Modeling Coastal Waters from Hyperspectral Imagery using Manifold Coordinates

In [1] [2], we introduced a direct data driven method of modeling nonlinear structure in hyperspectral imagery based on Isometric Mapping [15]. More recently, we have further improved the scaling of the approach [2], making it a practical method for large-scale hyperspectral scenes. The new method extracts a set of data manifold coordinates that directly parameterize nonlinearities present in hyperspectral imagery, both on land and in the water column. In the water column, this is particularly important because of the nonlinear, attenuating properties of the medium. In this paper, we model hyperspectral imagery acquired by the NRL PHILLS [5] at the Indian River Lagoon, Florida in July 2004. In our previous efforts [3] using a small subset of data derived from the surf zone outside of the lagoon, dominant manifold coordinates were shown to parameterize bathymetry directly with a high degree of correlation to a radiative transfer look-up table (LUT) approach. In the present work, we construct a full scene manifold coordinate representation and use this as the basis of a LUT for samples with known depths as determined by the SHOALS LIDAR. Sequestered test data presented to the manifold based LUT yield a mean estimated depth which differs from the LOAR retrieved depth by less than 0.44 m for depths between 0-10 m with a standard deviation less than 1.2 m.