24 May 2012 Assessing the impact of background spectral graph construction techniques on the topological anomaly detection algorithm
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Anomaly detection algorithms have historically been applied to hyperspectral imagery in order to identify pixels whose material content is incongruous with the background material in the scene. Typically, the application involves extracting man-made objects from natural and agricultural surroundings. A large challenge in designing these algorithms is determining which pixels initially constitute the background material within an image. The topological anomaly detection (TAD) algorithm constructs a graph theory-based, fully non-parametric topological model of the background in the image scene, and uses codensity to measure deviation from this background. In TAD, the initial graph theory structure of the image data is created by connecting an edge between any two pixel vertices x and y if the Euclidean distance between them is less than some resolution r. While this type of proximity graph is among the most well-known approaches to building a geometric graph based on a given set of data, there is a wide variety of dierent geometrically-based techniques. In this paper, we present a comparative test of the performance of TAD across four dierent constructs of the initial graph: mutual k-nearest neighbor graph, sigma-local graph for two different values of σ > 1, and the proximity graph originally implemented in TAD.
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Amanda K. Ziemann, Amanda K. Ziemann, David W. Messinger, David W. Messinger, James A. Albano, James A. Albano, William F. Basener, William F. Basener, } "Assessing the impact of background spectral graph construction techniques on the topological anomaly detection algorithm", Proc. SPIE 8390, Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XVIII, 83901Z (24 May 2012); doi: 10.1117/12.918889; https://doi.org/10.1117/12.918889

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