A Family of Spectral Target Signature Transforms: Relationship to the Past, New Transforms, and Sensitivity Tests

Abstract

Previous studies introduced, examined, and tested a variety of registration-free transformations, specifically the diagonal, whitening/dewhitening, and target CV (covariance) transformations, that temporally evolve spectral signatures under varying conditions. Target spectral signatures were transformed using imagery of spatially overlapping regions from datasets collected at different times. This letter shows that these previously studied registration-free transformations can be described using a single general equation and form a subset of a family of valid transforms. Further, this letter finds only a small reduction in target detection results from using nonoverlapping but similar regions to transform target signatures in matched filter searches. The diagonal, whitening/dewhitening, and target CV transformations appear in this formulation as having integral exponent parameter ( = 0 1 2, respectively). These transformed target signatures, used in matched filter searches, were tested on images taken from two very different data collects using different sensors, targets, and backgrounds. In one dataset, the transform was applied to multispectral images taken from an airborne longwave infrared sensor binned to 30 bands. The other dataset used images of a variety of targets that were collected using broad-band, bore-sighted, staring array sensors sensitive to visible, shortwave infrared, midwave infrared, and longwave infrared wavelengths. Transformation performance was tested using target-to-clutter ratio (TCR) and receiver operator characteristic (ROC) curve. Transforms with exponents between 0 and 2 yielded the largest TCR and remained relatively constant. Optimal exponents for the transformation were target dependent for both datasets. Further, only minimal reduction in TCR was observed for transforms ( 2) that had no shared overlapping regions, although the areas used to transform the spectral signatures shared similar content (trees, roads, etc.).

A metric of background candidate assessment for spectral target signature transforms

“…In addition, this work examines whether the average correlation coefficient between histograms of corrected multispectral images histograms can assess background image mismatch, and whether this metric is associated with target detection performance in statistical transforms. This study investigates the accuracy of placing mismatched backgrounds into registration-free algorithms, Manuscript specifically, diagonal, [1], [2] target covariance (CV) [1], [2], and whitening/dewhitening [3], [4] transforms [5]. The average correlation between corrected histograms of multispectral images and target detection performance was tested in a number of situations using linear correlation.…”

“…In one situation, the overlapping areas are systematically displaced from each other from opposite directions. This scenario permits the introduction of backgrounds that did not share any common regions into transforms [5]. Such tests examine the transforms resilience to displacement errors found in registration and airborne global positioning and inertial measurement systems.…”

“…The statistical transforms are tested on images taken from two independent data collects. The TCR assesses the ability to transform spectral signatures as demonstrated earlier [1]- [5] in receiver operator characteristic (ROC) curves. One data collect used an airborne multispectral longwave imager and the other collect used data from a visible/near-infrared sensor.…”

Segmentation Approach and Comparison to Hyperspectral Object Detection Algorithms

“…1) surrounding the object. ACE confines object detection to a narrow cone with angle θ k as shown in Figure 1 Earlier studies [6,7] …”

“…These matrices are associated with image cubes collected at Times 1, 2, as denoted by the subscript. The parameter n distinguishes among the transforms and was previously [6] found to yield accurate statistical transforms for parameter n (0≤n≤2). This study only considers the transform with n=1, the whitening/dewhitening transform [6,7].…”