A new data-driven approach to modeling coastal bathymetry from hyperspectral imagery using manifold coordinates

Recently a new approach to modeling nonlinear structure in hyperspectral imagery was introduced [Bachmann et al., 2005]. The new method is a data-driven approach which extracts a set of coordinates that directly parameterize nonlinearities present in hyperspectral imagery, both on land and in the water column. The motivation for such a parameterization and its applicability to coastal bathymetry is based on the physical expectation that in shallow waters in a region that is homogeneous in bottom type and dissolved constituents, the reflectance at any particular wavelength should decay exponentially as a function of depth. If the rate varies with wavelength, then the reflectance should best be described by a nonlinear sheet or manifold in spectral space. Other changes in the structure of the data manifold can be expected as inherent optical properties (IOP) and bottom type vary. The manifold coordinates can be used to extract information concerning the latter as well. In the present work, we compare a manifold coordinate based approach to extracting bathymetry with prior work [Maness et al., 2005] based on radiative transfer modeling; the latter defined a set of look-up tables produced by repeated execution of a radiative transfer software package known as EcoLight. Comparative results for the two approaches are presented for the same Portable Hyperspectral Imager for low-light spectroscopy (PHILLS) airborne hyperspectral scene, acquired over the Indian River Lagoon in Florida in July 2004 and described in [Maness et al., 2005].