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Admissible Concentration Factors for Edge Detection from Non-uniform Fourier Data

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Abstract

Edge detection from Fourier data has been emerging in many applications. The concentration factor method has been widely used in detecting edges from Fourier data. We present a theoretic analysis of the concentration factor method for non-uniform Fourier data in this paper. Specifically, we propose admissible conditions for the concentration factors such that the edge detector converges to a smoothed approximation of the jump function. Moreover, we also introduce some specific choices of admissible concentration factors and present estimates of convergence rates correspondingly.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Old Dominion University, Norfolk, VA, 23529, USA

    Guohui Song & Gabe Tucker

  2. Division of Science and Technology, Quincy University, Quincy, IL, 62301, USA

    Congzhi Xia

Authors
  1. Guohui Song
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  2. Gabe Tucker
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  3. Congzhi Xia
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Correspondence to Guohui Song.

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G. Song: Supported in part by National Science Foundation under grants DMS-1521661 and DMS-1939203.

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Song, G., Tucker, G. & Xia, C. Admissible Concentration Factors for Edge Detection from Non-uniform Fourier Data. J Sci Comput 85, 3 (2020). https://doi.org/10.1007/s10915-020-01307-9

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  • DOI: https://doi.org/10.1007/s10915-020-01307-9