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Wavelet–Shearlet Edge Detection and Thresholding Methods in 3D

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Excursions in Harmonic Analysis, Volume 3

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

Edge detection in images is well studied, but using full three-dimensional information to display volumes from 3D-imaging devices or to perform pixel-level tracking of moving objects from a sequence of frames in a movie is less well understood. In this work, we study the interplay between 3D wavelet–shearlet edge detection and thresholding in accomplishing these two tasks. We find that a simple thresholding algorithm, modeling the edge image as a sum of two distributions, is very effective.

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References

  1. Aydin T, Yemez Y, Anarim E, Sankur B. Multidirectional and multiscale edge detection via m-band wavelet transform. IEEE Trans Image Process. 1996;5(9):1370–7.

    Article  Google Scholar 

  2. Canny JF. A computational approach to edge detection. IEEE Trans Pattern Anal Mach Intell. 1986; PAMI-8(6):679–98.

    Article  Google Scholar 

  3. Gonzalez RC, Woods RE. Digital image processing. Saddle River: Prentice Hall; 2002.

    Google Scholar 

  4. Guo K, Labate D. Analysis and detection of surface discontinuities using the 3D continuous shearlet transform. Appl Comput Harmon Anal. 2010;30(2):231–49.

    Article  MathSciNet  Google Scholar 

  5. Mallat SA, Hwang WL. Singularity detection and processing with wavelets. IEEE Trans Inf Theory. 1992;38(2):617–643.

    Article  MATH  MathSciNet  Google Scholar 

  6. Mallat SA, Zhong S. Characterization of signals from multiscale edges. IEEE Trans Pattern Anal Mach Intell. 1992;14(7):710–732.

    Article  Google Scholar 

  7. Pietro P. Steerable-scalable kernels for edge detection and junction analysis. Image Vision Comput. 1992;10(10):663–72.

    Article  Google Scholar 

  8. Schug DA, Easley GR, O’Leary DP. Tracking objects using three dimensional edge detection, SIAMCSE, 2013.

    Google Scholar 

  9. Toklu C, Murat Tekalp A, Tanju Erdem A. Simultaneous alpha map generation and 2-D mesh tracking for multimedia applications. In Image Processing, 1997. Proceedings., International Conference on, volume 1, pp. 113–116. IEEE, 1997.

    Google Scholar 

  10. Tu C-L, Wen-Liang H, Ho J. Analysis of singularities from modulus maxima of complex wavelets. IEEE Trans Inform Theory. 2005;51(3):1049–62.

    Article  MATH  MathSciNet  Google Scholar 

  11. Yi S, Labate D, Easley GR, Krim H. A shearlet approach to edge analysis and detection. IEEE Trans Image Process. 2009;18(5):929–41.

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. NAWCAD, Patuxent River, MD, USA

    David A. Schug

  2. The MITRE Corporation, 7515 Colshire Drive, 22102, McLean, VA, USA

    Glenn R. Easley

  3. Computer Science Department and Institute for Advanced Computer Studies, University of Maryland, 20742, College Park, MD, USA

    Dianne P. O’Leary

Authors
  1. David A. Schug
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  2. Glenn R. Easley
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  3. Dianne P. O’Leary
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Corresponding author

Correspondence to David A. Schug .

Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, Maryland, USA

    Radu Balan

  2. Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, Maryland, USA

    Matthew J. Begué

  3. Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, Maryland, USA

    John J. Benedetto

  4. Department of Mathematics, University of Maryland, Norbert Weiner Center, College Park, Maryland, USA

    Wojciech Czaja

  5. Department of Mathematics, University of Maryland, Norbert Wiener Center, College Park, Maryland, USA

    Kasso A. Okoudjou

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Schug, D., Easley, G., O’Leary, D. (2015). Wavelet–Shearlet Edge Detection and Thresholding Methods in 3D. In: Balan, R., Begué, M., Benedetto, J., Czaja, W., Okoudjou, K. (eds) Excursions in Harmonic Analysis, Volume 3. Applied and Numerical Harmonic Analysis. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-13230-3_4

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