Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Erschienen in:
Buchtitelbild

2014 | OriginalPaper | Buchkapitel

1. Introduction

verfasst von : Agnieszka Lisowska

Erschienen in: Geometrical Multiresolution Adaptive Transforms

Verlag: Springer International Publishing

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter, the motivation of this book was presented based on the human visual system. Then, the state-of-the-art review was given of the geometrical multiresolution methods of image approximation together with the contribution of this book. The chapter ends with the outline of this book.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren
Nächstes Kapitel Smoothlets
Literatur
1.
Mallat, S.: A Wavelet Tour of Signal Processing: The Sparse Way. Academic Press, USA (2008)
2.
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)CrossRef
3.
Welland, G.V. (ed.): Beyond Wavelets. Academic Press, Netherlands (2003)MATH
4.
Soille, P.: Morphological Image Analysis. Principles and Applications. Springer, Heidelberg (2010)
5.
Gonzales, R.C., Woods, R.E.: Digital Image Processing. Prentice Hall, Upper Saddle River (2008)
6.
Won, C.S., Gray, R.M.: Stochastic Image Processing. Springer, New York (2004)CrossRef
7.
Vese, L.A.: Variational Methods in Image Processing. Chapman and Hall/CRC Press, Boca Raton (2013)
8.
Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus Variations. Springer, New York (2002)
9.
Gabor, D.: Guest editorial. IRE Trans. Inf. Theory 5(3), 97–97 (1959)CrossRef
10.
Christopoulos, C., Skodras, A., Ebrahimi, T.: The JPEG2000 still image coding system: an overview. IEEE Trans. Consum. Electron. 46(4), 1103–1127 (2000)CrossRef
11.
Humphreys, G.W.: Case Studies in the Neuropsychology of Vision. Psychology Press, UK (1999)
12.
13.
Lisowska, A.: Geometrical wavelets and their generalizations in digital image coding and processing. PhD Thesis, University of Silesia, Poland (2005)
14.
Lisowska, A.: Multiwedgelets in image denoising. Lect. Notes Electr. Eng. 240, 3–11 (2013)CrossRef
15.
Lisowska, A.: Smoothlets: multiscale functions for adaptive representations of images. IEEE Trans. Image Process. 20(7), 1777–1787 (2011)CrossRefMathSciNet
16.
Chandrasekaran, V., Wakin, M.B., Baron, D., Baraniuk, R.: Surflets: a sparse representation for multidimensional functions containing smooth discontinuities. In: IEEE International Symposium on Information Theory, Chicago, New Orleans (2004)
17.
Darkner, S., Larsen, R., Stegmann, M.B., Ersbøll, B.K.: Wedgelet Enhanced Appearance Models, pp. 177–184. In: Proceedings of the Computer Vision and Pattern Recognition Workshops, IEEE (2004)
18.
Demaret, L., Friedrich, F., Führ, H., Szygowski, T.: Multiscale wedgelet denoising algorithms. Proceedings of SPIE, Wavelets XI, San Diego 5914, 1–12 (2005)
19.
Friedrich, F., Demaret, L., Führ, H., Wicker, K.: Efficient moment computation over polygonal domains with an application to rapid wedgelet approximation. SIAM J. Sci. Comput. 29(2), 842–863 (2007)CrossRefMATHMathSciNet
20.
Lisowska, A.: Second order wedgelets in image coding. In: Proceedings of EUROCON ’07 Conference, Warsaw, Poland, pp. 237–244 (2007)
21.
Lisowska, A.: Geometrical multiscale noise resistant method of edge detection. Lect. Notes Comput. Sci. Springer 5112, 182–191 (2008)CrossRef
22.
Lisowska, A.: Image denoising with second order wedgelets. Int. J. Signal Imaging Syst. Eng. 1(2), 90–98 (2008)CrossRef
23.
Lisowska, A.: Efficient denoising of images with smooth geometry. Lect. Notes Comput. Sci. Springer, Heidelberg 5575, 617–625 (2009)
24.
25.
Lisowska, A.: Edge detection by sliding wedgelets. Lect. Notes Comput. Sci. Springer, Heidelberg 6753(1), 50–57 (2011)
26.
Romberg, J., Wakin, M., Baraniuk, R.: Multiscale wedgelet image analysis: fast decompositions and modeling. IEEE Int. Conf. Image Process. 3, 585–588 (2002)CrossRef
27.
Romberg, J., Wakin, M., Baraniuk, R.: Approximation and compression of piecewise smooth images using a Wavelet/Wedgelet geometric model. IEEE Int. Conf. Image Process. 1, 49–52 (2003)
28.
Wakin, M., Romberg, J., Choi, H., Baraniuk, R.: Rate-distortion optimized image compression using Wedgelets. IEEE Int. Conf. Image Process. 3, 237–244 (2002)
29.
Willet, R.M., Nowak, R.D.: Platelets: a multiscale approach for recovering edges and surfaces in photon limited medical imaging. IEEE Trans. Med. Imaging 22, 332–350 (2003)CrossRef
30.
Bruckstein, A.M., Donoho, D.L., Elad, M.: From sparse solutions of systems of equations to sparse modeling of signals and images. SIAM Rev. 51(1), 34–81 (2009)CrossRefMATHMathSciNet
31.
Elad, M.: Sparse and Redundant Representations: From Theory to Applications in Signal and Image Processing. Springer, New York, USA (2010)CrossRef
32.
Elad, M., Figueiredo, M.A.T., Ma, Y.: On the role of sparse and redundant representations in image processing. Proc. IEEE 98(6), 972–982 (2010)CrossRef
33.
Rubinstein, R., Bruckstein, A.M., Elad, M.: Dictionaries for sparse representation modeling. Proc. IEEE 98(6), 1045–1057 (2010)CrossRef
34.
Wright, J., Ma, Y., Mairal, J., Sapiro, G., Huang, T.S., Yan, S.: Sparse representation for computer vision and patternrecognition. Proc. IEEE 8(6), 1031–1044 (2010)CrossRef
35.
Breiman, L., Friedman, J., Olshen, R., Stone, C.: Classification and Regression Trees. Chapman and Hall/CRC, Boca raton (1984)MATH
36.
Candès, E.: Ridgelets: theory and applications. PhD Thesis, Department of Statistics, Stanford University, Stanford, USA (1998)
37.
Candès, E., Donoho, D.L.: Curvelets–A surprisingly effective nonadaptive representation for objects with edges. In: Cohen, A., Rabut, C., Schumaker, L.L. (eds.) Curves and Surface Fitting, Vanderbilt University Press, pp. 105–120 (1999)
38.
Do, M.N., Vetterli, M.: Contourlets. In: Stoeckler, J., Welland, G.V. (eds.) Beyond Wavelets, pp. 83–105. Academic Press, San Diego (2003)CrossRef
39.
Kutyniok, G., Labate, D. (eds.): Shearlets: Multiscale Analysis for Multivariate Data. Springer, New York, USA (2012)
40.
Labate, D., Lim, W., Kutyniok, G., Weiss, G.: Sparse multidimensional representation using shearlets. Proc. SPIE 5914, 254–262 (2005)
41.
Velisavljevic, V., Beferull-Lozano, B., Vetterli, M., Dragotti, P.L.: Directionlets: anisotropic multidirectional representation with separable filtering. IEEE Trans. Image Process. 15(7), 1916–1933 (2006)CrossRef
42.
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)
43.
Lisowska, A.: Effective coding of images with the use of geometrical wavelets. In: Proceedings of Decision Support Systems Conference, Zakopane, Poland (in Polish) (2003)
44.
Meyer, F.G., Coifman, R.R.: Brushlets: a tool for directional image analysis and image compression. Appl. Comput. Harmonic Anal. 4, 147–187 (1997)CrossRefMATHMathSciNet
45.
Pennec, E., Mallat, S.: Sparse geometric image representations with bandelets. IEEE Trans. Image Process. 14(4), 423–438 (2005)CrossRefMathSciNet
46.
47.
Krommweh, J.: Image approximation by adaptive tetrolet transform. In: International Conference on Sampling Theory and Applications, Marseille, France (2009)
48.
Starck, J.-L., Murtagh, F., Fadili, J.M.: Sparse Image and Signal Processing: Wavelets. Curvelets. Cambridge University Press, USA, Morphological Diversity (2010)CrossRef
49.
Alzubi, S., Islam, N., Abbod, M.: Multiresolution analysis using wavelet, ridgelet, and curvelet transforms for medical image segmentation. Int. J. Biomed. Imaging 2011, 136034 (2011)CrossRef
50.
Gómez, F., Romero, E.: Texture characterization using curvelet based descriptor. Pattern Recognit. Lett. 32(16), 2178–2186 (2011)
51.
Yi, S., Labate, D., Easley, G., Krim, H.: A shearlet approach to edge analysis and detection. IEEE Trans. Image Process. 18(5), 929–941 (2009)CrossRefMathSciNet
52.
Shukla, R., Dragotti, P.L., Do, M.N., Vetterli, M.: Rate-distortion optimized tree structured compression algorithms for piecewise polynomial images. IEEE Trans. Image Process. 14(3), 343–359 (2005)CrossRefMathSciNet
53.
Peyré, G., Mallat, S.: Discrete bandelets with geometric orthogonal filters. In: Proceedings from ICIP’05, vol. 1, pp. 65–68 (2005)
54.
Peyré, G., Mallat, S.: Surface compression with geometric bandelets. Proc. ACM SIGGRAPH 24(3), 601–608 (2005)CrossRef
55.
Maalouf, A., Carré, P., Augereau, B., Fernandez-Maloigne, C.: Inpainting using geometrical grouplets. EUSIPCO’08, Lausanne, Switzerland (2008)
56.
Plonka, G.: The easy path wavelet transform: a new adaptive wavelet transform for sparse representation of two-dimensional data. SIAM Multiscale Model. Simul. 7(9), 1474–1496 (2009)CrossRefMATHMathSciNet
57.
Wang, D.M., Zhang, L., Vincent, A., Speranza, F.: Curved wavelet transform for image coding. IEEE Trans. Image Process. 15(8), 2413–2421 (2006)CrossRefMathSciNet
58.
Huo, X., Chen, J., Donoho, D.L.: JBEAM: Coding Lines and Curves via Digital Beamlets. In: IEEE Proceedings of the Data Compression Conference, Snowbird, USA (2004)
59.
Lisowska, A., Kaczmarzyk, T.: JCURVE–Multiscale curve coding via second order beamlets. Mach. Graph. Vis. 19(3), 265–281 (2010)
60.
Candès, E., Romberg, J., Tao, T.: Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information. IEEE Trans. Inf. Theory 52(2), 489–509 (2006)CrossRefMATH
61.
Metadaten
Titel
Introduction
verfasst von
Agnieszka Lisowska
Copyright-Jahr
2014
Buch
Geometrical Multiresolution Adaptive Transforms

Print ISBN: 978-3-319-05010-2

Electronic ISBN: 978-3-319-05011-9

Copyright-Jahr: 2014

DOI
https://doi.org/10.1007/978-3-319-05011-9_1