Abstract: Concerning highly accurate sub-pixel motion estimation, an improved algorithm based on gradient cross-correlation with kernel regression refining is proposed. Firstly, the spatial gradient of the image is generated using an optimal filter. Secondly, an upsampled gradient cross-correlation is computed efficiently by means of matrix-multiply discrete Fourier transform, and the initial estimation of motion vector with sub-pixel accuracy procured by the peak of it. Finally, a kernel regression function is fit to the upsampled gradient cross-correlation values in a neighborhood of initial estimation, then refines the initial estimation 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, the accuracy of motion estimation of proposed scheme increases by more than 74% in the case of noise-free; while under the noise condition, the accuracy is improved by more than 68%. Experimental results show that the proposed algorithm can not only achieve good robustness to the influence of noise, but can also improve the accuracy of motion estimation significantly.

Key words: motion estimation, gradient cross-correlation, optimal filter, upsampling, matrix-multiplication, kernel regression

摘要： 为实现亚像素运动矢量的精确估计，探讨一种基于核回归修正的梯度互相关精确运动估计算法。引入优化滤波中心差分估计器计算图像梯度；基于矩阵相乘离散傅里叶变换方法快速计算上采样梯度互相关函数，以该函数的峰值坐标生成运动矢量的亚像素级初始估计值；在上采样梯度互相关曲面上，采用核回归方法对以初始估计值为中心的邻域进行拟合，并通过检测核回归拟合函数的峰值坐标获得初始估计的精确修正值，从而实现任意精度级别的精确运动估计。与相关文献的算法进行实验比较，在无噪声影响的情况下，所探讨算法的运动估计准确度提高了74%以上；而在噪声影响的情况下，运动估计的准确度则提高了68%以上。实验结果表明，所探讨算法不仅具备良好的抗噪性能，同时能够有效地提高运动估计的精确性。

关键词: 运动估计, 梯度互相关, 优化滤波器, 上采样, 矩阵相乘, 核回归