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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.

Deformation-induced martensitic transformation (DIMT) has been used for designing high-performance alloys to prevent structural failure under static loads. Its effectiveness against fatigue, however, is unclear. This limits the application of DIMT for parts that are exposed to variable loads, although such scenarios are the rule and not the exception for structural failure. Here we reveal the dual role of DIMT in fatigue crack growth through in situ observations. Two antagonistic fatigue mechanisms mediated by DIMT are identified, namely, transformation-mediated crack arresting, which prevents crack growth, and transformation-mediated crack coalescence, which promotes crack growth. Both mechanisms are due to the hardness and brittleness of martensite as a transformation product, rather than to the actual transformation process itself. In fatigue crack growth, the prevalence of one mechanism over the other critically depends on the crack size and the mechanical stability of the parent austenite phase. Elucidating the two mechanisms and their interplay allows for the microstructure design and safe use of metastable alloys that experience fatigue loads. The findings also generally reveal how metastable alloy microstructures must be designed for materials to be fatigue-resistant.

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