Signal Processing 84 (2004) 2115–2137 Scale-adaptive detection and local characterization of edges based on wavelet transform C. Ducottet à , T. Fournel, C. Barat Laboratoire Traitement du Signal et Instrumentation, UMR CNRS 5516, Baˆtiment F, 10 rue Barrouin, 42000 Saint Etienne, France Received 24 July 2003 Abstract In this paper, we present an edge detection and characterization method based on wavelet transform. This method relies on a modelization of contours as smoothed singularities of three particular types (transition, peak and line). Using the wavelet transform modulus maxima lines of the edge models, position and descriptive parameters of each edge point can be inferred. Indeed, on the one hand, the proposed algorithm allows to detect and locate edges at a locally adapted scale. On the other hand, it is able to identify the type of each detected edge point and to measure both its amplitude and smoothness degree. The latter parameters represent, respectively, the contrast and the blur level of the edge point. Evaluation of the method is performed on both synthetic and real images. Synthetic data are used to investigate the influence of different factors and the sensitivity to noise, whereas real images allow to highlight the performance and interests of the method. In particular, we point out that the measured smoothness degree provides a cue to recover depth from defocused images or a cue to diffusion measurements in images of cloud structures. Moreover, from an indoor scene, we demonstrate the relevance of type identification for segmentation purposes. r 2004 Elsevier B.V. All rights reserved. Keywords: Edge detection; Multiscale analysis; Wavelet transform; Blurred images 1. Introduction Edge detection is an important issue in signal and image processing. A number of problems indeed become less complex when an image is summarized by its most important features. Edges are precisely considered as important features for analyzing the information contained in images [13,19]. They are generally detected using gradient or Laplacian operators combined with a low-pass filtering. The choice of the size of the filter is then the result of a compromise between sensitivity to noise and fine localization. A large filter indeed allows to be less sensitive to noise (particularly in the case of blurred edges), but the localization is ARTICLE IN PRESS www.elsevier.com/locate/sigpro 0165-1684/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.sigpro.2004.07.003 à Corresponding author. E-mail addresses: ducottet@univ-st-etienne.fr (C. Ducottet), fournel@univ-st-etienne.fr (T. Fournel), cecile.barat@ univ-st-etienne.fr (C. Barat).