﻿ 基于傅里叶域卷积表示的目标跟踪算法<sup>*</sup>
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Convolution representation-based object tracking algorithm in Fourier domain
ZHU Ridong, YANG Xiaoyuan, WANG Jingkai
School of Mathematics and Systems Science, Beijing University of Aeronautics and Astronautics, Beijing 100083, China
Received: 2017-01-18; Accepted: 2017-04-07; Published online: 2017-05-16 14:30
Foundation item: National Natural Science Foundation of China (61671002); Beijing Natural Science Foundation (4152029)
Corresponding author. YANG Xiaoyuan, E-mail: xiaoyuanyang@vip.163.com
Abstract: A novel object tracking algorithm based on convolution representation in Fourier domain is proposed for object tracking. Object tracking question can be treated as a convolution representation model. By finding the best filters, which reconstruct the target function with minimum loss, fast and robust object tracking can be realized. When the optimal multi-channel convolution representation model is mapped to the Fourier domain, it is equal to solving the least squares solution to linear equations. First, all solutions of the system of linear equations can be expressed through the theory of pseudo inverse, which provide a general format of convolution filters. Then, filters updated in the previous frame and feature templates extracted from current frame are used to generate current filters, and the pseudo inverse can be obtained fast through the full rank algorithm. Finally, tracking filters are updated and applied in both translation and scale. Experimental results on the object tracking benchmark (OTB) database show that our algorithm performs better than some state-of-the-art tracking methods in terms of accuracy and offers a general format to design filters.
Key words: object tracking     convolution representation     Moore-Penrose pseudo inverse     Fourier transform     optimal approximation

1 Moore-Penrose广义逆矩阵

，方程可表示为ax=1。方程的通解为y为任意C5×1中的向量。

2 卷积表示模型

 (1)

 (2)
 图 1 响应函数预测位置 Fig. 1 Location estimation by response function

 (3)

 (4)

 (5)

 (6)

 (7)

 (8)
 (9)
 (10)

，则滤波器可表示为

 (11)
 (12)

 图 2 响应函数及其傅里叶变换 Fig. 2 Response function and its Fourier transform

1  初始化，输入初始参数

2  生成平移和尺度目标函数，并做傅里叶变换

3  输入初始帧图像F1、初始目标位置P1，提取目标特征

4  通过推论1快速求解广义逆，然后利用式(8)求解初始平移滤波器X1tran与初始尺度滤波器X1scal

5  k=2

6  重复

7  输入当前帧图像Fk，提取候选目标特征

8  由式(1)求解当前平移响应函数

9  根据平移响应函数峰值确定当前位置Pk

10  由式(1)求解当前尺度响应函数

11  根据尺度响应函数峰值确定当前尺度Sk

12  在当前位置和尺度下，提取目标特征，利用推论1快速求解广义逆，通过式(9)求解当前平移滤波器Xtran和尺度滤波器Xscal

13  由式(10)更新尺度滤波器得到Xkscal，更新平移滤波器得到Xktran

14   k=k+1

15  直到最后一帧

3 实验结果与分析

 图 3 多通道特征和多尺度采样 Fig. 3 Multi-channel features and multi-scale sampling
 图 4 OTB[19]数据库中的32个图像序列 Fig. 4 32 image sequences of OTB[19] database

 图 5 评估算法 Fig. 5 Evaluation algorithm

 图 6 在32个图像序列上的成功率和精度曲线 Fig. 6 Success rate and precision curves over 32 image sequences

 算法 本文算法 SRDCF[12] DSST[5] KCF[4] MEEM[13] SCM[16] Struck[14] ASLA[15] L1-APG[17] CT[18] AUC 0.684 0.677 0.653 0.589 0.586 0.541 0.533 0.510 0.461 0.354 排名 1 2 3 4 5 6 7 8 9 10

 算法 本文算法 SRDCF[12] DSST[5] KCF[4] MEEM[13] Struck[14] SCM[16] ASLA[15] L1-APG[17] CT[18] 精度 0.900 0.889 0.858 0.847 0.821 0.722 0.691 0.619 0.561 0.452 排名 1 2 3 4 5 6 7 8 9 10

 图 7 本文算法与其他算法在Fleetface、Soccer、Walking2和Skating1序列上的跟踪结果 Fig. 7 Tracking results of proposed algorithm and other algorithms on Fleetface, Soccer, Walking2 and Skating1 sequences

 图 8 快速运动、形变、尺度变化、遮挡、面外旋转、面内旋转场景下的成功率曲线 Fig. 8 Success rate curves of fast motion, deformation, scale variation, occlusion, out-of-plane rotation and in-plane rotation

4 结论

1) 本文提出一种在傅里叶域求解卷积表示的目标跟踪算法。将卷积表示问题变换到傅里叶域，可以通过广义逆的满秩算法快速求解，得到多样的滤波器设计方法。

2) 信号在傅里叶域的共轭对称性和稀疏性可以辅助降低算法的计算复杂度。

3) 在OTB图像库的32个序列上进行跟踪实验，与当前比较先进的9种目标跟踪算法进行对比。实验结果显示，本文跟踪算法在跟踪性能上优于其他9种跟踪算法。

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文章信息

ZHU Ridong, YANG Xiaoyuan, WANG Jingkai

Convolution representation-based object tracking algorithm in Fourier domain

Journal of Beijing University of Aeronautics and Astronsutics, 2018, 44(1): 151-159
http://dx.doi.org/10.13700/j.bh.1001-5965.2017.0038