CAREER: Shape Model Selection: Theory and Practice

该项目探索了结合人类形状感知、计算可追溯性和数学严谨性的形状模型。特别是，它为骨架模型建立了基于几何的选择标准，将最佳模型定义为在指定的误差容限内需要最少的近似位的模型。该项目的目标是发展理论结果，建立骨骼模型的选择标准，并将这些结果应用于依赖形状的工业项目。骨架形状模型对于基于形状的应用程序很有吸引力，因为它们将形状分解为可以独立操作的突出部分。它们在实际应用中的主要缺点是对形状边界的噪声缺乏鲁棒性，直到最近才得到解决。在骨骼模型的经典定义中，每个形状都有一个独特的骨架。独特性创建一个几何刚度,反过来导致缺乏鲁棒性。最近的广义骨架定义放宽了唯一性约束，允许每个形状有多个骨架模型。多模型提供了适应噪声形状边界的灵活性，但在为给定形状选择最佳骨架模型时引入了一个新问题。该项目吸引有能力但处境不利的学生，否则他们就不会意识到研究是一项令人兴奋和相关的研究。更广泛的影响包括研究生和未来教师之间的广泛合作，为K-12教室开发学习活动，开发课程模块，将数字图像分析的概念纳入标准的二年级数学课程，以及与学生和工业合作伙伴合作开发工业应用。

This project explores shape models that unite human shape perception, computational tractability and mathematical rigor. In particular, it establishes geometry-based selection criteria for skeletal models, defining the best model to be the one that requires the fewest bits to approximate within a specified error tolerance. The goals of the project are to develop theoretical results establishing selection criteria for skeletal models and to apply those results to shape-dependent industrial projects.Skeletal shape models are attractive for shape-based applications because they decompose shapes into salient parts that can be manipulated independently. Their primary downfall for practical applications, a lack of robustness to noises in the shape boundary, has only recently been addressed. In the classical definition of the skeletal model, each shape has a unique skeleton. That uniqueness creates a geometric rigidity that in turn leads to the lack of robustness. A recent generalized skeletal definition relaxes the uniqueness constraint, allowing multiple skeletal models for each shape. Multiple models provide the flexibility to accommodate noisy shape boundaries, but introduce a new problem in selecting the best skeletal model for a given shape.The project engages capable but disadvantaged students who would otherwise be unaware of research as a career in exciting and relevant research. Broader impacts include extensive collaboration between research students and future teachers to develop learning activities for K-12 classrooms, development of course modules to incorporate concepts from digital image analysis into standard sophomore-level mathematics courses, and development of industrial applications in collaboration with students and industrial partners.