# American Institute of Mathematical Sciences

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
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