Non-Commutative Harmonic Analysis in Object Recognition and Tracking

首席研究员是一位数学教授，他将访问宾夕法尼亚大学工程与应用科学学院的计算机与信息科学系，发起一项计算机视觉合作研究计划，重点是全向传感器，这是一种具有异常大视野的视觉传感器。这些新传感器在监视、导航和通信方面有着众多的应用，但它们也提出了许多复杂的新数学问题，因为它们不能用传统的计算机视觉和图像处理方法准确建模。值得注意的是，相关的数学是非紧李群的表示理论，非交换调和分析，以及相关的算法。为了在这一领域做出贡献，主要研究者必须沉浸在一个活跃的视觉研究实验室中，在那里，性能和设备的不可避免的技术进步导致模型的要求和复杂性不断变化。 PI将研究李群及其齐次空间上的非交换调和分析在计算机视觉中的两个主要问题中的应用：对象识别和跟踪。非交换傅立叶变换将特别有助于这些问题，以及在发现分析不变量的模板匹配所需的图像。在PI离开宾夕法尼亚大学后，他打算在德雷克塞尔大学建立一个图像科学小组，其中包括镜子设计和微分几何方面的专家。该小组将开发课程和研讨会，促进工程学院计算机科学、电气和计算机工程系的学生和教师之间的交流。 由于宾大与德崇学院的地理位置非常接近，PI希望在他休假期间启动的合作将继续进行联合研讨会，联合研究学生和研究项目。该IGMS项目由MPS多学科活动办公室（OMA）和数学科学部（DMS）共同支持。

The principal investigator, a professor of mathematics, will visit the Department of Computer and Information Science in the School of Engineering and Applied Science at the University of Pennsylvania to initate a collaborative research program in computer vision emphasizing omnidirectional sensors, which are visual sensors with unusually large fields of view. These new sensors have numerous applications in surveillance, navigation, and communications, yet they have raised a host of complex new mathematical questions because they are not accurately modelled with the conventional methods of computer vision and image processing. Remarkably, the relevant mathematics is the representation theory of non-compact Liegroups, non-commutative harmonic analysis, and the associated algorithms.To make a contribution to this field, it is essential for the principal investigator to be immersed in a laboratory active in vision research where inevitable technological advances in performance and equipment cause continuous change in the requirements and complexity of the models. The PI will investigate applications of noncommutative harmonic analysis on Lie groups and their homogeneous spaces to two of the major problems in computer vision: object recognition and tracking. The noncommutative Fourier transform will be especially helpful for these problems as well as in discovering analytical invariants for images needed for template matching. After the PI's leave at Penn, he intends to establish an image science group at Drexel that includessa colleagues who are experts in mirror design and differential geometry. This group will develop courses and seminars fostering cross-fertilization among students and faculty from computer science and electrical and computer engineering departments in the College of Engineering. With the close physical proximity of Penn with Drexel, the PI expects the collaborations initiated during his leave will continue with joint seminars, joint research students, and research projects.This IGMS project is jointly supported by the MPS Office of Multidisciplinary Activities (OMA) and the Division of Mathematical Sciences (DMS).