Shape reconstruction from images: Pixel fields and Fourier transform

Matti Viikinkoski; Mikko Kaasalainen

doi:10.3934/ipi.2014.8.885

Article Contents

2014, Volume 8, Issue 3: 885-900. Doi: 10.3934/ipi.2014.8.885

This issue Previous Article Rellich type theorems for unbounded domains Next Article Learning circulant sensing kernels

Shape reconstruction from images: Pixel fields and Fourier transform

Matti Viikinkoski^1, and
Mikko Kaasalainen^1,

1.
Department of Mathematics, Tampere University of Technology, PO Box 553, 33101 Tampere

Received: December 2013

Revised: April 2014

Published: August 2014

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Abstract

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.

Keywords:

Mathematics Subject Classification: 68U05, 68T45, 65D18, 52B10, 49N45, 65J22, 85-08.

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