基于李代数的变形目标跟踪

Deformable Object Tracking Based on Lie Algebra

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.

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.