RX (Reed-Xiaoli) Anomaly Detection in ENVI
This Help Article describes the RX (Reed-Xiaoli) Anomaly Detection Tool in further detail. This module is available as a plug-in for ENVI 4.2 and has been incorporated into later versions of ENVI.
In surveillance applications, we are often interested in anomalies that are relatively small objects with low probabilities in an image, but do not belong to the image background. These anomalous targets are generally unknown a priori and cannot be identified from an image scene visually. An anomaly detector does not extract targets randomly. It extracts unknown targets, which are supposed to be interesting and meaningful, particularly spectrally distinct from their surroundings. The techniques developed for detecting anomalous targets in a blind scene where targets are generally unknown and small work via suppression of image background. A commonly used method is to use the sample spectral correlation (or covariance) matrix for background suppression. Therefore, such detection can be viewed as sample correlation-based spectral target detection. Anomaly detectors work in a functional form of a matched filter with a different matched signature (basically, the pixel vector r).
How RXD Works:
Mathematically, RX detection can be considered as an inverse operation of the principal components analysis (PCA). PCA decorrelates the data matrix in such a matter that different amounts of the image information can be preserved in separate component images, each of which represents a different piece of uncorrelated image information. The strength of PCA is to compress most of significant image information into a few major principal components specified by the eigenvectors of the sample covariance matrix that correspond to large eigenvalues. If the image data contain interesting target samples which only occur with low probabilities in the data (i.e. the size of the target samples is small), the targets will not be shown in major principal components, but rather in minor components specified by small eigenvalues. The RX equation will produce very high values for anomalous values that have very small eigenvalues in a PC analysis. One problem with this approach is how to separate small eigenvalues from noise variance in the data. This is determined by the intrinsic dimensionality of the data and can be derived mathematically using the spectral decomposition of a covariance matrix.
Specifically, for each image pixel vector r, RX detection implements a filter specified by:
UTD (Uniform Target Detector) variant:
The UTD uses the unity vector as its matched signature. This basically has the effect of acting as a background detector, as background signatures are detected as anomalies because anomalous targets are assumed to have radiance uniformly distributed over all spectral bands. If you then use this in combination with the RX detector, as a subtractive term, you can enhance the results obtained from the RX analysis.
Benefits of RX:
- RXD is an ideal tool for the novice spectral exploiter, as nothing more is required than selecting the input and output files.
- The results are unambiguous, and quite excellent over a range of cases.
Potential limitations of RX:
- Anomaly detectors cannot classify the targets it detects since it can not discriminate its detected targets from one another.
- Bad pixels or lines will appear as being anomalous, but will not affect the detection of other, valid anomalies
- User interpretation is required to analyze the results.
Review on 12/31/2013 MM