## 3 The CFSA Tracker
### Generating Candidate Proposals with Modified EdgeBoxes  
To improve the computational efficiency of object detection, several proposal generators were proposed recently, such as BING [37] and EdgeBoxes [26]. Compared with other existing proposal generators, EdgeBoxes has the advantages of high computational efficiency, high quality of proposals, and flexible parameter setting without training. All these advantages make it the most suitable proposal generator in a tracking algorithm. However, most of the generated proposals with high scores are large images or nearly the whole image. We modify the scoring metric of the EdgeBoxes generator, in which the closer the scale of the generated candidate object proposals to the tracked object, the higher the score. Given an image patch \(I\), the generation of object proposals for tracking using the modified EdgeBoxes generator mainly includes five steps, namely, getting edges and edge groups, computing affinities of edge groups, computing weights of edge groups, computing scores of bounding boxes, and refining and ranking all bounding boxes. The detailed descriptions are as follows. For each pixel in an image, EdgeBoxes initially compute an edge response with the structured edge detector [41] that has shown good performance and efficiency in predicting object boundaries. Then, edge groups are formed by combining 8 connected edges until the sum of their orientation differences is above a threshold (\(\pi/2\)). Small edge groups are merged with neighboring groups. Given a set of edge groups \(g_{i}\in G\), the affinity of a pair of groups \(g_{i}\) and \(g_{j}\) is computed using:  
\[\alpha\big{(}g_{i},\ g_{j}\big{)}=\ \big{|}cos\big{(}\theta_{i}-\theta_{ij} \big{)}cos\big{(}\theta_{j}-\theta_{ij}\big{)}\big{|}^{\lambda} \tag{1}\]  
where \(\theta_{i}\) and \(\theta_{i}\) are mean orientations of edge group \(g_{i}\) and \(g_{j}\), respectively, \(\theta_{ij}\) is the angle between the mean position \(x_{i}\) of group \(g_{i}\) and the mean position \(x_{j}\) of group \(g_{j}\). The value of \(\lambda\) may be used to adjust the affinity's sensitivity to changes in orientation, with \(\lambda=2\) used in the literature. The object proposal score of a candidate bounding box \(b\) can be calculated according to the set of edge groups \(G\) and their affinities. In this paper, we propose to calculate the bounding box score \(h_{b}\) by combining the scale of target object to be tracked:  
\[h_{b}=\frac{\sum_{i}w_{b}(g_{i})m_{i}-\sum_{p\in b^{in}}m_{p}}{2(b_{w}+b_{h}) ^{\kappa}}\exp\left(-\frac{\big{(}\mathcal{S}-\sqrt{b_{w}b_{h}}\big{)}^{2}}{2 \phi^{2}}\right) \tag{2}\]  
where each \(i\) corresponds to a pixel within the bounding box \(b\), \(m_{i}\) denotes the sum of the magnitudes for all edges in the group \(g_{i}\), and \(m_{p}\) is the magnitude of edges \(p\). \(b^{in}\) denotes the central part of \(b\), whose size is \(b_{w}/2\times b_{h}/2\), while \(b_{w}\) and \(b_{h}\) are the width and height of \(b\), respectively. \(\kappa\) is used to offset the bias of larger windows having more edges on average. \(\mathcal{S}\) is the arithmetic square root of the scale of the target object, which is used to offset the bias of large scale variations. For an image sequence, the above-mentioned target object is either the ground truth in the initial frame or the estimated target object in previous frame. The value of \(\phi\) is used to control the speed at which the score decays with the  
Figure 1: Illustration of the proposed Correlation Filters based Scale Adaptive tracking method. scale of target object to be tracked. \(w_{b}(g_{i})\) is a continuous value in \([0,1]\) that indicates whether \(g_{i}\) is wholly contained in the bounding box \(b\), which can be defined as:  
\[w_{b}(g_{i})=1-\max_{T}\prod_{j=1}^{|T|-1}\alpha\big{(}t_{j},\ t_{j+1}\big{)} \tag{3}\]  
where \(T\) is an ordered path of edge groups with a length of \(|T|\) that begins with some \(t_{1}\in G_{b}\) and ends at \(t_{|T|}=g_{i}\).