CAREER: Reconstructing Geometrically and Topologically Correct Models

摘要：PI：鞠，陶 （0846072）职业：重建几何和拓扑正确的模型生物医学成像和3D扫描广泛用于获取现实世界物体的逼真数字模型，从我们周围的物体，如咖啡杯和雕像，到我们体内的物体，如蛋白质和器官。在许多应用中，多边形表面需要从通过扫描或成像捕获的数据重建。除了可视化，这些多边形模型在计算和制造中有广泛的用途，其中几何和拓扑正确的模型是必需的。然而，由于输入数据往往是噪声或不完整的，它仍然是在实践中很难获得正确的多边形曲面使用现有的重建算法。重建的曲面可能会表现出几何不一致性，包括间隙、孔洞和交叉点，更常见的是拓扑伪影，如手柄和断开。此外，大多数保证几何正确输出的重建算法都是针对具有明确内部和外部的闭合表面设计的，因此不适用于包含预期开放边界或内部膜的表面。这些更一般的表面通常用于CAD以及生物医学建模。本研究正在开发强大的多边形表面重建算法，提供几何和拓扑正确性的保证。为了实现这一目标，开发了一个集成框架，该框架结合并扩展了现有的表面重建和模型修复算法，以生成正确的多边形模型，这些模型以3D点云或灰度体积的形式最好地表示输入数据。该研究还探索了开放和非流形表面的新重建和修复算法，从而将正确性保证扩展到比现有方法更大的一类模型。

Abstract:PI: Ju, Tao (0846072)CAREER: Reconstructing Geometrically and Topologically Correct ModelsBio-medical imaging and 3D scanning are widely used for acquiring realistic digital models of real-world objects, from those that are around us, like coffee mugs and statues, to those within us, like proteins and organs. In many applications, polygonal surfaces need to be reconstructed from the data captured by scanning or imaging. Besides visualization, these polygonal models have wide uses in computation and manufacturing, where geometrically and topologically correct models are required. However, as the input data is often noisy or incomplete, it is still difficult in practice to obtain correct polygonal surfaces using existing reconstruction algorithms. The reconstructed surface may exhibit geometric inconsistencies including gaps, holes and intersections, and more often, topological artifacts such as handles and disconnections. Furthermore, most reconstruction algorithms that promise geometrically correct outputs are designed for closed surfaces with well-defined inside and outside, and hence not applicable to surfaces that contain intended open boundaries or interior membranes. These more general surfaces are commonly used in CAD as well as bio-medical modeling.This research is developing robust polygonal surface reconstruction algorithms that offer guarantees for geometric and topological correctness. To achieve this goal, an integrated framework is developed that combines and extends existing surface reconstruction and model repair algorithms to produce correct polygonal models that best represent the input data, in the form of either 3D point clouds or grayscale volumes. The research is also exploring new reconstruction and repair algorithms for open and non-manifold surfaces, thereby extending the correctness guarantees to a much larger class of models than those can be handled by existing methods.