Contour Estimation by Array Processing Methods
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Contour Estimation by Array Processing Methods Salah Bourennane1, 2 and Julien Marot1, 2 1 GSM,
Institut Fresnel/CNRS-UMR 6133, Universit´e Aix-Marseille III, D.U. de Saint J´erˆome, 13397 Marseille Cedex 20, France 2 Ecole ´ G´en´eraliste d’Ing´enieurs de Marseille (EGIM), Technopˆole de Chˆateau-Gombert, 38 rue Joliot Curie, 13451 Marseille Cedex 20, France Received 8 February 2005; Revised 16 November 2005; Accepted 29 December 2005 Recommended for Publication by Gloria Menegaz This work is devoted to the estimation of rectilinear and distorted contours in images by high-resolution methods. In the case of rectilinear contours, it has been shown that it is possible to transpose this image processing problem to an array processing problem. The existing straight line characterization method called subspace-based line detection (SLIDE) leads to models with orientations and offsets of straight lines as the desired parameters. Firstly, a high-resolution method of array processing leads to the orientation of the lines. Secondly, their offset can be estimated by either the well-known method of extension of the Hough transform or another method, namely, the variable speed propagation scheme, that belongs to the array processing applications field. We associate it with the method called “modified forward-backward linear prediction” (MFBLP). The signal generation process devoted to straight lines retrieval is retained for the case of distorted contours estimation. This issue is handled for the first time thanks to an inverse problem formulation and a phase model determination. The proposed method is initialized by means of the SLIDE algorithm. Copyright © 2006 Hindawi Publishing Corporation. All rights reserved.
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INTRODUCTION
The estimation of the characteristics of lines and object contours from a sequence of binary images has been a widely studied problem over the past few years [1–3]. This type of problem is faced in robotic way screening, in the measurement of wafer track width in microelectronics, and generally in aerial image analysis. The image contains straight lines compound of black pixels with value “1,” over a white background with pixels value “0.” The detection and localization of these straight lines are essential issues in image processing [4]. The Hough transform can be used for this purpose [1, 2]. Although this method gives a good resolution even in presence of a relatively strong noise, some restrictions remain in its use. These restrictions are due to the dependence on the choice of the quantization step and the computational cost for the bidimensional search of the maxima. Array processing methods consist in conjugating the parameters of both arrays and received signals. Their efficiency has been improved and led to efficient algorithms [5]. In order to keep the resolution and reduce the computational cost, the array processing methods [6, 7] have recently been
adapted to give the characteristics of multiple straight lines out of an image. In this paper, we first recall in Section 2 how to adapt the es
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