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:
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