R-tree can achieve better performance in lowdimensional space, but its performance suffers greatly in high-dimensional space. So the reduction of the dimensionality is the key to the problem. Z curve can fill d dimensional space linearly, divide the space into equal-size grids and map points lying in the grids into the linear space. B Z -tree is constructed using Z curve. B Z -tree is a balanced multi-branch tree. B Z -tree has the characteristic of B + -tree and R-tree. In B Z -tree, Z values of the points are the keywords, and all points are stored in leaf nodes, ordered by Z values. Using the reduction of the dimensionality of B Ztree, the paper presents an approximate k-nearest neighbor query algorithm. According to the test, its running time is shorter than the Brute-Force method and the algorithm based on R-tree, and the quality of the approximate knearest neighbors is better.Keywords-k-nearest neighbor query algorithm; the reduction of the dimensionality; Z curve; B Z -tree; approximate algorithm I. INTRODUCTION Nearest neighbor query is an important research problem in many fields, such as Geographical Information System, Data Dining and Pattern Recognition and so on.Paper [1] presents a branch and bound nearest neighbor query algorithm, which traverses R-tree in depth-first method. In the recursion and backtrack, the algorithm deletes the sub-trees, which do not contain the nearest neighbors based on three rules which are based on two distance functions, MINDIST and MINMAXDIST. Paper [2] presents a best-first nearest neighbor query algorithm. The algorithm only traverses the nodes which are nearest to query point. The number of visiting the nodes is smaller than the algorithm of the paper [1]. Paper [3] demonstrates that two of the three rules cannot efficiently delete the subtrees, and presents an algorithm based on only one rule.In the construction of R-tree and its variants, there exists the overlapping problem between the minimum bounding rectangles. In high-dimensional space, the overlapping problem is serious. The nearest neighbor query algorithm based on R-tree will access many useless nodes. Paper [4] indicates the execution time of the algorithm depends exponentially on the dimension of the space.The space-filling curve is a way of the reduction of the dimension. Z curve is one kind of the space-filling curve. The clustering characteristic of Z curve is better [5] . The

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Given the difficulty of manually annotating motion in video, the current best motion estimation methods are trained with synthetic data, and therefore struggle somewhat due to a train/test gap. Self-supervised methods hold the promise of training directly on real video, but typically perform worse. These include methods trained with warp error (i.e., color constancy) combined with smoothness terms, and methods that encourage cycle-consistency in the estimates (i.e., tracking backwards should yield the opposite trajectory as tracking forwards). In this work, we take on the challenge of improving state-of-the-art supervised models with self-supervised training. We find that when the initialization is supervised weights, most existing self-supervision techniques actually make performance worse instead of better, which suggests that the benefit of seeing the new data is overshadowed by the noise in the training signal. Focusing on obtaining a "clean" training signal from real-world unlabelled video, we propose to separate labelmaking and training into two distinct stages. In the first stage, we use the pre-trained model to estimate motion in a video, and then select the subset of motion estimates which we can verify with cycle-consistency. This produces a sparse but accurate pseudo-labelling of the video. In the second stage, we fine-tune the model to reproduce these outputs, while also applying augmentations on the input. We complement this boot-strapping method with simple techniques that densify and re-balance the pseudo-labels, ensuring that we do not merely train on "easy" tracks. We show that our method yields reliable gains over fully-supervised methods in real videos, for both short-term (flow-based) and long-range (multiframe) pixel tracking. Our code can be found here: https: //github.com/AlexSunNik/refining-motion-code.

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