August  2014, 8(3): 885-900. doi: 10.3934/ipi.2014.8.885

Shape reconstruction from images: Pixel fields and Fourier transform

1. 

Department of Mathematics, Tampere University of Technology, PO Box 553, 33101 Tampere, Finland, Finland

Received  December 2013 Revised  April 2014 Published  August 2014

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.
Citation: Matti Viikinkoski, Mikko Kaasalainen. Shape reconstruction from images: Pixel fields and Fourier transform. Inverse Problems & Imaging, 2014, 8 (3) : 885-900. doi: 10.3934/ipi.2014.8.885
References:
[1]

B. Bertotti, P. Farinella and D. Vokrouhlický, Physics of the Solar System, Astrophysics and Space Science Library (Kluwer), 293 (2003). doi: 10.1007/978-94-010-0233-2.  Google Scholar

[2]

B. Carry, C. Dumas, M. Kaasalainen and 9 colleagues, Physical properties of 2 Pallas, Icarus, 205 (2010), 460-472. doi: 10.1016/j.icarus.2009.08.007.  Google Scholar

[3]

B. Carry, M. Kaasalainen, W. J. Merline and 12 colleagues, Shape modeling technique KOALA validated by ESA Rosetta at (21) Lutetia, Planet. Space Sci., 66 (2012), 200-212. doi: 10.1016/j.pss.2011.12.018.  Google Scholar

[4]

M. Delbó, The Nature of Near-Earth Asteroids from the Study of Their Thermal Infrared Emission, Ph.D. thesis, Freie Universität Berlin, 2004. Google Scholar

[5]

M. Kaasalainen, L. Lamberg, K. Lumme and E. Bowell, Interpretation of lightcurves of atmosphereless bodies. I. General theory and new inversion schemes, Astron. Astrophys., 259 (1992), 318-332. Google Scholar

[6]

M. Kaasalainen, J. Torppa and K. Muinonen, Optimization methpds for asteroid lightcurves inversion. II. The complete inverse problem, Icarus, 153 (2001), 37-51. doi: 10.1006/icar.2001.6674.  Google Scholar

[7]

M. Kaasalainen and L. Lamberg, Inverse problems of generalized projection operators, Inverse Problems, 22 (2006), 749-769. doi: 10.1088/0266-5611/22/3/002.  Google Scholar

[8]

M. Kaasalainen, Multimodal inverse problems: Maximum compatibility estimate and shape reconstruction, Inverse Problems and Imaging, 5 (2011), 37-57. doi: 10.3934/ipi.2011.5.37.  Google Scholar

[9]

M. Kaasalainen and M. Viikinkoski, Shape reconstruction of irregular bodies with multiple complementary data sources, Astron. Astrophys, 543 (2012), 9pp. doi: 10.1051/0004-6361/201219267.  Google Scholar

[10]

M. Kaasalainen and H. Nortunen, Compact YORP formulation and stability analysis, Astron. Astrophys, 558 (2013), 8pp. doi: 10.1051/0004-6361/201322221.  Google Scholar

[11]

D. Nesvorný and D. Vokrouhlický, Analytic theory for the Yarkovsky-O'Keefe-Radzievski-Paddack effect on obliquity, Astron. J., 136 (2008), 291-299. doi: 10.1088/0004-6256/136/1/291.  Google Scholar

[12]

S. J. Ostro, R. S. Hudson, L. Benner and 4 colleagues, Asteroid Radar Astronomy, in Asteroids III, Arizona University Press, 151, 2002. Google Scholar

[13]

A. R. Thompson, J. M. Moran and G. W. Swenson, Interferometry and Synthesis in Radio Astronomy, Interferometry and Synthesis in Radio Astronomy, Second Edition, 2007. doi: 10.1002/9783527617845.  Google Scholar

show all references

References:
[1]

B. Bertotti, P. Farinella and D. Vokrouhlický, Physics of the Solar System, Astrophysics and Space Science Library (Kluwer), 293 (2003). doi: 10.1007/978-94-010-0233-2.  Google Scholar

[2]

B. Carry, C. Dumas, M. Kaasalainen and 9 colleagues, Physical properties of 2 Pallas, Icarus, 205 (2010), 460-472. doi: 10.1016/j.icarus.2009.08.007.  Google Scholar

[3]

B. Carry, M. Kaasalainen, W. J. Merline and 12 colleagues, Shape modeling technique KOALA validated by ESA Rosetta at (21) Lutetia, Planet. Space Sci., 66 (2012), 200-212. doi: 10.1016/j.pss.2011.12.018.  Google Scholar

[4]

M. Delbó, The Nature of Near-Earth Asteroids from the Study of Their Thermal Infrared Emission, Ph.D. thesis, Freie Universität Berlin, 2004. Google Scholar

[5]

M. Kaasalainen, L. Lamberg, K. Lumme and E. Bowell, Interpretation of lightcurves of atmosphereless bodies. I. General theory and new inversion schemes, Astron. Astrophys., 259 (1992), 318-332. Google Scholar

[6]

M. Kaasalainen, J. Torppa and K. Muinonen, Optimization methpds for asteroid lightcurves inversion. II. The complete inverse problem, Icarus, 153 (2001), 37-51. doi: 10.1006/icar.2001.6674.  Google Scholar

[7]

M. Kaasalainen and L. Lamberg, Inverse problems of generalized projection operators, Inverse Problems, 22 (2006), 749-769. doi: 10.1088/0266-5611/22/3/002.  Google Scholar

[8]

M. Kaasalainen, Multimodal inverse problems: Maximum compatibility estimate and shape reconstruction, Inverse Problems and Imaging, 5 (2011), 37-57. doi: 10.3934/ipi.2011.5.37.  Google Scholar

[9]

M. Kaasalainen and M. Viikinkoski, Shape reconstruction of irregular bodies with multiple complementary data sources, Astron. Astrophys, 543 (2012), 9pp. doi: 10.1051/0004-6361/201219267.  Google Scholar

[10]

M. Kaasalainen and H. Nortunen, Compact YORP formulation and stability analysis, Astron. Astrophys, 558 (2013), 8pp. doi: 10.1051/0004-6361/201322221.  Google Scholar

[11]

D. Nesvorný and D. Vokrouhlický, Analytic theory for the Yarkovsky-O'Keefe-Radzievski-Paddack effect on obliquity, Astron. J., 136 (2008), 291-299. doi: 10.1088/0004-6256/136/1/291.  Google Scholar

[12]

S. J. Ostro, R. S. Hudson, L. Benner and 4 colleagues, Asteroid Radar Astronomy, in Asteroids III, Arizona University Press, 151, 2002. Google Scholar

[13]

A. R. Thompson, J. M. Moran and G. W. Swenson, Interferometry and Synthesis in Radio Astronomy, Interferometry and Synthesis in Radio Astronomy, Second Edition, 2007. doi: 10.1002/9783527617845.  Google Scholar

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