison. A conventional way to evaluate trackers is onepass evaluation (OPE). However, some trackers are sensitive to the initialization errors. To measure the performance with different initializations, we use spatial robustness evaluation (SRE) and temporal robustness evaluation (TRE). SRE uses different bounding boxes in first frame and TRE starts at different frames for initialization. As shown in Fig. 6
, our method outperforms over recent stateoftheart realtime trackers in terms of the overlap success rate and precision for OPE, SRE, and TRE, respectively. Compared with our baseline SiamFc3s, the results demonstrate that our training method is able to generate more robust and powerful features for tracking. Among all trackers, our tracker outperforms in five evaluation metric except the precision for TRE. In this metric, our method achieves the 4th rank (0.828), which is in fact very close to the 3rd SANF (0.828) and the 2nd MEEM (0.829). SAMF ranks 1st in precision while it ranks 6th in success for TRE.
5.5 Results on OTB50 and OTB100
On OTB50 and OTB100 benchmarks, we also compare the recent trackers mentioned on OTB2013 comparison.
Attributebased Performance Analysis. In OTB100 benchmark, the sequences are annotated with 11 attributes for different challenging scenarios including Illumination Variation (IV), Scale Variation (SV), Occlusion (OCC), Deformation (DEF), Motion Blur (MB), Fast Motion (FM), InPlane Rotation (IPR), OutofPlane Rotation (OPR), OutofView (OV), Background Clutters (BC), and Low Resolution (LR).
We evaluate our method on these different attributes as shown in Fig. 7
where the overlap success rates of OPE for overlap threshold is set to 0.5. As visible, our method outperforms all other trackers in 8 categories: SV, OCC, LR, MB, FM, IPR, OPR, and OV, especially in LR and IPR. In 3 categories, Staple performs the best while our approach ranks the third best. Staple tracker is based on the correlation filter and applies Fourier transform. We believe, integrating Fourier transform into our method will further improve the performance our method. Compared to the baseline SiamFc3s, our tracker has superior performance in all categories except DEF. The reason might be that the triplet loss has to be customized to handle this situation.
Overall comparison. Both precision and success metrics are reported for OPE. Fig. 8 shows that our tracker also achieve improvement compared with our baseline SiamFc3s in these two benchmarks in terms of precision and success metrics. In success metric, our method performs better than all trackers on these two benchmarks. In precision metric, our tracker achieves second best performance on OTB50 following the first one MEEM with slight reducing from 0.7122 to 0.7117 while we get significant improvement from 0.542 to 0.660. Similarly, on OTB100, our tracker ranks second (0.782) slightly lower than the first one Staple (0.784) in precision while increases the success rate from 0.710 to 0.739.
Quad(ours)  SiamFc3s  BDF  NCC  FOT  ASMS  FCT  matFlow  SKCF  PKLTF  sumShift  

EAO  0.261  0.248  0.153  0.080  0.139  0.212  0.151  0.150  0.162  0.152  0.234 
Acc.  0.553  0.550  0.401  0.500  0.432  0.507  0.431  0.420  0.485  0.453  0.517 
Rob.  1.791  1.818  3.106  11.345  4.360  1.846  3.338  3.121  2.681  2.721  1.682 
FPS  78  78  175*  135*  126*  101*  73*  71*  58*  26*  15* 
5.6 Results on VOT2015
In our evaluations, we use the Visual Object Tracking 2015 (VOT2015) toolkit, which contains the evaluation in shortterm visual object tacking tasks.
Fast speed: We compare our tracker with SiamFc3s [3] and 9 top participants in the VOT2015 including BDF [34], FOT [35], ASMS [36], NCC, FCT, matFlow, SKCF, PKLTF [30], and sumShift [37]. Table 1 shows that our tracker achieves the best Expected Average Overlap (EAO) and the highest accuracy among the most accurate trackers with speed more than 15 fps. Among the fast trackers, the highest robustness (1.682) belongs to sumShift followed by ours Quad (1.791). Our tracker significantly improves the accuracy and robustness of most participants with top speed in VOT2015 (BDF, FOT, ASMS, NCC, FCT, matFlow, SKCF, PKLTF) and SiamFc3s. For reference, the comparisons of other trackers are provided in supplementary material.
6 Conclusion
We demonstrated that the proposed quadruplet network using multituples for training allows accurate mining of the potential connections among instances and achieves more robust representations for oneshot learning. We showed that by automatically adjusting the combinational weights between triplet and pair loss, we improve the training performance. We analyzed the feasibility of our quadruplet network in visual object tracking. Our results indicate that our tracking method outperforms others while maintaining beyond realtime speed. As future work, we employ different loss functions and extend the quadruplet networks to other computer vision tasks.
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