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In this paper, we examine the accuracy of manifold coordinate representations as a reduced representation of a hyperspectral imagery (HSI) lookup table (LUT) for bathymetry retrieval. We also explore on a more limited basis the potential for using these coordinates for modeling other in water properties. Manifold coordinates are chosen because they are a datadriven intrinsic set of coordinates, which naturally parameterize nonlinearities that are present in HSI of water scenes. The approach is based on the extraction of a reduced dimensionality representation in manifold coordinates of a sufficiently large representative set of HSI. The manifold coordinates are derived from a scalable version of the isometric mapping algorithm. In the present and in our earlier works, these coordinates were used to establish an interpolating LUT for bathymetric retrieval by associating the representative data with ground truth data, in this case from a Light Detection and Ranging (LIDAR) estimate in the representative area. While not the focus of the present paper, the compression of LUTs could also be applied, in principle, to LUTs generated by forward radiative transfer models, and some preliminary work in this regard confirms the potential utility for this application. In this paper, we analyze the approach using data acquired by the Portable Hyperspectral Imager for Low-Light Spectroscopy (PHILLS) hyperspectral camera over the Indian River Lagoon, Florida, in 2004. Within a few months of the PHILLS overflights, Scanning Hydrographic Operational Airborne LIDAR Survey, LIDAR data were obtained for a portion of this study area, principally covering the beach zone and, in some instances, portions of contiguous river channels. Results demonstrate that significant compression of the LUTs is possible with little loss in retrieval accuracy. Index Terms--Bathymetry, bottom type, hyperspectral imagery, isometric mapping, manifold coordinates, manifold learning, nonlinear estimation, optical data processing, optical image processing, remote sensing, spectral analysis, spectroscopy, water.

In recent publications, we have presented a data-driven approach to representing the nonlinear structure of hyperspectral imagery using manifold coordinates. The approach relies on graph methods to derive geodesic distances on the high-dimensional hyperspectral data manifold. From these distances, a set of intrinsic manifold coordinates that parameterizes the data manifold is derived. Scaling the solution relied on divide-conquer-and-merge strategies for the manifold coordinates because of the computational and memory scaling of the geodesic coordinate calculations. In this paper, we improve the scaling performance of isometric mapping (ISOMAP) and achieve full-scene global manifold coordinates while removing artifacts generated by the original methods. The CPU time of the enhanced ISOMAP approach scales as O(N [log.sup.2](N)), where N is the number of samples, while the memory requirement is bounded by O(N log(N)). Full hyperspectral scenes of O([10.sup.6]) samples or greater are obtained via a reconstruction algorithm, which allows insertion of large numbers of samples into a representative 'backbone' manifold obtained for a smaller but representative set of O([10.sup.5]) samples. We provide a classification example using a coastal hyperspectral scene to illustrate the approach. Index Terms--Automatic classification, hyperspectral imagery, isometric mapping (ISOMAP), Jeffries-Matsushita distance, manifold coordinates, manifold geodesics, manifold learning, multidimensional scaling, nonlinear dimensionality reduction, tree searching, trees (graphs), Vantage Point Forest, vantage point tree, Virginia Coast Reserve.

A new algorithm for exploiting the nonlinear structure of hyperspectral imagery is developed and compared against the de facto standard of linear mixing. This new approach seeks a manifold coordinate system that preserves geodesic distances in the high-dimensional hyperspectral data space. Algorithms for deriving manifold coordinates, such as isometric mapping (ISOMAP), have been developed for other applications. ISOMAP guarantees a globally optimal solution, but is computationally practical only for small datasets because of computational and memory requirements. Here, we develop a hybrid technique to circumvent ISOMAP's computational cost. We divide the scene into a set of smaller tiles. The manifolds derived from the individual tiles are then aligned and stitched together to recomplete the scene. Several alignment methods are discussed. This hybrid approach exploits the fact that ISOMAP guarantees a globally optimal solution for each tile and the presumed similarity of the manifold structures derived from different tiles. Using land-cover classification of hyperspectral imagery in the Virginia Coast Reserve as a test case, we show that the new manifold representation provides better separation of spectrally similar classes than one of the standard linear mixing models. Additionally, we demonstrate that this technique provides a natural data compression scheme, which dramatically reduces the number of components needed to model hyperspectral data when compared with traditional methods such as the minimum noise fraction transform. Index Terms--Airborne Visible Imaging Spectrometer (AVIRIS), bidirectional reflectance distribution function (BRDF), compression, Cuprite, geodesic distance, hyperspectral, isometric mapping (ISOMAP), land-cover classification, linear mixture, local linear embedding (LLE), manifold coordinates, nonlinearity, PROBE2, Virginia Coast Reserve.

A credit assignment approach to decision-based classifier fusion is developed and applied to the problem of land-cover classification from multiseason airborne hyperspectral imagery. For each input sample, the new method uses a smoothed estimated reliability measure (SERM) in the output domain of the classifiers. SERM requires no additional training beyond that needed to optimize the constituent classifiers in the pool, and its generalization (test) accuracy exceeds that of a number of other extant methods for classifier fusion. Hyperspectral imagery from HyMAP and PROBE2 acquired at three points in the growing season over Smith Island, VA, a barrier island in the Nature Conservancy's Virginia Coast Reserve, serves as the basis for comparing SERM with other approaches. Index Terms--Barrier Islands, decision-based classifier fusion, hyperspectral remote sensing, land-cover classification, maximum estimated reliability measure (MAXERM), multiple classifier systems, multiple classification system, multiseason classification, smooth estimated reliability measure (SERM), Virginia Coast Reserve.

Automatic land cover classification maps were developed from Airborne Hyperspectral Scanner (HyMAP) imagery acquired May 8, 2000 over Smith Island, VA, a barrier island in the Virginia Coast Reserve. Both unsupervised and supervised classification approaches were used to create these products to evaluate relative merits and to develop models that would be useful to natural resource managers at higher spatial resolution than has been available previously. Ground surveys made by us in late October and early December 2000 and again in May, August, and October 2001 and May 2002 provided ground truth data for 20 land cover types. Locations of pure land cover types recorded with global positioning system (GPS) data from these surveys were used to extract spectral end-members for training and testing supervised and cover classification models. Unsupervised exploratory models were also developed using spatial-spectral windows and projection pursuit (PP), a class of algorithms suitable for extracting multimodal views of the data. PP projections were clustered by ISODATA to produce an unsupervised classification. Supervised models, which relied on the GPS data, used only spectral inputs because for some categories in particular areas, labeled data consisted of isolated single-pixel waypoints. Both approaches to the classification problem produced consistent results for some categories such as Spartina alterniflora, although there were differences for other categories. Initial models for supervised classification based on 112 HyMAP spectra, labeled in ground surveys, obtained reasonably consistent results for many of the dominant categories, with a few exceptions. For an invasive plant species, Phragmites australis, a particular concern of natural resource managers, this approach initially had an excessively high false-alarm rate. Increasing the number of spectral training samples by an order of magnitude and making concomitant improvements to the georectification led to dramatic improvements in this and other categories. The unsupervised spatial-spectral approach also found a cluster closely associated with Phragmites patches near the thicket boundary, but this approach did not identify the exposed Phragmites. Examples of in situ reflectance measurements obtained with an Analytical Spectral Devices FR spectrometer in early May 2001 are compared against HyMAP image spectra at model-predicted pixels and at validated GPS waypoints. Index Terms--Barrier islands, hyperspectral, in situ spectrometry, invasive plant species, land cover classification, neural networks, principle component analysis, projection pursuit, supervised classification, unsupervised classification.

We demonstrate the ability of interferometric radar imagery to determine both relative and absolute surface velocities in the open ocean. Absolute phase calibration is accomplished by noting the azimuthal displacement of range-travelling targets - demonstrating for the first time that under favorable circumstances phase calibration can be achieved in open-ocean in the absence of ground truth. The high resolution of radar imagery permits observation of sharp velocity discontinuities, e.g. the Gulf Stream boundary and the wave field. The recent SIR-C/X-SAR shuttle missions dramatically emphasize the experimental and observational aspects of space-based radar. The combination of absolute velocities, high spatial resolution, and wide-area coverage suggest that interferometric radar imagery can provide a unique and powerful aid both for studies of global circulation patterns and detailed analysis of slope/shelf water interactions with ocean currents. In particular, we employ this measurement of the surface currents and wave field near a velocity front to help refine and bound results of our modeling of calculated radar images of the front. The results of this paper are compared with available ground truth.

Bright linear features have been observed in radar imagery taken near the Gulf Stream (GS) boundary on two separate occasions. In each case, these have been observed directly over strong current convergences. Progress has been made in understanding the origin of these signatures through simulations that incorporate environmental forcing from the winds and currents. These simulations significantly underestimate the backscatter unless wave-breaking (WB) effects are included at least approximately. Using a new, quasistatistical procedure that generalizes and quantifies earlier procedures for including WB effects, we have been able to successfully simulate the magnitude and behavior of these signatures. The approach combines the statistically based, composite model of radar backscatter with a deterministic feature model that relates backscatter from breaking waves to a particular geometrical model of a spilling breaker. This is accomplished using localized criteria, defined by local wave crest acceleration, to determine the probability of breaking, and by extending the feature model so that its unknown parameters may be evaluated directly from wave-current interaction calculations. The new approach provides an estimate of the critical crest acceleration of a potentially breaking wave, as a function of wind speed, that agrees with independent measurements. Index Terms - Gulf Stream, radar, wave-breaking, wave-current interaction.