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Equivalence of Correlation Filter and Convolution Filter in Visual Tracking

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Image and Graphics (ICIG 2021)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 12890))

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Abstract

(Discriminative) Correlation Filter has been successfully applied to visual tracking and has advanced the field significantly in recent years. Correlation filter-based trackers consider visual tracking as a problem of matching the feature template of the object and candidate regions in the detection sample, in which correlation filter provides the means to calculate the similarities. In contrast, convolution filter is usually used for blurring, sharpening, embossing, edge detection, etc. in image processing. On the surface, correlation filter and convolution filter are usually used for different purposes. In this paper, however, we prove, for the first time, that correlation filter and convolution filter are equivalent in the sense that their minimum mean-square errors (MMSEs) in visual tracking are equal, under the condition that the optimal solutions exist and the ideal filter response is Gaussian and centrosymmetric. This result gives researchers the freedom to choose correlation or convolution in formulating their trackers. It also suggests that the explanation of the ideal response in terms of similarities is not essential.

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Acknowledgment

This work is supported by the National Natural Science Foundation of China (No. 61773270, 61971005, 62066042).

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Authors and Affiliations

  1. National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, Chengdu, China

    Qijun Zhao & Ziliang Feng

  2. College of Computer Science, Sichuan University, Chengdu, China

    Shuiwang Li, Qijun Zhao, Ziliang Feng & Li Lu

  3. Guilin University of Technology, Guilin, China

    Shuiwang Li

Authors
  1. Shuiwang Li
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  2. Qijun Zhao
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  3. Ziliang Feng
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  4. Li Lu
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Corresponding author

Correspondence to Qijun Zhao .

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Editors and Affiliations

  1. Peking University, Beijing, China

    Yuxin Peng

  2. Tsinghua University, Beijing, China

    Shi-Min Hu

  3. Tampere University, Tampere, Finland

    Moncef Gabbouj

  4. Zhejiang University, Hangzhou, China

    Kun Zhou

  5. Technion – Israel Institute of Technology, Haifa, Israel

    Michael Elad

  6. Tsinghua University, Beijing, China

    Kun Xu

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Li, S., Zhao, Q., Feng, Z., Lu, L. (2021). Equivalence of Correlation Filter and Convolution Filter in Visual Tracking. In: Peng, Y., Hu, SM., Gabbouj, M., Zhou, K., Elad, M., Xu, K. (eds) Image and Graphics. ICIG 2021. Lecture Notes in Computer Science(), vol 12890. Springer, Cham. https://doi.org/10.1007/978-3-030-87361-5_51

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  • DOI: https://doi.org/10.1007/978-3-030-87361-5_51

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-87360-8

  • Online ISBN: 978-3-030-87361-5

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