A generalized graph model used for image clustering and classification

One of the most prevalent problems in image and signal processing is the curse of dimensionality. As sensor resolution and throughput have improved, the physical memory size of the imagery and signals produced by those sensors has increased proportionally. With the accumulation of high dimensional data comes the exponential growth of database size. The result is a collection of signals and images residing in a redundant and sometimes non-relevant high dimensional space. It is therefore, of extreme importance, to have the means to efficiently find and analyze low dimensional descriptions of high dimensional datasets.;It is well established that data embedded in high dimensional spaces not only lie on nonlinear manifolds but are also difficult to discriminate with linear methods such as Principal Component Analysis (PCA). A major shortcoming of existing dimensionality reduction techniques lies in their inability to discover a global description of data without input from the "user" that suggests how the data should be embedded. "Good" algorithms will preserve neighborhood-distance relationships, i.e., minimize intraclass dispersion while at the same time maximizing interclass separation.;In this dissertation, we present a generalized graph model entitled Generalized Diffusion Maps (GDM). GDM is used to cluster, classify and visualize objects extracted from digital image sequences. Using the proposed model, the process to find low-dimensional descriptions of images is fully automated and machine learned. Next, we introduce the Subspace Learning Performance Metric (SLPM). SLPM is based on GDM and is used to evaluate the performance of image fusion algorithms. Lastly, we present an original philosophy on how to realize a real-time (R/T), adaptive, end-to-end system for multispectral fusion. The system consists of three modules: R/T data acquisition and processing, automated nonlinear dimensionality reduction (GDM) and a metric to analyze algorithm/sensor performance (SLPM).