  Visual tracking (VT) is the process of locating a moving object of interest in a video. It is a fundamental problem in computer vision, with various applications in human-computer interaction, security and surveillance, robot perception, traffic control, etc. In this paper, we address this problem for the first time in the quantum setting, and present a quantum algorithm for VT based on the framework proposed by Henriques et al. [IEEE Trans. Pattern Anal. Mach. Intell., 7, 583 (2015)]. Our algorithm comprises two phases: training and detection. In the training phase, in order to discriminate the object and background, the algorithm trains a ridge regression classifier in the quantum state form where the optimal fitting parameters of ridge regression are encoded in the amplitudes. In the detection phase, the classifier is then employed to generate a quantum state whose amplitudes encode the responses of all the candidate image patches. The algorithm is shown to be polylogarithmic in scaling, when the image data matrices have low condition numbers, and therefore may achieve exponential speedup over the best classical counterpart. However, only quadratic speedup can be achieved when the algorithm is applied to implement the ultimate task of Henriques's framework, i.e., detecting the object position. We also discuss two other important applications related to VT: (1) object disappearance detection and (2) motion behavior matching, where much more significant speedup over the classical methods can be achieved. This work demonstrates the power of quantum computing in solving computer vision problems. 
Quantum algorithm for visual tracking