On the Language of Standard Discrete Planes and Surfaces

International audienceA standard discrete plane is a subset of Z^3 verifying the double Diophantine inequality mu =< ax+by+cz < mu + omega, with (a,b,c) != (0,0,0). In the present paper we introduce a generalization of this notion, namely the (1,1,1)-discrete surfaces. We first study a combinatorial representation of discrete surfaces as two-dimensional sequences over a three-letter alphabet and show how to use this combinatorial point of view for the recognition problem for these discrete surfaces. We then apply this combinatorial representation to the standard discrete planes and give a first attempt of to generalize the study of the dual space of parameters for the latter [VC00]

Thick Line Segment Detection with Fast Directional Tracking

International audienceThis paper introduces a fully discrete framework for a new straight line detector in gray-level images, where line segments are enriched with a thickness parameter intended to provide a quality criterion on the extracted feature. This study is based on a previous work on interactive line detection in gray-level images. At first, a better estimation of the segment thickness and orientation is achieved through two main improvements: adaptive directional scans and control of assigned thickness. Then, these advances are exploited for a complete unsupervised detection of all the line segments in an image. The new thick line detector is left available in an online demonstration

A near-linear time guaranteed algorithm for digital curve simplification under the Fréchet distance

Softcover, ISBN 978-3-642-19866-3International audienceGiven a digital curve and a maximum error, we propose an algorithm that computes a simplification of the curve such that the Fréchet distance between the original and the simplified curve is less than the error. The algorithm uses an approximation of the Fréchet distance, but a guarantee over the quality of the simplification is proved. Moreover, even if the theoretical complexity of the algorithm is in O(n log(n)), experiments show a linear behaviour in practice

Blurred Segments in Gray Level Images for Interactive Line Extraction

International audienceAbstract. The recognition of discrete straight segments is a significant topic in the field of discrete geometry and for many applications dealing with geometric feature extraction. It can be performed from noisy binary data using the concept of blurred segments [3,2]. However, to our best knowledge, these algorithms have never been defined to directly extract straight segments in gray level images. This article proposes a solution to extend the recognition by using gray level image information. Although initially intended to be implemented within a semi-automatic line selec- tion tool used in an interactive 3D modeling application, it also meets more general parameter extraction requirements

Digital Plane Recognition with Fewer Probes

International audienceWe present a new plane-probing algorithm, i.e., an algorithm that computes the normal vector of a digital plane from a starting point and a predicate "Is a point x in the digital plane?". This predicate is used to probe the digital plane as locally as possible and decide on-the-fly the next points to consider. We show that this algorithm returns the same vector as another plane-probing algorithm proposed in Lachaud et al. (J. Math. Imaging Vis., 59, 1, 23-39, 2017), but requires fewer probes. The theoretical upper bound is indeed lowered from O(ω log ω) to O(ω) calls to the predicate, where ω is the arithmetical thickness of the digital plane, and far fewer calls are experimentally observed on average. This reduction is made possible by a study that shows how to avoid computations that do not contribute to the final solution. In the context of digital surface analysis, this new algorithm is expected to be of great interest for normal estimation and shape reconstruction

Parallel Strip Segment Recognition and Application to Metallic Tubular Object Measure

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