Abstract
Discriminative correlation filters (DCF) are efficient in visual tracking and have advanced the field significantly. However, the symmetry of correlation (or convolution) operator results in computational problems and does harm to the generalized translation equivariance. The former problem has been approached in many ways, whereas the latter one has not been well recognized. In this paper, we analyze the problems with the symmetry of circular convolution and propose an asymmetric one, which as a generalization of the former has a weak generalized translation equivariance property. With this operator, we propose a tracker called the asymmetric discriminative correlation filter (ADCF), which is more sensitive to translations of targets. Its asymmetry allows the filter and the samples to have different sizes. This flexibility makes the computational complexity of ADCF more controllable in the sense that the number of filter parameters will not grow with the sample size. Moreover, the normal matrix of ADCF is a block matrix with each block being a two-level block Toeplitz matrix. With this well-structured normal matrix, we design an algorithm for multiplying an N × N two-level block Toeplitz matrix by a vector with time complexity O(NlogN) and space complexity O(N), instead of O(N2). Unlike DCF-based trackers, introducing spatial or temporal regularization does not increase the essential computational complexity of ADCF. Comparative experiments are performed on a synthetic dataset and four benchmarks, including OTB-2013, OTB-2015, VOT-2016, and Temple-Color, and the results show that our method achieves state-of-the-art visual tracking performance.
Similar content being viewed by others
References
Bertinetto L, Valmadre J, Golodetz S, et al., 2016. Staple: complementary learners for real-time tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.1401–1409. https://doi.org/10.1109/CVPR.2016.156
Bolme DS, Beveridge JR, Draper BA, et al., 2010. Visual object tracking using adaptive correlation filters. Proc IEEE Computer Society Conf on Computer Vision and Pattern Recognition, p.2544–2550. https://doi.org/10.1109/CVPR.2010.5539960
Chen BY, Wang D, Li PX, et al., 2018. Real-time ‘actor-critic’ tracking. Proc 15th European Conf on Computer Vision, p.318–334. https://doi.org/10.1007/978-3-030-01234-2_20
Choi J, Chang HJ, Yun S, et al., 2017. Attentional correlation filter network for adaptive visual tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.4828–4837. https://doi.org/10.1109/CVPR.2017.513
Dalal N, Triggs B, 2005. Histograms of oriented gradients for human detection. Proc IEEE Computer Society Conf on Computer Vision and Pattern Recognition, p.886–893. https://doi.org/10.1109/CVPR.2005.177
Danelljan M, Khan FS, Felsberg M, et al., 2014. Adaptive color attributes for real-time visual tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.1090–1097. https://doi.org/10.1109/CVPR.2014.143
Danelljan M, Häger G, Khan FS, et al., 2015. Learning spatially regularized correlation filters for visual tracking. Proc IEEE Int Conf on Computer Vision, p.4310–4318. https://doi.org/10.1109/ICCV.2015.490
Danelljan M, Häger G, Khan FS, et al., 2016a. Adaptive decontamination of the training set: a unified formulation for discriminative visual tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.1430–1438. https://doi.org/10.1109/CVPR.2016.159
Danelljan M, Robinson A, Khan FS, et al., 2016b. Beyond correlation filters: learning continuous convolution operators for visual tracking. Proc 14th European Conf on Computer Vision, p.472–488. https://doi.org/10.1007/978-3-319-46454-1_29
Danelljan M, Häger G, Khan FS, et al., 2017a. Discriminative scale space tracking. IEEE Trans Patt Anal Mach Intell, 39(8):1561–1575. https://doi.org/10.1109/TPAMI.2016.2609928
Danelljan M, Bhat G, Khan FS, et al., 2017b. ECO: efficient convolution operators for tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.6638–6646. https://doi.org/10.1109/CVPR.2017.733
Dong XP, Shen JB, 2018. Triplet loss in Siamese network for object tracking. Proc 15th European Conf on Computer Vision, p.459–474. https://doi.org/10.1007/978-3-030-01261-8_28
Galoogahi HK, Sim T, Lucey S, 2013. Multi-channel correlation filters. Proc IEEE Int Conf on Computer Vision, p.3072–3079. https://doi.org/10.1109/ICCV.2013.381
Galoogahi HK, Fagg A, Lucey S, 2017. Learning background-aware correlation filters for visual tracking. Proc IEEE Int Conf on Computer Vision, p.1135–1143. https://doi.org/10.1109/ICCV.2017.129
Henriques JF, Caseiro R, Martins P, et al., 2015. High-speed tracking with kernelized correlation filters. IEEE Trans Patt Anal Mach Intell, 37(3):583–596. https://doi.org/10.1109/TPAMI.2014.2345390
Kart U, Lukezic A, Kristan M, et al., 2019. Object tracking by reconstruction with view-specific discriminative correlation filters. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.1339–1348. https://doi.org/10.1109/CVPR.2019.00143
Kristan M, Leonardis A, Matas J, et al., 2016. The visual object tracking VOT2016 challenge results. Proc Amsterdam on Computer Vision, p.191–217. https://doi.org/10.1007/978-3-319-48881-3_54
Lee D, 1986. Fast multiplication of a recursive block Toeplitz matrix by a vector and its application. J Complex, 2(4):295–305. https://doi.org/10.1016/0885-064x(86)90007-5
Li B, Yan JJ, Wu W, et al., 2018. High performance visual tracking with Siamese region proposal network. Proc IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.8971–8980. https://doi.org/10.1109/CVPR.2018.00935
Li F, Tian C, Zuo WM, et al., 2018. Learning spatial-temporal regularized correlation filters for visual tracking. Proc IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.4904–4913. https://doi.org/10.1109/CVPR.2018.00515
Li Y, Zhu JK, 2014. A scale adaptive kernel correlation filter tracker with feature integration. Proc European Conf on Computer Vision, p.254–265. https://doi.org/10.1007/978-3-319-16181-5_18
Liang PP, Blasch E, Ling HB, 2015. Encoding color information for visual tracking: algorithms and benchmark. IEEE Trans Image Process, 24(12):5630–5644. https://doi.org/10.1109/TIP.2015.2482905
Lukezic A, Vojí T, Zajc LC, et al., 2017. Discriminative correlation filter with channel and spatial reliability. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.4847–4856. https://doi.org/10.1109/CVPR.2017.515
Ma C, Huang JB, Yang XK, et al., 2015. Hierarchical convolutional features for visual tracking. Proc IEEE Int Conf on Computer Vision, p.3074–3082. https://doi.org/10.1109/ICCV.2015.352
Mueller M, Smith N, Ghanem B, 2017. Context-aware correlation filter tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.1387–1395. https://doi.org/10.1109/CVPR.2017.152
Nam H, Han B, 2016. Learning multi-domain convolutional neural networks for visual tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.4293–4302. https://doi.org/10.1109/CVPR.2016.465
Pu S, Song Y, Ma C, et al., 2018. Deep attentive tracking via reciprocative learning. Proc 32nd Conf on Neural Information Processing Systems, p.1931–1941.
Qi YK, Zhang SP, Qin L, et al., 2016. Hedged deep tracking. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.4303–4311. https://doi.org/10.1109/CVPR.2016.466
Sun C, Wang D, Lu HC, et al., 2018. Correlation tracking via joint discrimination and reliability learning. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.489–497. https://doi.org/10.1109/CVPR.2018.00058
Sun YX, Sun C, Wang D, et al., 2019. ROI pooled correlation filters for visual tracking. Proc IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.5783–5791. https://doi.org/10.1109/CVPR.2019.00593
Tang M, Yu B, Zhang F, et al., 2018. High-speed tracking with multi-kernel correlation filters. Proc IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.4874–4883. https://doi.org/10.1109/CVPR.2018.00512
Wang Q, Zhang L, Bertinetto L, et al., 2019. Fast online object tracking and segmentation: a unifying approach. Proc IEEE/CVF Conf on Computer Vision and Pattern Recognition, p.1328–1338. https://doi.org/10.1109/CVPR.2019.00142
Wu Y, Lim J, Yang MH, 2013. Online object tracking: a benchmark. Proc IEEE Conf on Computer Vision and Pattern Recognition, p.2411–2418. https://doi.org/10.1109/CVPR.2013.312
Wu Y, Lim J, Yang MH, 2015. Object tracking benchmark. IEEE Trans Patt Anal Mach Intell, 37(9):1834–1848. https://doi.org/10.3389/FNINS.2016.00405
Zhang JM, Ma SG, Sclaroff S, 2014. MEEM: robust tracking via multiple experts using entropy minimization. Proc 13th European Conf on Computer Vision, p.188–203. https://doi.org/10.1007/978-3-319-10599-4_13
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (No. 61773270) and the Key Research and Development Project of Sichuan Province, China (No. 2019YFG0491)
Contributors
Shui-wang LI and Qian-bo JIANG designed the research. Qi-jun ZHAO, Li LU, and Zi-liang FENG guided the research. Shui-wang LI drafted the manuscript. Qi-jun ZHAO and Li LU revised and finalized the paper.
Compliance with ethics guidelines
Shui-wang LI, Qian-bo JIANG, Qi-jun ZHAO, Li LU, and Zi-liang FENG declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Li, Sw., Jiang, Qb., Zhao, Qj. et al. Asymmetric discriminative correlation filters for visual tracking. Front Inform Technol Electron Eng 21, 1467–1484 (2020). https://doi.org/10.1631/FITEE.1900507
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1900507