The variational approach to shape from shading
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Estimation of surface topography from SAR imagery using shape from shading techniques
Artificial Intelligence
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Surface shape and curvature scales
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Tracking level sets by level sets: a method for solving the shape from shading problem
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New Constraints on Data-Closeness and Needle Map Consistency for Shape-from-Shading
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Line and boundary detection in speckle images
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Median radial basis function neural network
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Acquiring height data from a single image of a face using local shape indicators
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Kernel-based classification using quantum mechanics
Pattern Recognition
Novel Shape-From-Shading Methodology with Specular Reflectance Using Wavelet Networks
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Pattern Recognition
Vector transport for shape-from-shading
Pattern Recognition
Surface radiance correction for shape from shading
Pattern Recognition
Smoothing of optical flow using robustified diffusion kernels
Image and Vision Computing
Approximating 3D facial shape from photographs using coupled statistical models
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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.