La Comedia Cordobesa

The results of a comparative analysis of stochastic background characterization techniques have led to many observations about the way each method attempts to match the source of detection interference, improve the multivariate normality of the data, and handle the influence of target contamination. The main experiment removed the influence of target contamination through perfect exclusion and each technique improved the multivariate normality of the background to a level where small variations did not equate to improved detection performance. The observed differences in average false alarm rate (AFAR) are therefore more closely related to the ability of each technique to match the interference-causing false alarms. In the direct comparison of detection results, the RX sliding window and pre-clustering using the class mean neighbor guided – mode method consistently outperformed the scene-wide and target approach backgrounds. Improvements in the AFAR of one-tenth to two orders of magnitude were observed for all pixels on low and high contrast targets in the Forest Radiance I Run05 and Desert Radiance II Run03 images. Throughout the experiment, observations were made which may assist in the practical implementation of these methods. Possibilities for additional experimentation to further inform real world applications of background characterization were also noted.

For the target approach method, the scene-wide statistics provided a good matched filter background for an image with a relatively good measure of multivariate normality. The forest scene, with the targets removed, did not stray far enough from normality to confound detection results. The desert scene, however, provided an example of scene-wide statistics that failed as a

background. In this case, it was suggested that the scene-wide measure of MVN or a measure of sensor noise levels would prompt the selection of a mixed target approach region to serve as background. The influence of target contamination was proven using the target approach method as target pixels were implanted in a target-free data pool and a steady change in the shape of the covariance matrix was observed. This change was correlated to a decrease in the performance of detection with only a few pixels added to a pool of 18,000 samples.

The RX sliding window algorithm with four concentric windows was tested to identify the proper sizing for the covariance window. The commonly accepted rule of selecting the number of samples equal to ten times the number of bands held for these targets and backgrounds. This result conflicted with the application of RX using selection of the most multivariate normal background. The number of samples used to estimate the covariance created a statistical stability that was more important than the statistical MVN in the application of the matched filter. In practical application, the type of data, noise levels, and scene clutter content will change this relationship. Additionally, the possibility of target contamination, which is driven by the level of a priori knowledge about the target and scene, must influence window size selection. The trade space includes the desire to capture the immediate surroundings of the target, the MVN of the data in the covariance window, the possibility of including targets, and the influence those targets will have on the background. The use of spatial and spectral target exclusion is extremely valuable when needed, but can lead to suboptimal performance if improperly implemented.

Pre-clustering was performed by classifying the imagery, developing statistics using the classmaps, and then deciding how to apply those statistics to the detection problem. K-Means and stochastic expectation maximization (SEM) were compared, and SEM was shown to generate backgrounds that provided modest improvements in detection but considerable improvements in background MVN. Eight methods were developed to apply pre-clustered statistics to detection by the selection of a local or class mean, and by guiding of class selection by the target spectrum, the pixel class assignment, or the class assignment of the neighbors of the test pixel (for use in either the mode or linear mixture of class statistics). The target guided methods required the use of a statistical distance classifier (SDC) in order to allow for predictability in the selection of the best background class given the target spectrum. The other methods, which used statistics from more than one class, employed the results of SEM classification. From the comparison of detection results, the class mean neighbor guided – mode (CMNG-M) technique demonstrated an advantage over other pre-clustering background characterization methods. CMNG-M was the best method for the desert scene and performed well in the forest scene for the detection of low contrast targets. The local mean target guided method performed well for the high contrast targets in the forest scene and represents a conceptual counterpart to the CMNG-M method. The pixel guided and neighbor guided – mixture methods consistently underperformed the other techniques.

The influence of target on the pre-clustered backgrounds was studied using the SAM algorithm as well as the matched filter results of a given method with a contaminated background. Several levels of exclusion were tested, and the best detection performance was achieved when spectral angle mapper (SAM)

was used to eliminate all of the target pixels. While a large number of background pixels were excluded during pre-filtering to this level, it was apparent that the species in the overlapping portion of the SAM detection statistic distribution did not represent the highest likelihood matched filter false alarm. In this case, mixing modalities between the pre-filtering and detection algorithm seemed to provide an advantage.

The removal of pixels from the background using statistical distance exclusion (SDE) was another method studied. Discarding the outliers of the background distribution served to remove pixels that did not truly belong to their assigned class and to increase the multivariate normality of the background. MVN improvements were demonstrated, but SDE did not translate into improved detection in every case. In these instances, the benefit of including outliers in the distribution in order to suppress the unwanted signal outweighed the benefit from improved MVN.

An alternative mean subtraction method, which was aimed at improved detection for low contrast targets, was tested using all of the low contrast targets from the forest scene test set. The method provided improvement for two targets with an original AFAR of greater than one-tenth, but was detrimental to two targets with an AFAR less than one-tenth. This technique may be valuable only for extremely low contrast targets.