Estimation of Surface Topography from SAR Imagery Using Shape from Shading Techniques

Abstract In this paper a practical method is demonstrated for estimating topography of natural terrain from the radiometric, or shading, information in a synthetic aperture radar (SAR) image. While this problem has been considered before for radar, methods available in the computer vision literature have not previously been utilized in its solution. We treat this as a computer vision problem, viz. shape from shading (SFS). A review of the relevant characteristics of SAR imagery is presented followed by a formulation of the SFS problem for SAR. Because of the noise inherent in SAR imagery a cost minimization approach is used which allows for noise and incorporates a regularization term in the cost function. Previously developed numerical methods are adapted to SAR imagery by incorporating radar reflectance models and by solving for surface slopes in a rotated system of coordinates—one which represents surface height relative to a plane parallel to the line-of-sight. Two difficulties are recognized. First, unknown reflectance model parameters must be estimated from the image data. Second, shading provides reliable information about the high frequency components of the surface but not the low frequency components. Both difficulties are reduced if auxiliary low resolution surface height information is available. This is demonstrated by combining Shuttle Imaging Radar-B (SIR-B) SAR images with much lower resolution terrain elevation data to construct high resolution terrain elevation estimates. The estimation of Venusian surface topography from Magellan SAR imagery is discussed and methods are suggested for combining shading information with geometric stereo.

[1]  Robert J. Woodham,et al.  Photometric method for determining surface orientation from multiple images , 1980 .

[2]  R. Haralick,et al.  Automatic inference of elevation and drainage models from a satellite image , 1985, Proceedings of the IEEE.

[3]  Rama Chellappa,et al.  Lognormal Random-Field Models and Their Applications to Radar Image Synthesis , 1987 .

[4]  T. Rindfleisch.  Photometric method for lunar topography. , 1966 .

[5]  A. Pentland.  The visual inference of shape : computation from local features , 1982 .

[6]  Rama Chellappa,et al.  A Method for Enforcing Integrability in Shape from Shading Algorithms , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[7]  Wolfgang Keydel,et al.  Application and Experimental Verification of an Empirical Backscattering Cross Section Model for the Earth's Surface , 1982, IEEE Transactions on Geoscience and Remote Sensing.

[8]  Gitta Domik,et al.  Multiple Incidence Angle SIR-B Expenment Over Argentina: Stereo-Radargrammetrc Analysis , 1986, IEEE Transactions on Geoscience and Remote Sensing.

[9]  Ezekiel Bahar,et al.  Full-Wave Theory Applied to Computer-Aided Graphics for 3D Objects , 1987, IEEE Computer Graphics and Applications.

[10]  Robert Thomas Frankot,et al.  Computational vision algorithms for synthetic aperture radar imagery , 1987 .

[11]  Robert T. Frankot.  SAR Image Registration By Multi-Resolution Correlation , 1984, Optics + Photonics.

[12]  H. Ramapriyan,et al.  Automated Matching of Pairs of SIR-B Images for Elevation Mapping , 1986, IEEE Transactions on Geoscience and Remote Sensing.

[13]  Bui Tuong Phong.  Illumination for computer generated pictures , 1975, Commun. ACM.

[14]  Berthold K. P. Horn.  Obtaining shape from shading information , 1989 .

[15]  Fawwaz Ulaby,et al.  Relating Polaization Phase Difference of SAR Signals to Scene Properties , 1987, IEEE Transactions on Geoscience and Remote Sensing.

[16]  J. Head,et al.  Reports: venus: identification of banded terrain in the mountains of ishtar terra. , 1983, Science.

[17]  Michael J. Brooks,et al.  The variational approach to shape from shading , 1986, Comput. Vis. Graph. Image Process..

[18]  Berthold K. P. Horn.  Robot vision , 1986, MIT electrical engineering and computer science series.

[19]  P. Eliason,et al.  Extraction of topographic and spectral albedo information from multispectral images. , 1981 .

[20]  Eric M. Eliason,et al.  Pioneer Venus Radar results altimetry and surface properties , 1980 .

[21]  Paul S. Heckbert,et al.  Survey of Texture Mapping , 1986, IEEE Computer Graphics and Applications.

[22]  A. Fung,et al.  A noncoherent model for microwave emissions and backscattering from the sea surface , 1972 .

[23]  Julian Holtzman,et al.  Radar Image Simulation , 1978, IEEE Transactions on Geoscience Electronics.

[24]  Michael J. Brooks,et al.  Shape and Source from Shading , 1985, IJCAI.

[25]  P. Beckmann,et al.  The scattering of electromagnetic waves from rough surfaces , 1963 .

[26]  B. Huneycutt,et al.  An introduction to the interim digital SAR processor and the characteristics of the associated Seasat SAR imagery , 1981 .

[27]  K. Torrance,et al.  Theory for off-specular reflection from roughened surfaces , 1967 .

[28]  Stephen T. Barnard,et al.  A Stochastic Approach to Stereo Vision , 1986, AAAI.

[29]  L. Spetner,et al.  Two statistical models for radar terrain return , 1960 .

[30]  L. C. Graham,et al.  Synthetic interferometer radar for topographic mapping , 1974 .

[31]  Katsushi Ikeuchi,et al.  Numerical Shape from Shading and Occluding Boundaries , 1981, Artif. Intell..

[32]  M. W. Long.  Radar reflectivity of land and sea , 1983 .

[33]  Ikeuchi,et al.  Constructing a Depth Map from Images , 1983 .

[34]  G. Pettengill,et al.  Pioneer Venus Radar results: Geology from images and altimetry , 1980 .

[35]  Rama Chellappa,et al.  Model Based Approaches For Some Image Understanding Problems , 1987, Photonics West - Lasers and Applications in Science and Engineering.

[36]  R L Wildey,et al.  Topography from Single Radar Images , 1984, Science.

[37]  Tomaso Poggio,et al.  Probabilistic Solution of Ill-Posed Problems in Computational Vision , 1987 .

[38]  Donald E. Barrick,et al.  Rough Surface Scattering Based on the Specular Point Theory , 1968 .