Anomaly Clustering in Hyperspectral Images
Timothy J. Doster
a
, David S. Ross
a
, David W. Messinger
b
, William F. Basener
a
a
Rochester Institute of Technology School of Mathematical Sciences, Rochester, NY;
b
Rochester Institute of Technology Center for Imaging Science, Rochester, NY
ABSTRACT
The topological anomaly detection algorithm (TAD) differs from other anomaly detection algorithms in that
it uses a topological/graph-theoretic model for the image background instead of modeling the image with a
Gaussian normal distribution. In the construction of the model, TAD produces a hard threshold separating
anomalous pixels from background in the image. We build on this feature of TAD by extending the algorithm
so that it gives a measure of the number of anomalous objects, rather than the number of anomalous pixels, in
a hyperspectral image. This is done by identifying, and integrating, clusters of anomalous pixels via a graph
theoretical method combining spatial and spectral information. The method is applied to a cluttered HyMap
image and combines small groups of pixels containing like materials, such as those corresponding to rooftops and
cars, into individual clusters. This improves visualization and interpretation of objects.
Keywords: graph theory, TAD, clustering
1. INTRODUCTION
A hyperspectral image, in contrast to a multispectral image, has in general hundreds of spectral bands instead of
one to ten spectral bands. For example, in the Cooke City image that is used throughout the paper, there are 126
channels
1
. A normal digital image can be viewed as having three spectral bands (blue, red, and green), but in
hyperspectral images a more extensive and continuous part of the light spectrum is represented. Hyperspectral
images include spectral bands representing the visible, near-infrared, and shortwave infrared and thus are favored
over multispectral images for some applications such as forestry and crop analysis as well as military exercises.
Clustering is the grouping of like pixels from an image together based on their characteristics, typically their
spectral response. The level of cluster differentiation is a choice of the user. For example the user can choose to
cluster all trees into one group or have a cluster of elms, pines, and oak trees. An anomalous, for this research,
is one that has some degree of dissimilarity from the rest of the pixels in the image. For most algorithms this
measure is based solely on the spectral information.
In more classic applications of anomaly detection Gaussian statistics are used - this however, from a theoret-
ical aspect, would require that the image’s pixels follow a normal distribution. For a naturally-occurring image,
i.e. one that is not artificially created, this will not be the case. The most popular of these detection algorithms,
which we will briefly describe in the next section is the RX algorithm
2
. The Topological Anomaly Detection
Algorithm
3
, TAD, addresses this shortcoming in the RX Algorithm. The output of TAD however only declares
anomalous pixels, it does not give a true count of the number of anomalous objects in an image. For example it
may be advantageous to have all the anomalous pixels making up a camouflage net be grouped together and called
one whole anomaly. The extension to the TAD algorithm discussed in this paper does just that. It improves
the visualization of anomalies by differentiating between point anomalies and those that belong to a larger group.
Further author information: (Send correspondence to W.F.B)
W.F.B: E-mail: wfbsma@rit.edu
Algorithms and Technologies for Multispectral, Hyperspectral, and Ultraspectral Imagery XV,
edited by Sylvia S. Shen, Paul E. Lewis, Proc. of SPIE Vol. 7334, 73341P · © 2009 SPIE
CCC code: 0277-786X/09/$18 · doi: 10.1117/12.818407
Proc. of SPIE Vol. 7334 73341P-1