Discriminative correlation filters (DCF) are efficient in visual tracking and have advanced the field significantly. However, the symmetry of correlation (or convolution) operator results in computational problems and does harm to the generalized translation equivariance. The former problem has been approached in many ways, whereas the latter one has not been well recognized. In this paper, we analyze the problems with the symmetry of circular convolution and propose an asymmetric one, which as a generalization of the former has a weak generalized translation equivariance property. With this operator, we propose a tracker called the asymmetric discriminative correlation filter (ADCF), which is more sensitive to translations of targets. Its asymmetry allows the filter and the samples to have different sizes. This flexibility makes the computational complexity of ADCF more controllable in the sense that the number of filter parameters will not grow with the sample size. Moreover, the normal matrix of ADCF is a block matrix with each block being a two-level block Toeplitz matrix. With this well-structured normal matrix, we design an algorithm for multiplying an N × N two-level block Toeplitz matrix by a vector with time complexity O(NlogN) and space complexity O(N), instead of O(N²). Unlike DCF-based trackers, introducing spatial or temporal regularization does not increase the essential computational complexity of ADCF. Comparative experiments are performed on a synthetic dataset and four benchmarks, including OTB-2013, OTB-2015, VOT-2016, and Temple-Color, and the results show that our method achieves state-of-the-art visual tracking performance.

判别相关滤波器（DCF）在视觉跟踪方面非常有效，并已大大推动了该领域的发展。但是，相关性（或卷积）算符的对称性会导致计算问题，并且会损害广义的翻译等方差。前一种问题已通过多种方式解决，而后一种尚未得到很好的认识。在本文中，我们分析了具有圆卷积对称性的问题，并提出了一个不对称的卷积，作为前者的推广，它具有较弱的广义平移等方差性质。借助此运算符，我们提出了一种称为非对称判别相关滤波器（ADCF）的跟踪器，该跟踪器对目标的转换更加敏感。它的不对称性使滤波器和样本具有不同的大小。从滤波器参数的数量不会随样本大小增加的意义上讲，这种灵活性使ADCF的计算复杂度更加可控。此外，ADCF的标准矩阵是块矩阵，每个块是两级块Toeplitz矩阵。利用这个结构良好的法线矩阵，我们设计了一种将N×N两级块Toeplitz矩阵由具有时间复杂度O（N log N）和空间复杂度O（N）的向量代替O（N ²）。与基于DCF的跟踪器不同，引入空间或时间正则化不会增加ADCF的基本计算复杂性。在合成数据集和四个基准（包括OTB-2013，OTB-2015，VOT-2016和Temple-Color）上进行了比较实验，结果表明我们的方法实现了最新的视觉跟踪性能。