Terrain analysis using radar shape-from-shading

This paper develops a maximum a posteriori (MAP) probability estimation framework for shape-from-shading (SFS) from synthetic aperture radar (SAR) images. The aim is to use this method to reconstruct surface topography from a single radar image of relatively complex terrain. Our MAP framework makes explicit how the recovery of local surface orientation depends on the whereabouts of terrain edge features and the available radar reflectance information. To apply the resulting process to real world radar data, we require probabilistic models for the appearance of terrain features and the relationship between the orientation of surface normals and the radar reflectance. We show that the SAR data can be modeled using a Rayleigh-Bessel distribution and use this distribution to develop a maximum likelihood algorithm for detecting and labeling terrain edge features. Moreover, we show how robust statistics can be used to estimate the characteristic parameters of this distribution. We also develop an empirical model for the SAR reflectance function. Using the reflectance model, we perform Lambertian correction so that a conventional SFS algorithm can be applied to the radar data. The initial surface normal direction is constrained to point in the direction of the nearest ridge or ravine feature. Each surface normal must fall within a conical envelope whose axis is in the direction of the radar illuminant. The extent of the envelope depends on the corrected radar reflectance and the variance of the radar signal statistics. We explore various ways of smoothing the field of surface normals using robust statistics. Finally, we show how to reconstruct the terrain surface from the smoothed field of surface normal vectors. The proposed algorithm is applied to various SAR data sets containing relatively complex terrain structure

Linear Differential Constraints for Photo-polarimetric Height Estimation

In this paper we present a differential approach to photo-polarimetric shape estimation. We propose several alternative differential constraints based on polarisation and photometric shading information and show how to express them in a unified partial differential system. Our method uses the image ratios technique to combine shading and polarisation information in order to directly reconstruct surface height, without first computing surface normal vectors. Moreover, we are able to remove the non-linearities so that the problem reduces to solving a linear differential problem. We also introduce a new method for estimating a polarisation image from multichannel data and, finally, we show it is possible to estimate the illumination directions in a two source setup, extending the method into an uncalibrated scenario. From a numerical point of view, we use a least-squares formulation of the discrete version of the problem. To the best of our knowledge, this is the first work to consider a unified differential approach to solve photo-polarimetric shape estimation directly for height. Numerical results on synthetic and real-world data confirm the effectiveness of our proposed method.Comment: To appear at International Conference on Computer Vision (ICCV), Venice, Italy, October 22-29, 201

A Dark Target Algorithm for the GOSAT TANSO-CAI Sensor in Aerosol Optical Depth Retrieval over Land

Cloud and Aerosol Imager (CAI) onboard the Greenhouse Gases Observing Satellite (GOSAT) is a multi-band sensor designed to observe and acquire information on clouds and aerosols. In order to retrieve aerosol optical depth (AOD) over land from the CAI sensor, a Dark Target (DT) algorithm for GOSAT CAI was developed based on the strategy of the Moderate Resolution Imaging Spectroradiometer (MODIS) DT algorithm. When retrieving AOD from satellite platforms, determining surface contributions is a major challenge. In the MODIS DT algorithm, surface signals in the visible wavelengths are estimated based on the relationships between visible channels and shortwave infrared (SWIR) near the 2.1 µm channel. However, the CAI only has a 1.6 µm band to cover the SWIR wavelengths. To resolve the difficulties in determining surface reflectance caused by the lack of 2.1 μm band data, we attempted to analyze the relationship between reflectance at 1.6 µm and at 2.1 µm. We did this using the MODIS surface reflectance product and then connecting the reflectances at 1.6 µm and the visible bands based on the empirical relationship between reflectances at 2.1 µm and the visible bands. We found that the reflectance relationship between 1.6 µm and 2.1 µm is typically dependent on the vegetation conditions, and that reflectances at 2.1 µm can be parameterized as a function of 1.6 µm reflectance and the Vegetation Index (VI). Based on our experimental results, an Aerosol Free Vegetation Index (AFRI2.1)-based regression function connecting the 1.6 µm and 2.1 µm bands was summarized. Under light aerosol loading (AOD at 0.55 µm < 0.1), the 2.1 µm reflectance derived by our method has an extremely high correlation with the true 2.1 µm reflectance (r-value = 0.928). Similar to the MODIS DT algorithms (Collection 5 and Collection 6), a CAI-applicable approach that uses AFRI2.1 and the scattering angle to account for the visible surface signals was proposed. It was then applied to the CAI sensor for AOD retrieval; the retrievals were validated by comparisons with ground-level measurements from Aerosol Robotic Network (AERONET) sites. Validations show that retrievals from the CAI have high agreement with the AERONET measurements, with an r-value of 0.922, and 69.2% of the AOD retrieved data falling within the expected error envelope of ± (0.1 + 15% AODAERONET)

Brewster-angle measurements of sea-surface reflectance using a high resolution spectroradiometer

This paper describes the design, construction and testing of a ship-borne spectroradiometer based on an imaging spectrograph and cooled CCD array with a wavelength range of 350-800 nm and 4 nm spectral sampling. The instrument had a minimum spectral acquisition time of 0.1 s, but in practice data were collected over periods of 10 s to allow averaging of wave effects. It was mounted on a ship's superstructure so that it viewed the sea surface from a height of several metres at the Brewster angle (53 degrees) through a linear polarizing filter. Comparison of sea-leaving spectra acquired with the polarizer oriented horizontally and vertically enabled estimation of the spectral composition of sky light reflected directly from the sea surface. A semi-empirical correction procedure was devised for retrieving water-leaving radiance spectra from these measurements while minimizing the influence of reflected sky light. Sea trials indicated that reflectance spectra obtained by this method were consistent with the results of radiance transfer modelling of case 2 waters with similar concentrations of chlorophyll and coloured dissolved organic matter. Surface reflectance signatures measured at three locations containing blooms of different phytoplankton species were easily discriminated and the instrument was sufficiently sensitive to detect solar-stimulated fluorescence from surface chlorophyll concentrations down to 1 mg m−3

Capturing and Reconstructing the Appearance of Complex {3D} Scenes

In this thesis, we present our research on new acquisition methods for reflectance properties of real-world objects. Specifically, we first show a method for acquiring spatially varying densities in volumes of translucent, gaseous material with just a single image. This makes the method applicable to constantly changing phenomena like smoke without the use of high-speed camera equipment. Furthermore, we investigated how two well known techniques -- synthetic aperture confocal imaging and algorithmic descattering -- can be combined to help looking through a translucent medium like fog or murky water. We show that the depth at which we can still see an object embedded in the scattering medium is increased. In a related publication, we show how polarization and descattering based on phase-shifting can be combined for efficient 3D~scanning of translucent objects. Normally, subsurface scattering hinders the range estimation by offsetting the peak intensity beneath the surface away from the point of incidence. With our method, the subsurface scattering is reduced to a minimum and therefore reliable 3D~scanning is made possible. Finally, we present a system which recovers surface geometry, reflectance properties of opaque objects, and prevailing lighting conditions at the time of image capture from just a small number of input photographs. While there exist previous approaches to recover reflectance properties, our system is the first to work on images taken under almost arbitrary, changing lighting conditions. This enables us to use images we took from a community photo collection website