K. S. Shanmugham, F. M. Dickey, and J. A. Green, An Optimal Frequency Domain Filter for Edge Detection in Digital Pictures, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.1, issue.1, pp.37-49, 1979.
DOI : 10.1109/TPAMI.1979.4766874

A. Rosenfeld, The Max Roberts Operator is a Hueckel-Type Edge Detector, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.3, issue.1, pp.101-102, 1981.
DOI : 10.1109/TPAMI.1981.4767056

S. W. Zucker and R. A. , Hummel: A Three-Dimensional Edge Operator, IEEE PAMI, vol.3, pp.324-331, 1981.

D. G. Morgenthaler and A. Rosenfeld, Multidimensional Edge Detection by Hypersurface Fitting, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.3, issue.4, pp.482-486, 1981.
DOI : 10.1109/TPAMI.1981.4767134

H. K. Liu, Two- and three-dimensional boundary detection, Computer Graphics and Image Processing, vol.6, issue.2, pp.123-134, 1938.
DOI : 10.1016/S0146-664X(77)80008-7

M. E. Jernigan and R. W. , Wardell: Does the eye contain optimal edge detection mechanisms, IEEE Trans. Syst, issue.11, pp.441-444, 1981.

D. Marr and E. Hildreth, Theory of Edge Detection, Proceedings of the Royal Society B: Biological Sciences, vol.207, issue.1167, pp.187-217, 1980.
DOI : 10.1098/rspb.1980.0020

A. J. Tabatabai and R. Mitchell, Edge Location to Subpixel Values in Digital Imagery, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.6, issue.2, pp.188-201, 1984.
DOI : 10.1109/TPAMI.1984.4767502

I. Pitas and A. N. , Venetsalopoulous: Edge Detectors Based on Nonlinear Filters, IEEE PAMI, vol.8, pp.538-550, 1986.

V. S. Nalwa and T. O. , Binford: On Detecting Edges, IEEE PAMI, vol.8, pp.699-714, 1986.

V. Torre and T. A. , Poggio: On edge detection, IEEE PAMI, vol.8, pp.147-163, 1986.

E. Hildreth, Implementation of a theory of edge detection, Massachusetts Inst. Technol, vol.579, issue.1, 1980.

O. Faugeras, Three-dimensional computer vision:a geometric viewpoint, 1993.

A. L. Yuille and T. A. , Poggio: Scaling Theorems for Zero Crossings, IEEE PAMI, vol.8, pp.15-25, 1986.

A. J. Bell and T. J. Sejnowski, The ???independent components??? of natural scenes are edge filters, Vision Research, vol.37, issue.23, pp.3327-3338, 1997.
DOI : 10.1016/S0042-6989(97)00121-1

M. C. Morrone and D. C. Burr, Feature detection in human vision: A phasedependent energy model, Proceedings of the Royal Society of London. Series B, biological sciences, 1988.

P. Kovesi, Image features from phase congruency, Journal of Computer Vision Research, 1999.

Z. Wang and E. P. , Simoncelli: Local phase coherence and the perception of blur, Advances in Neural Information Processing Systems, 2004.

A. Turiel and N. Parga, The Multifractal Structure of Contrast Changes in Natural Images: From Sharp Edges to Textures, Neural Computation, vol.12, issue.4, pp.763-793, 2000.
DOI : 10.1098/rspb.1998.0303

J. H. Van-hateren, Theoretical predictions of spatiotemporal receptive fields of fly LMCs, and experimental validation, Journal of Comparative Physiology A, vol.171, issue.2, pp.157-170, 1992.
DOI : 10.1007/BF00188924

J. H. Van-hateren, A. Van, and . Schaaf, Independent component filters of natural images compared with simple cells in primary visual cortex, Proceedings of the Royal Society B: Biological Sciences, vol.265, issue.1394, pp.359-366, 1998.
DOI : 10.1098/rspb.1998.0303

A. Lesne, Méthodes de renormalisation, Eyrolles Science, 1995.

A. Witkin, SCALE-SPACE FILTERING, Proc. IJCAI, pp.1019-1021, 1983.
DOI : 10.1016/B978-0-08-051581-6.50036-2

T. Lindeberg, Scale-Space Theory in Computer Vision, 1994.
DOI : 10.1007/978-1-4757-6465-9

J. J. Clark, Singularity theory and phantom edges in scale space, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.10, issue.5, pp.720-727, 1988.
DOI : 10.1109/34.6782

P. Bouthemy, A maximum likelihood framework for determining moving edges, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.11, issue.5, pp.499-511, 1989.
DOI : 10.1109/34.24782

URL : https://hal.archives-ouvertes.fr/inria-00075857

P. Perona and J. Malik, Scale-space and edge detection using anisotropic diffusion, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.12, issue.7, pp.629-639, 1990.
DOI : 10.1109/34.56205

P. Sarkar and K. L. Boyer, On optimal infinite impulse response edge detection filters, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.13, issue.11, pp.1154-1171, 1991.
DOI : 10.1109/34.103275

P. Jeong and C. I. Kim, Adaptive determination of filter scales for edge detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.5, pp.579-585, 1992.
DOI : 10.1109/34.134062

S. Mallat and S. Zhong, Characterization of signals from multiscale edges, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.14, issue.7, pp.710-732, 1992.
DOI : 10.1109/34.142909

A. Arenodo, E. Bacry, and J. , The thermodynamics of fractals revisited with wavelets, Physica A: Statistical Mechanics and its Applications, vol.213, issue.1-2, pp.232-275, 1995.
DOI : 10.1016/0378-4371(94)00163-N

A. Turiel, C. J. Pérz-vicente, and J. Grazzini, Numerical methods for the estimation of multifractal singularity spectra on sampled data: A comparative study, Journal of Computational Physics, vol.216, issue.1, pp.362-390, 2006.
DOI : 10.1016/j.jcp.2005.12.004

H. Yahia, J. Sudre, C. Pottier, and V. Garon, Motion analysis in oceanographic satellite images using multiscale methods and the energy cascade, Pattern Recognition, vol.43, issue.10, pp.43-3591, 2010.
DOI : 10.1016/j.patcog.2010.04.011

URL : https://hal.archives-ouvertes.fr/inria-00423748

F. Van-der-heijden, Edge and line feature extraction based on covariance models, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.17, issue.1, pp.16-33, 1995.
DOI : 10.1109/34.368155

N. Ahuja, A transform for multiscale image segmentation by integrated edge and region detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.18, issue.12, pp.1211-1235, 1996.
DOI : 10.1109/34.546258

S. Geman and D. Geman, Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images*, Journal of Applied Statistics, vol.1, issue.5-6, pp.721-741, 1984.
DOI : 10.1109/TIT.1972.1054786

P. Liang and Y. W. Wang, Local Scaled Controlled Anisotropic Diffusion with Local Noise Estimate for Image Smoothing and Edge Detection, 1998.

D. H. Marimont and Y. , Rubner: A Probabilistic Framework for Edge Detection and Scale Selection, pp.207-214, 1998.

S. Z. Li, Close-form solution and parameter selection for convex minimization-based edge-preserving smoothing, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.9, pp.916-932, 1998.
DOI : 10.1109/34.713359

J. H. Elder and S. W. , Local scale control for edge detection and blur estimation, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.20, issue.7, pp.699-716, 1998.
DOI : 10.1109/34.689301

J. H. Elder and S. W. , Zucker: Local scale control for edge detection and blur estimation, Proc. 4th European Conf. on Computer Vision, pp.57-69, 1996.

K. Suzuki, I. Oriba, and N. Sugie, Neural edge enhancer for supervised edge enhancement from noisy images, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.25, issue.12, pp.1582-1596, 2003.
DOI : 10.1109/TPAMI.2003.1251151

X. Wang, Laplacian Operator-Based Edge Detectors, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.29, issue.5, pp.886-890, 2007.
DOI : 10.1109/TPAMI.2007.1027

O. Laligant and F. Truchetet, A Nonlinear Derivative Scheme Applied to Edge Detection, IEEE Transactions on Pattern Analysis and Machine Intelligence, vol.32, issue.2, pp.242-257, 2010.
DOI : 10.1109/TPAMI.2008.282

URL : https://hal.archives-ouvertes.fr/hal-00582610

D. Galun, M. Basri, and A. Brandt, Multiscale Edge Detection and Fiber Enhancement Using Differences of Oriented Means, 2007 IEEE 11th International Conference on Computer Vision, 2007.
DOI : 10.1109/ICCV.2007.4408920

W. and M. Ilhagga, The Canny Edge Detector Revisited, Int. J. Comput. Vis, vol.91, pp.251-261, 2011.

R. Kimmel and A. M. Bruckstein, Regularized Laplacian Zero Crossings as Optimal Edge Integrators, International Journal of Computer Vision, vol.53, issue.3, pp.225-243, 2003.
DOI : 10.1023/A:1023030907417

J. H. Elder, Are Edges Incomplete ?, International Journal of Computer Vision, vol.34, issue.2/3, pp.97-122, 1999.
DOI : 10.1023/A:1008183703117

S. Mallat, A wavelet tour of signal processing: the sparse way, 2008.

G. Bofetta, M. Cencini, M. Falcioni, and A. Vulpiani, Predictability: a way to characterize complexity, Physics Reports, vol.356, issue.6, pp.367-474, 2001.
DOI : 10.1016/S0370-1573(01)00025-4

T. Lindeberg, Edge detection and ridge detection with automatic scale selection, Proceedings CVPR IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp.117-154, 1998.
DOI : 10.1109/CVPR.1996.517113

T. Lindeberg and . Ter-haar-romeny, Linear scale-space: (I) Basic theory and (II) Early visual operations, Geometry-Driven Diffusion, pp.1-77, 1994.

H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena, pp.0-19, 1971.

A. Turiel and A. Del, Pozo: Reconstructing images from their most singular fractal manifold, IEEE Transactions Image Processing, issue.11, pp.345-50, 2002.

A. Agrawal, R. Raskar, and R. , Chellappa: What is the Range of Surface Reconstructions from a Gradient Field, 2006.

Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, Image Quality Assessment: From Error Visibility to Structural Similarity, IEEE Transactions on Image Processing, vol.13, issue.4, pp.600-612, 2004.
DOI : 10.1109/TIP.2003.819861

O. Pont, A. Turiel, and C. J. Pérez-vicente, Empirical evidences of a common multifractal signature in economic, biological and physical systems, Physica A: Statistical Mechanics and its Applications, vol.388, issue.10, pp.2025-2035, 2009.
DOI : 10.1016/j.physa.2009.01.041

URL : https://hal.archives-ouvertes.fr/inria-00438521

H. Wendt and P. , Abry: Multifractality Tests Using Bootstrapped Wavelet Leaders, IEEE Transactions on signal processing, vol.55, p.10, 2007.

A. Turiel, H. Yahia, and C. J. Pérez-vicente, Microcanonical multifractal formalism???a geometrical approach to multifractal systems: Part I. Singularity analysis, Journal of Physics A: Mathematical and Theoretical, vol.41, issue.1, p.15501, 2008.
DOI : 10.1088/1751-8113/41/1/015501

URL : https://hal.archives-ouvertes.fr/hal-00937370

O. Pont, A. Turiel, and H. , Yahia: An optimized algorithm for the evaluation of local singularity exponents in digital signals, pp.346-357, 2011.