Construction of Geometric Data Processing Optimization Theory by Using Global Norms

建立了基于全局范数优化的几何数据处理新理论。我们给出了几何对象的最优压缩和视觉图像关于全局范数的最优逼近。此外，我们还提出了网格上离散欧几里得公理的新概念，给出了一族数字段的新构造及其理论上的最优性。我们已在31篇参考期刊/会议论文上发表了我们的成果，并在36次国际/国内会议上发表了演讲。我们还通过三本教科书和一次电视采访开展了教育活动。

We have established novel theory of geometric data processing based on optimization using global norms. We have given optimal compression of geometric objects and optimal approximation of visual images with respect to global norms. Moreover, we proposed new concept of discrete Euclidean axioms on a grid, and gave a novelconstruction of a family of digital segments together with its theoretical optimality. We have published our results in 31 refereed journal/conference papers, and given 36 international/domestic conference presentations. We also did educational campaign via three textbooks and a TV interview.