基于李代数的变形目标跟踪

史泽林; 刘云鹏; 李广伟

doi:10.3724/SP.J.1004.2012.00420

基于李代数的变形目标跟踪

doi: 10.3724/SP.J.1004.2012.00420

史泽林^1,2,
刘云鹏^1,2,3,4, ,,
李广伟⁵

1.
中国科学院沈阳自动化研究所沈阳 110016;
2.
中国科学院光电信息处理重点实验室沈阳 110016;
3.
辽宁省图像理解与视觉计算重点实验室沈阳 110016;
4.
中国科学院研究生院北京 100049;
5.
青岛大学管理科学与工程系青岛 266071

详细信息

通讯作者:
刘云鹏, 中国科学院沈阳自动化研究所博士研究生. 主要研究方向为目标跟踪和识别.E-mail: ypliu@sia.cn

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出版历程
- 收稿日期: 2010-08-23
- 修回日期: 2010-12-27
- 刊出日期: 2012-03-20

Deformable Object Tracking Based on Lie Algebra

SHI Ze-Lin^1,2,
LIU Yun-Peng^{1,2,3,4
, ,},
LI Guang-Wei⁵

1.
Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang 110016;
2.
Key Laboratory of Opto-Electronic Information Processing, Chinese Academy of Sciences, Shenyang 110016;
3.
Key Laboratory of Image Understanding and Computer Vision, Liaoning Province, Shenyang 110016;
4.
Graduate University of Chinese Academy of Sciences, Beijing 100049;
5.
Department of Management Science and Engineering, Qingdao University, Qingdao 266071

摘要

摘要: 动态几何变形是图像跟踪技术面临的突出难题之一. 本文提出基于李代数的变形目标跟踪方法, 用Gabor特征表征目标, 以仿射李群建立目标几何变形, 利用李代数和李群之间的指数映射将参数的最优化求解从欧氏空间转至光滑流形, 实现了对变形目标的稳定跟踪.从物理层面分析了目标跟踪过程中的参数几何变换的实质, 从理论上对在光滑流形上进行迭代求解的优点进行了详细分析, 并对其收敛性做出了证明.图像序列跟踪测试的对比实验表明, 本文方法较现有基于欧氏空间的算法在收敛速度、跟踪稳定性和精确性方面有显著提高.
- 李群 /
- 李代数 /
- 目标跟踪 /
- 几何变形 /
- 指数映射
Abstract: Dynamic deformation of object is a distinct problem in image-based tracking. A novel deformable object tracking method based on Lie algebra is presented. This method uses Gabor feature as target token, models deformation using affine Lie group, and optimizes parameters directly on manifold, which can be solved by exponential mapping between Lie group and its Lie algebra. We physically illustrate the essential of the geometric transformation in the tracking, then analyze the advantage of our method and give a direct proof of local quadratic convergence of the algorithm. The experimental results demonstrate that the Lie algebra based method makes significant improvements in convergence speed, tracking stability and accuracy in comparison to Euclidean based algorithms.
- Lie group /
- Lie algebra /
- object tracking /
- geometric deformation /
- exponential mapping

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参考文献(1)

[1]

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