On Straight Line Detection - J Math Imaging Vis DOI...

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J Math Imaging Vis DOI 10.1007/s10851-008-0102-5 On Straight Line Segment Detection Rafael Grompone von Gioi · Jérémie Jakubowicz · Jean-Michel Morel · Gregory Randall © Springer Science+Business Media, LLC 2008 Abstract In this paper we propose a comprehensive method for detecting straight line segments in any digital image, accurately controlling both false positive and false nega- tive detections. Based on Helmholtz principle, the proposed method is parameterless. At the core of the work lies a new way to interpret binary sequences in terms of unions of seg- ments, for which a dynamic programming implementation is given. The proposed algorithm is extensively tested on syn- thetic and real images and compared with the state of the art. Keywords Straight line segment detection · Helmholtz principle · A contrario detection · Number of false alarms (NFA) 1 Introduction It might seem futile to address the problem of detecting seg- ments, that is, local straight edges in an image. First of all, edge detection has been the object of intense research for more than thirty years and many, more and more sophisti- cated algorithms have been proposed. Second, alignments R. Grompone von Gioi ( ± ) · J. Jakubowicz · J.-M. Morel CMLA, ENS Cachan, CNRS, UniverSud, 61 Avenue du Président Wilson, 94230 Cachan, France e-mail: grompone@cmla.ens-cachan.fr J. Jakubowicz e-mail: jakubowi@cmla.ens-cachan.fr J.-M. Morel e-mail: morel@cmla.ens-cachan.fr G. Randall IIE, Universidad de la República, Julio Herrera y Reissig 565, Montevideo, Uruguay e-mail: randall@fing.edu.uy often coincide with edges (most edges are locally straight or smooth as illustrated e.g. in [ 7 ]). On the other hand, the de- finition of an edge has never been fixed because it depends on a highly subjective and varying measurement, namely the contrast. Segments instead, or alignments, can receive a purely geometric definition as intervals of a straight line in an image that are orthogonal to the image gradient at many of their points. This requirement is independent of contrast and relies only on image geometry. Segments in images give important information about their geometric content. Segments as features can help in several problems. To cite just a few: stereo analysis [ 26 ], classification tasks like on-board selection of relevant im- ages [ 35 ], crack detection in materials [ 36 ], stream and roadbeds detection [ 50 ], and image compression [ 18 ]. They serve as a basic tool to find sailing ships and their V-shaped wakes [ 8 , 29 ], to detect filamentous structures in cryo-electron microscopy images [ 52 ], or to detect lines in forms [ 51 ]. On other problems line segments are just a con- venient way to handle structure, e.g., in [ 19 , 30 , 48 ] line networks are approximated by small segments. Segments are one of the basic shapes in graphics. The gestalt school [ 28 ] has gone so far as to analyze human per- ception with line drawings essentially made of straight seg- ments. Most human-made environments and in particular ar- chitectures are based on alignments. All photographs made
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On Straight Line Detection - J Math Imaging Vis DOI...

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