Abstract
In this paper the sliding wedgelet algorithm is presented together with its application to edge detection. The proposed method combines two theories: image filtering and geometrical edge detection. The algorithm works in the way that an image is filtered by a sliding window of different scales. Within the window the wedgelet is computed by the use of the fast moments-based method. Depending on the difference between two wedgelet parameters the edge is drawn. In effect, edges are detected geometrically and multiscale. The computational complexity of the sliding wedgelet algorithm is O(N 2) for an image of size N ×N pixels. The experiments confirmed the effectiveness of the proposed method, also in the application to noisy images.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Deans, S.R.: The Radon Transform and Some of Its Applications. John Wiley and Sons, New York (1983)
Canny, J.: Computational Approach To Edge Detection. IEEE Transactions on Pattern Analysis and Machine Intelligence 8, 679–714 (1986)
Gonzalez, R., Woods, R.: Digital Image Processing. Addison-Wesley, Reading (1992)
Olshausen, B.A., Field, D.J.: Emergence of Simple-Cell Receptive Field Properties by Learning a Sparse Code for Natural Images. Nature 381, 607–609 (1996)
Meyer, F.G., Coifman, R.R.: Brushlets: A Tool for Directional Image Analysis and Image Compression. Applied and Computational Harmonic Analysis 4, 147–187 (1997)
Donoho, D.L.: Wedgelets: Nearly-minimax estimation of edges. Annals of Statistics 27, 859–897 (1999)
Humphreys, G.W. (ed.): Case Studies in the Neuropsychology of Vision. Psychology Press, UK (1999)
Donoho, D.L., Huo, X.: Beamlet Pyramids: A New Form of Multiresolution Analysis, Suited for Extracting Lines, Curves and Objects from Very Noisy Image Data. In: Proceedings of SPIE, vol. 4119 (2000)
Demaret, L., Friedrich, F., Führ, H., Szygowski, T.: Multiscale Wedgelet Denoising Algorithms. In: Proceedings of SPIE, vol. 5914, pp. 1–12 (2005)
Labate, D., Lim, W., Kutyniok, G., Weiss, G.: Sparse Multidimensional Representation Using Shearlets. In: Proceedings of the SPIE, vol. 5914, pp. 254–262 (2005)
Mallat, S., Pennec, E.: Sparse Geometric Image Representation with Bandelets. IEEE Transactions on Image Processing 14(4), 423–438 (2005)
Popovici, I., Withers, W.D.: Custom-Built Moments for Edge Location. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(4), 637–642 (2006)
Lisowska, A.: Geometrical Multiscale Noise Resistant Method of Edge Detection. In: Campilho, A., Kamel, M.S. (eds.) ICIAR 2008. LNCS, vol. 5112, pp. 182–191. Springer, Heidelberg (2008)
Lisowska, A.: Multiscale Moments-Based Edge Detection. In: Proceedings of EUROCON 2009 Conference, St.Petersburg, Russia, pp. 1414–1419 (2009)
Mallat, S.: Geometrical Grouplets. Applied and Computational Harmonic Analysis 26(2), 161–180 (2009)
Lisowska, A.: Moments-Based Fast Wedgelet Transform. Journal on Mathematical Imaging and Vision 39(2), 180–192 (2011)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Lisowska, A. (2011). Edge Detection by Sliding Wedgelets. In: Kamel, M., Campilho, A. (eds) Image Analysis and Recognition. ICIAR 2011. Lecture Notes in Computer Science, vol 6753. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21593-3_6
Download citation
DOI: https://doi.org/10.1007/978-3-642-21593-3_6
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21592-6
Online ISBN: 978-3-642-21593-3
eBook Packages: Computer ScienceComputer Science (R0)