Exploiting the Anisotropy of Correlation Filter Learning for Visual Tracking


Correlation filtering based tracking model has received significant attention and achieved great success in terms of both tracking accuracy and computational complexity. However, due to the limitation of the loss function, current correlation filtering paradigm could not reliably respond to the abrupt appearance changes of the target object. This study focuses on improving the robustness of the correlation filter learning. An anisotropy of the filter response is observed and analyzed for the correlation filtering based tracking model, through which the overfitting issue of previous methods is alleviated. Three sparsity related loss functions are proposed to exploit the anisotropy, leading to three implementations of visual trackers, correspondingly resulting in improved overall tracking performance. A large number of experiments are conducted and these experimental results demonstrate that the proposed approach greatly improves the robustness of the learned correlation filter. The proposed trackers performs comparably against state-of-the-art tracking methods on four latest standard tracking benchmark datasets.

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  1. 1.

    The Gaussian shaped response is not necessarily isotropic because the covariance matrix determines the shape of a Gaussian. It is isotropic only if the covariance matrix is diagonal and all the diagonal elements have equal values. In previous methods, only the isotropic Gaussian response is employed since it is considered as the continuous version of an impulse signal in the image space. For the sake of simplicity, the Gaussian shaped response refers to the isotropic Gaussian case in this work hereafter.

  2. 2.

    The exact equivalence between regression and correlation filtering under the circulant structure assumption is proved in Henriques et al. (2015).

  3. 3.

    The rows of the kernel matrix \({\mathbf {K}}\) are actually obtained from the fully cyclic shifts of the vector \({\mathbf {k}}_1\).


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Correspondence to Yao Sui.

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This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grants 61132007 and 61573351, in part by the Kansas NASA EPSCoR Program under Grant KNEP-PDG-10-2017-KU, and in part by the joint fund of Civil Aviation Research by the National Natural Science Foundation of China (NSFC) and Civil Aviation Administration under Grant U1533132.

Communicated by Xiaoou Tang.

Appendix: Baseline Trackers

Appendix: Baseline Trackers

Extensive visual trackers are employed in the experimental evaluations as the baseline trackers. In this appendix section, we present the citations of these baseline trackers.

Baseline Trackers on the OTB 2015 Benchmark

PSCF (Sui et al. 2018b), RCF (Sui et al. 2016b), KCF_AT (Bibi et al. 2016), SRDCF (Danelljan et al. 2015), HCFT (Ma et al. 2015a), SAMF (Li and Zhu 2014), DSST (Danelljan et al. 2014a), KCF (Henriques et al. 2015), CN (Danelljan et al. 2014b), and CSK (Henriques et al. 2012).

Baseline Trackers on the VOT 2015 Benchmark

MDNet (Nam and Han 2016b), DeepSRDCF (Danelljan et al. 2015), EBT (Zhu et al. 2016), SRDCF(Danelljan et al. 2015), LDP (Lukezic et al. 2015), sPST (Hua et al. 2015), SC-EBT (Wang et al. 2015b), NSAMF (Li and Zhu 2015), Struck (Hare et al. 2011), RAJSSC (Zhang et al. 2015a), S3Tracker (Lee et al. 2015), SumShift (Lee and Yu 2011), SODLT (Wang et al. 2015c), DAT (Possegger et al. 2015), MEEM (Zhang et al. 2014a), RobStruck (Bogun and Ribeiro 2015), OACF (Bertinetto et al. 2015), MCT (Duffner and Garcia 2015), HMMTxD (Vojir et al. 2015), ASMS (Vojir et al. 2014).

Baseline Trackers on the VOT 2016 Benchmark

C-COT (Danelljan et al. 2016), TCNN (Nam and Han 2016a), SSAT (Qi et al. 2016a), MLDF (Wang et al. 2016a), Staple (Bertinetto et al. 2016b), DDC (Gao et al. 2016), EBT (Zhu et al. 2016), SRBT (Lee and Kim 2016), STAPLE+ (Xu et al. 2016), DNT (Chi et al. 2016), SSKCF (Lee et al. 2016), SiamFC-R (Bertinetto et al. 2016a), DeepSRDCF (Danelljan et al. 2015), SHCT (Wen et al. 2016), MDNet-N (Nam and Han 2016b), FCF (Zhang et al. 2016), SRDCF (Danelljan et al. 2015), RFD-CF2 (Walsh and Mederios 2016), GGTv2 (Hu et al. 2016), DPT (Lukezic et al. 2016).

Baseline Trackers on the VOT 2017 Benchmark

LSART (Sun et al. 2017), CFWCR (He et al. 2017), CFCF (Gundogdu and Alatan 2017), ECO (Danelljan et al. 2017b), Gnet (Singh and Mishra 2017), MCCT (Wang et al. 2017a), CCOT (Danelljan et al. 2016), CSRDCF (Lukezic et al. 2017a), SiamDCF (Wang et al. 2017b), MCPF (Zhang et al. 2017b), CRT (Chen and Tao 2016), ECOhc (Danelljan et al. 2017a), DLST (Yang et al. 2017), CSRDCFf (Lukezic et al. 2017b), RCPF (Zhang et al. 2017a), UCT (Zhu et al. 2017), SPCT (Poostchi et al. 2017), ATLAS (Mocanu et al. 2017), MEEM (Zhang et al. 2014a), FSTC (Chen et al. 2017).

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Sui, Y., Zhang, Z., Wang, G. et al. Exploiting the Anisotropy of Correlation Filter Learning for Visual Tracking. Int J Comput Vis 127, 1084–1105 (2019). https://doi.org/10.1007/s11263-019-01156-6

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  • Object tracking
  • Anisotropy
  • Correlation filtering
  • Loss function
  • Sparsity
  • Robustness
  • Sensitivity