Shape reconstruction from images: pixel fields and Fourier transform. (English) Zbl 1302.68301
Summary: We discuss shape reconstruction methods for data presented in various image spaces. We demonstrate the usefulness of the Fourier transform in transferring image data and shape model projections to a domain more suitable for shape inversion. Using boundary contours in images to represent minimal information, we present uniqueness results for shapes recoverable from interferometric and range-Doppler data. We present applications of our methods to adaptive optics, interferometry, and range-Doppler images.
MSC:
68U10 | Computing methodologies for image processing |
68T45 | Machine vision and scene understanding |
65D18 | Numerical aspects of computer graphics, image analysis, and computational geometry |
52B10 | Three-dimensional polytopes |
49N45 | Inverse problems in optimal control |
65J22 | Numerical solution to inverse problems in abstract spaces |
85-08 | Computational methods for problems pertaining to astronomy and astrophysics |
94A08 | Image processing (compression, reconstruction, etc.) in information and communication theory |
Keywords:
inverse problems; three-dimensional polytopes; generalized projections; image analysis; adaptive optics; interferometry; radarReferences:
[1] | B. Bertotti, <em>Physics of the Solar System</em>,, Astrophysics and Space Science Library (Kluwer), 293 (2003) · doi:10.1007/978-94-010-0233-2 |
[2] | B. Carry, Physical properties of 2 Pallas,, Icarus, 205, 460 (2010) · doi:10.1016/j.icarus.2009.08.007 |
[3] | B. Carry, Shape modeling technique KOALA validated by ESA Rosetta at (21) Lutetia,, Planet. Space Sci., 66, 200 (2012) · doi:10.1016/j.pss.2011.12.018 |
[4] | M. Delbó, <em>The Nature of Near-Earth Asteroids from the Study of Their Thermal Infrared Emission</em>,, Ph.D. thesis (2004) |
[5] | M. Kaasalainen, Interpretation of lightcurves of atmosphereless bodies. I. General theory and new inversion schemes,, Astron. Astrophys., 259, 318 (1992) |
[6] | M. Kaasalainen, Optimization methpds for asteroid lightcurves inversion. II. The complete inverse problem,, Icarus, 153, 37 (2001) · doi:10.1006/icar.2001.6674 |
[7] | M. Kaasalainen, Inverse problems of generalized projection operators,, Inverse Problems, 22, 749 (2006) · Zbl 1095.44003 · doi:10.1088/0266-5611/22/3/002 |
[8] | M. Kaasalainen, Multimodal inverse problems: Maximum compatibility estimate and shape reconstruction,, Inverse Problems and Imaging, 5, 37 (2011) · Zbl 1217.68228 · doi:10.3934/ipi.2011.5.37 |
[9] | M. Kaasalainen, Shape reconstruction of irregular bodies with multiple complementary data sources,, Astron. Astrophys, 543 (2012) · doi:10.1051/0004-6361/201219267 |
[10] | M. Kaasalainen, Compact YORP formulation and stability analysis,, Astron. Astrophys, 558 (2013) · doi:10.1051/0004-6361/201322221 |
[11] | D. Nesvorný, Analytic theory for the Yarkovsky-O’Keefe-Radzievski-Paddack effect on obliquity,, Astron. J., 136, 291 (2008) · doi:10.1088/0004-6256/136/1/291 |
[12] | S. J. Ostro, <em>Asteroid Radar Astronomy</em>,, in Asteroids III (2002) |
[13] | A. R. Thompson, <em>Interferometry and Synthesis in Radio Astronomy</em>,, Interferometry and Synthesis in Radio Astronomy (2007) · doi:10.1002/9783527617845 |
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