Algebraic Geometry and Computational Algebraic Geometry for Image Database Indexing, Image Recognition, and Computer Vision

9508742 Stiller数学科学中的大学-产业合作研究项目是旨在为学术界和产业界在其职业生涯的不同阶段交流数学科学家的机制而设计的项目。这些计划将加强产业界和学术界之间的联系，并确定和鼓励数学科学研究的新途径。大学-工业博士后研究奖学金为最近获得数学科学博士学位的人提供两年的支持。这些奖项是为国家科学努力的未来活力做出贡献的一种手段。这位博士后研究员将与学术界和工业界的科学顾问密切合作。这位博士后研究员将参与一项联合研究工作，将德克萨斯农工大学的研究人员与新泽西州普林斯顿的大卫·萨诺夫研究中心的一个小组联合起来。这项研究将集中于代数几何中的技术，特别是几何不变量理论和计算代数几何中的技术在图像识别、基于内容的检索的图像数据库索引和计算机视觉中的应用。这位研究员将进行原创性研究，以发展一种等变对应理论，该理论源于将3-D对象与2-D图像联系起来的问题，反之亦然。这项工作将包括设计算法来实现结果，以及分析其相对于几何变化的稳健性。

9508742 Stiller The University-Industry Cooperative Research Programs in the Mathematical Sciences are programs designed to establish a mechanism for exchange of mathematical scientists between academia and industry at different stages of their careers. These programs will strengthen the links between industry and academia and identify and encourage new avenues of research in the mathematical sciences. The University-Industry Postdoctoral Research Fellowships provide two years of support for recent recipients of doctoral degrees in the mathematical sciences. These awards are a means of contributing to the future vitality of the scientific effort of the nation. The postdoctoral fellow will work closely with scientific advisors from both academia and industry. The Postdoctoral researcher will be engaged in a joint research effort that unites researchers at Texas A&M University with a group at the David Sarnoff Research Center in Princeton, New Jersey. The research will focus on the application of techniques in algebraic geometry, notably geometric invariant theory, and computational algebraic geometry to problems in image recognition, image database indexing for content-based retrieval, and computer vision. The fellow will do original research to develop a theory of equivariant correspondences coming out of questions motivated by problems in relating 3- D objects to 2-D images and vice versa. The work will involve the design of algorithms to implement the results, as well as an analysis of their robustness with respect to geometric variation.