A Radiative Transfer Model-Based Multi-Layered Regression Learning to Estimate Shadow Map in Hyperspectral Images

Abstract

The application of Empirical Line Method (ELM) for hyperspectral Atmospheric Compensation (AC) premises the underlying linear relationship between a material’s reflectance and appearance. ELM solves the Radiative Transfer (RT) equation under specialized constraint by means of in-scene white and black calibration panels. The reflectance of material is invariant to illumination. Exploiting this property, we articulated a mathematical formulation based on the RT model to create cost functions relating variably illuminated regions within a scene. In this paper, we propose multi-layered regression learning-based recovery of radiance components, i.e., total ground-reflected radiance and path radiance from reflectance and radiance images of the scene. These decomposed components represent terms in the RT equation and enable us to relate variable illumination. Therefore, we assume that Hyperspectral Image (HSI) radiance of the scene is provided and AC can be processed on it, preferably with QUick Atmospheric Correction (QUAC) algorithm. QUAC is preferred because it does not account for surface models. The output from the proposed algorithm is an intermediate map of the scene on which our mathematically derived binary and multi-label threshold is applied to classify shadowed and non-shadowed regions. Results from a satellite and airborne NADIR imagery are shown in this paper. Ground truth (GT) is generated by ray-tracing on a LIDAR-based surface model in the form of contour data, of the scene. Comparison of our results with GT implies that our algorithm’s binary classification shadow maps outperform other existing shadow detection algorithms in true positive, which is the detection of shadows when it is in ground truth. It also has the lowest false negative i.e., detecting non-shadowed region as shadowed, compared to existing algorithms.