Commun. Comput. Phys., 5 (2009), pp. 326-349.

Segmentation of Images from Fourier Spectral Data

Anne Gelb 1*, Dennis Cates 1

1 IDepartment of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287 USA.

Received 24 September 2007; Accepted (in revised version) 3 November 2007
Available online 1 August 2008


This paper designs a segmentation method for an image based on its Fourier spectral data. An edge map is generated directly from the Fourier coefficients without first reconstructing the image in pixelated form. Consequently the internal boundaries of the edge map are not blurred by any (filtered) Fourier reconstruction. The edge map is then processed with an edge linking segmentation algorithm. We include examples from magnetic resonance imaging (MRI). Our results illustrate some potential benefits of using high order methods in imaging.

AMS subject classifications: 42A50, 65D17, 68U10

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Key words: Fourier coefficients, edge detection, segmentation.

*Corresponding author.
Email: (A. Gelb), (D. Cates)

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