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A Contrario Detection

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A Contrario Line Segment Detection

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Abstract

At the turn of the century, Desolneux, Moisan, and Morel undertook the task of formalizing the Gestalt theory into a mathematical framework [19, 22]. The motivation for this ambitious project was to provide a foundation for computer vision based, like the Gestalt theory [46, 51, 61, 62], on a small set of fundamental principles. They identified the lack of a principle to guide the selection of detection thresholds and their main contribution was to propose the a contrario framework to cover this need. This chapter will introduce the a contrario approach and its application to line segment detection.

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Notes

  1. 1.

    The family \(\mathcal{S}\) does not include all the possible line segments in the image; it does not include all the discrete line segments, either. There is an extensive literature on the subject of digital straightness [47, 73]. Consider an N × N grid of pixel centers. A digital straight line is a set of points in the grid that corresponds to the digitalization of a line. For example, the line y = ax + b, has a corresponding digital line \(\big\{(n,y_{n}):\,\, n = 1, 2,\ldots,N,\,\,y_{n} = \lfloor an + b\rfloor,\,\, 1 \leq y_{n} \leq N\big\}\). Just the digital straight lines on an N × N grid are O(N 4), see [52]. Moreover, in most cases there are multiple digital straight line segments defined by the same end points; for example, \(\big\{(1, 1),\, (1, 2),\, (1, 3),\, (2, 4)\big\}\) and \(\big\{(1, 1),\, (2, 2),\, (2, 3),\, (2, 4)\big\}\) are both digital straight line segments from (1, 1) to (2, 4).

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Authors and Affiliations

  1. CMLA, ENS Cachan, Cachan, France

    Rafael Grompone von Gioi

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  1. Rafael Grompone von Gioi
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Grompone von Gioi, R. (2014). A Contrario Detection. In: A Contrario Line Segment Detection. SpringerBriefs in Computer Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0575-1_2

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  • DOI: https://doi.org/10.1007/978-1-4939-0575-1_2

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  • Print ISBN: 978-1-4939-0574-4

  • Online ISBN: 978-1-4939-0575-1

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