CAREER: Direct Manipulation of Numerical Optimization for Structured Geometry Creation

物理世界用几何和空间信息围绕着我们。各种各样的传感器和扫描设备可以很容易地将这些物理数据转换成非结构化的数字几何图形，如点云和三角网格。然而，下一代数字几何处理应用程序(例如，用于计算机辅助设计或用于医学图像分析)需要结构化数据，其中对象被组织成有意义的部分和关系。人们毫不费力地感知草图、核磁共振或扫描的汽车微型模型的结构，很容易识别存在哪些器官或机器部件以及每个器官或机械部件的大致位置。无论是由于我们学习的专业知识还是与生俱来的技能，这种人类感知能力的自动化都是极具挑战性的；解决输入中的歧义(例如，MRI中的黑色区域可能是恶性肿瘤或无害的阴影)通常需要人工参与。另一方面，我们还要为繁琐的低层次几何任务而苦苦挣扎，比如精确地勾勒出骨折或车门表面。虽然非线性优化算法擅长改进近似输入，但它们往往太慢，无法集成到交互式应用程序中。因此，在不断提供新用户输入的情况下会出现问题；如果反复取消并重新启动正在进行的非线性优化，则永远找不到任何解，但如果允许继续，它将计算出过时的解。在当前的研究中，PI的目标是解决交互性和非线性优化之间的根本冲突，并探索在医学和设计应用中创建结构化几何的最小交互方法。他的方法将功能强大且易于学习的直接操作界面与非线性优化相结合，后者能够在给定人类近似输入的情况下解决精确的几何问题。PI将综合来自人机交互、感知心理学和数值优化的技术，以利用这样一个事实，即人们通常以低维方式(例如，通过移动鼠标)与计算机交互，这使得人们能够预测人类输入以及并行优化过程是否会收敛到相同的解。他将使用界面来评估这些方法，以从噪声和不一致的部分数据创建高质量的结构化3D模型，这在计算机辅助设计的物理模型扫描和医学成像的解剖扫描中常见。项目成果将极大地增加交互式系统中可用于数值优化的计算资源，同时大大减少昂贵的操作员时间，还将有助于统一物理和数字设计。PI将寻求通过开源、可广泛重复使用的算法和向行业转让技术来广泛传播项目成果。他还将参与各种教育和外展活动，包括在当地一所高中举行的“反向科学博览会”，在此期间，嘉宾演讲者提供对最先进研究的介绍，学生实践科学新闻。

The physical world surrounds us with geometric and spatial information. A large variety of sensors and scanning equipment can readily turn this physical data into unstructured digital geometry, such as point clouds and triangle meshes. However, next generation digital geometry processing applications (say, for computer-aided design or for medical image analysis) require structured data in which an object is organized into meaningful parts and relationships. People have no trouble perceiving the structure of a sketch, MRI, or scanned car miniature, easily identifying which organs or machine parts are present and the approximate location of each. Whether due to our learned expertise or innate skill, such human perceptual abilities are extremely challenging to automate; resolving ambiguities in the input (e.g., a dark region in an MRI that could be a malignant tumor or an innocuous shadow) typically necessitates human involvement. On the other hand, we struggle with tedious low-level geometric tasks such as precisely delineating a bone fracture or the surface of a car door. While nonlinear optimization algorithms excel at improving approximate input, they are often too slow to integrate into interactive applications. Thus, a problem arises in situations where new user input is provided continuously; if an in-progress nonlinear optimization is repeatedly canceled and restarted no solution will ever be found, but if allowed to continue it will compute an outdated solution. The PI's objective in the current research is to resolve this fundamental conflict between interactivity and nonlinear optimization, and to explore minimal interactive approaches for creating structured geometry in medical and design applications. His approach merges direct manipulation interfaces, which are powerful and easily learned, with nonlinear optimization, which is capable of solving precise geometric problems given approximate input from a human. The PI will synthesize techniques from human-computer interaction, perceptual psychology, and numerical optimization to exploit the fact that people typically interact with computers in a low-dimensional manner (e.g., by moving a mouse), which allows one to predict both human input and whether parallel optimization processes will converge to the same solution. He will evaluate these approaches with interfaces for creating high-quality, structured 3D models from noisy and inconsistent partial data as is commonly found in scans of physical models for computer-aided design and anatomical scans for medical imaging. Project outcomes will vastly increase the computational resources available to numerical optimization in interactive systems while greatly reducing expensive operator time, and will also help unify physical and digital design. The PI will seek to widely disseminate project outcomes, by open-sourcing broadly-reusable algorithms and by technology transfer to industry. He will also engage in a variety of educational and outreach activities, including a "reverse science fair" at a local high school during which guest speakers deliver accessible introductions to state-of-the-art research and students practice science journalism.