RI: III: Small: IInterlinking Image Collections

数码相机的可用性、网络的改进以及内存成本的降低使得捕捉、共享和存储大型图像集合变得更加容易。通过密集采样，这些捕获的图像之间存在许多联系和相关性，因为它们有效地记录了相同或视觉上相似的对象。本项目旨在大规模构建这样的图像链接网络，将图像之间的关系以图形或简单复合体的形式存储，称为图像网络，研究这些网络的特性，并将其用于各种应用。基于图像内容分析建立图像部分之间的链接，并且在数百万图像的规模上这样做，是一项计算要求很高的任务。由于对所有图像对都这样做是不切实际的，因此开发了一些技术，试图仅在(1)可能存在链接的图像对之间建立链接，(2)该链接实质上增加了对特定Web的连接性的已知信息。更深入地了解图像网络作为拓扑复合体的整体结构可以帮助这种链接预测过程。开发了有效导航这些大型结构并在其上构建有用地图的方法。通过在这个庞大的网络中传递信息，与图像相关的更多符号信息的整合成为可能。该项目具有高度跨学科的性质，结合了传统上用于信号处理和图像分析的连续应用数学技术，以及离散数学和网络理论的方法。

The availability of digital cameras, improved networking, and the diminishing cost of memory has made it easy to capture, share, and store large image collections. With dense sampling, there are many connections and correlations among these captured images, as they effectively record the same or visually similar objects. This project aims to build such networks of linked images on a large scale, store the inter-image relationships in the form of a graph or simplicial complexes called Image Webs, study the properties of these networks, and exploit them for a variety of applications.Establishing links between parts of images based on image content analysis, and doing so on the scale of millions of images, is a computationally demanding task. Since it is impractical to do this for all image pairs, techniques are developed for attempting to establish links only between pairs for which (1) a link is likely to exist and, (2) the link adds substantially to what is already known about the connectivity of a particular Web. A deeper understanding of the global structure of image webs as topological complexes can aid this link prediction process. Methods are developed for effectively navigating these large structures and for constructing useful maps over them. Integration with more symbolic information associated with images is possible by transferring information around in this vast network.The project is of a highly interdisciplinary nature, combining techniques from continuous applied mathematics, traditionally used in signal processing and image analysis, with methods from discrete mathematics and network theory.