A family of spectral target signature transforms: relationship to the past, new transforms, and sensitivity tests

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 n (n = 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 (O < n < 2) that had no shared overlapping regions, although the areas used to transform the spectral signatures shared similar content (trees, roads, etc.).