CAREER: Shape Model Selection: Theory and Practice

职业：形状模型选择：理论与实践

• 批准号: 0954256
• 负责人: Kathryn Leonard
• 金额: $ 41.72万
• 依托单位: California State University Channel Islands
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-06-01 至 2016-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0954256&HistoricalAwards=false
• 关键词: CAREER; Shape; Model; Selection; Theory

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.

这个项目探索形状模型，将人类的形状感知，计算的易处理性和数学的严谨性结合起来。特别是，它建立了基于几何的骨架模型的选择标准，定义最好的模型是一个需要最少的位近似在指定的误差容限。该项目的目标是开发理论结果，建立骨骼模型的选择标准，并将这些结果应用于形状相关的工业项目。骨骼形状模型是有吸引力的形状为基础的应用程序，因为它们分解成突出的部分，可以独立操作的形状。它们在实际应用中的主要缺点是对形状边界中的噪声缺乏鲁棒性，直到最近才得到解决。在骨架模型的经典定义中，每个形状都有一个唯一的骨架。这种独特性造成了几何刚性，这反过来又导致缺乏鲁棒性。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。多个模型提供了灵活性，以适应嘈杂的形状边界，但在选择最佳的骨骼模型为给定的形状引入了一个新的问题。该项目从事有能力，但处于不利地位的学生，否则将不知道研究作为一个令人兴奋的和相关的研究事业。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数学课程，以及与学生和工业合作伙伴合作开发工业应用程序。