Abstract: Concerning highly accurate sub-pixel motion vector estimation, an accurate motion estimation algorithm based on upsampled phase correlation with kernel regression refining was proposed. Firstly, an upsampled phase correlation was computed efficiently by means of matrix-multiply discrete Fourier transform, and the initial estimation of motion vector with sub-pixel accuracy was achieved by simply locating its peak. Secondly, a kernel regression function was fit to the upsampled phase correlation values in a neighborhood of initial estimation. Finally, the initial estimation was refined with the location of peak found in the kernel regression fitting function, so as to obtain accurate estimation at arbitrary-precision. In the comparison experiments with some state-of-the-art algorithms such as Quadratic function Fitting (QuadFit), Linear Fitting (LinFit), Sinc Fitting (SincFit), Local Center of Mass (LCM) and Upsampling in the frequency domain (Upsamp), the proposed scheme achieved the average estimation error at 0.0070 in the case of noise-free, and increased the accuracy of motion estimation by more than 64%; while under the noise condition, the average estimation error of the proposed shceme was 0.0204, and the accuracy of motion estimation was improved by more than 47%. Experimental results show that the proposed scheme can not only improve the accuracy of motion estimation significantly, but also achieve good robustness to the influence of noise.

Key words: motion estimation, phase correlation, upsampling, matrix-multiplication, kernel regression

摘要： 针对亚像素运动矢量的精确估计问题，提出一种基于核回归修正的上采样相位相关精确运动估计算法。首先，使用矩阵相乘离散傅里叶变换方法快速计算上采样相位相关曲面，并通过检测其峰值坐标实现运动矢量的亚像素级初始估计；其次，在上采样相位相关曲面上，采用核回归方法对以初始估计值为中心的邻域进行拟合；最后，检测核回归拟合函数的峰值坐标，并以此坐标对初始估计值进行修正，从而实现任意精度级别的精确运动估计。与二次函数拟合（QuadFit）、线性拟合（LinFit）、Sinc拟合（SincFit）、局部质心（LCM）、频域上采样（Upsamp）等算法进行仿真对比，在无噪声污染的情况下，所提算法的平均估计误差为0.0070，运动估计的准确度提高了64%以上；而在有噪声污染的情况下，所提出的算法的平均估计误差为0.0204，运动估计的准确度提高了47%以上。实验结果表明，所提算法不仅能够有效地提高运动估计的精确性，而且具有良好的抗噪性。

关键词: 运动估计, 相位相关, 上采样, 矩阵相乘, 核回归