Robust Geometry Processing for Big Dirty Data

大脏数据的鲁棒几何处理

• 批准号: RGPIN-2017-05235
• 负责人: Jacobson, Alec
• 金额: $ 2.26万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2019
• 资助国家: 加拿大
• 起止时间: 2019-01-01 至 2020-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=684054
• 关键词: Robust; Geometry; Processing; Big; Dirty

Geometry processing--an extension of signal processing--interprets three-dimensional curves and surfaces as signals. Just as audio and image signal data have exploded in availability, geometric data is massively abundant. We encounter geometric data everywhere: depth scanning guides safe and effective self-driving cars, anatomical curves or surfaces enable medical visualizations and soon robotic telesurgery, and 3D printing brings customization of geometric design to the masses.******However, geometry processing has been outpaced by the data.******Unlike with audio and images, we are not seeing the full application of big data analytics and modern machine learning techniques to geometric data. The core roadblock is lack of robustness in our tool chest of geometry processing techniques.******Geometric data is corrupted with noise, ambiguity and inconsistency. Unlike the regular pixel grid of an image, discrete geometric representations are a zoo with trade-offs in terms of efficiency, accuracy and scope.******Conventional geometry processing is a direct application of continuous mathematical concepts. Its assumption of pristine input surfaces is prohibitively strict and applications suffer.******Objectives******Over the next five years, I will bring geometry processing up to speed with modern geometric data. I will pursue three parallel but complementary tracks:******1. Robust algorithms for recovering structure from unstructured, noisy geometric representations;******2. Robust mathematical and algorithmic foundations for solving partial differential equations (PDEs) on real-world geometric data; and******3. Robust user interfaces for direct manipulation and creation of geometric data.******While solutions uncovered along the way will have immediate practical implications, the long-term impact is a multiplication of progress across all tracks. The combination of successes will unlock machine learning to geometric data, just as robust image processing has done for image data.******Scientific Approach******My general scientific approach is to identify and eliminate unnecessarily strict expectations of "cleanliness" in input data. Often this means returning to first mathematical principles and adapting traditional definitions or concepts to accommodate problems witnessed in real-world data.

几何处理--信号处理的延伸--将三维曲线和曲面解释为信号。就像音频和图像信号数据的可用性呈爆炸式增长一样，几何数据也非常丰富。我们随处可见几何数据：深度扫描引导安全有效的自动驾驶汽车，解剖曲线或曲面使医学可视化，并很快实现机器人远程手术，3D打印为大众带来定制的几何设计。然而，几何处理已经被数据超越。*与音频和图像不同，我们没有看到大数据分析和现代机器学习技术在几何数据上的充分应用。我们的几何处理技术工具箱中的核心障碍是缺乏健壮性。*几何数据受到噪声、歧义和不一致的破坏。与图像的规则像素网格不同，离散几何表示是一个在效率、精度和范围方面进行权衡的动物园。*常规几何处理是连续数学概念的直接应用。它对原始输入表面的假设非常严格，应用程序受到影响。*目标*在接下来的五年里，我将使几何处理与现代几何数据保持同步。我将追求三个平行但互补的轨道：*1.从非结构化、噪声的几何表示中恢复结构的稳健算法；*2.在真实世界几何数据上求解偏微分方程组(PDE)的稳健的数学和算法基础；以及*3.用于直接操作和创建几何数据的稳健的用户界面。*虽然沿途发现的解决方案将具有直接的实际意义，但长期影响是所有轨道上的进展的倍增。这些成功的结合将解锁机器对几何数据的学习，就像稳健的图像处理对图像数据所做的那样。*科学方法*我的一般科学方法是识别并消除输入数据中不必要的严格要求。这通常意味着回到最初的数学原理，并调整传统的定义或概念，以适应现实世界数据中出现的问题。