REU: Implicit Polynomial Technology for Computer Vision and Image/Video Databases

这项研究的目标是将新的隐式多项式2D曲线和3D曲面对象识别概念推广到计算机视觉和图像处理领域的研究人员，并将计算快速的基于形状的索引发展到2D图像和3D图像数据库中。要使用的方法包括新的拟合概念和算法、新类型的不变量、用于隐式多项式2D曲线和3D曲面的单计算姿态估计的新概念和算法，以及通过将丰富的2D曲线集或丰富的3D曲面片集与已经自动提取并存储在图像数据库中的那些匹配来进行索引。这项工作将评估隐式多项式方法在2D和3D数据中对物体形状进行建模和推断的价值。这项研究还将为研究界提供有用的应用工具，并将提供对这项技术的优势和劣势的了解。在科学和商业领域，对图像数据库进行搜索和索引是一项快速增长的活动。该项目将使人们了解基于几何形状的索引的准确性和速度，以及使用新的隐式多项式方法可能实现的数据库编制的自动化。

The goals of this research are to bring new implicit polynomial 2D curve and 3D surface object recognition concepts to a state of general usefulness to researchers in computer vision and image processing, and to develop computationally-fast shape-based indexing into 2D image and 3D image databases. The approaches to be used include new fitting concepts and algorithms, new types of invariants, new concepts and algorithms for single-computation pose estimation for implicit polynomial 2D curves and 3D surfaces, and indexing by matching rich sets of 2D curvelets or rich sets of 3D surface patchlets with those that have been autonomously extracted and stored in the image databases. This work will assess the value of implicit polynomial methods for modeling and making inferences about object shape in 2D and 3D data. The research will also produce useful tools for the research community for applications, and will provide an understanding of the strengths and weaknesses of this technology. Searching and indexing into image databases is a rapidly growing activity in science and commerce. This project will provide an understanding of the geometric shape-based indexing accuracy and speed and the automation of database preparation possible with the new implicit polynomial methodology.