On digital plane preimage structure

In digital geometry, digital straightness is an important concept both for practical motivations and theoretical interests. Concerning the digital straightness in dimension 2, many digital straight line characterizations exist and the digital straight segment preimage is well known. In this article, we investigate the preimage associated to digital planes. More precisely, we present first structure theorems that describe the preimage of a digital plane. Furthermore, we present a bound on the number of preimage faces under some given hypotheses. Key words: digital plane preimage, digital straight line, dual transformation.

Ondigital plane preimage structure

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Discrete Contour Extraction from Reference Curvature Function

Abstract. A robust discrete curvature estimator was recently proposed by Kerautret et al. [1]. In this paper, we exploit the precision and stability of this estimator in order to define a contour extraction method for analysing geometric features. We propose to use a reference curvature function for extracting the frontier of a shape in a gray level image. The frontier extraction is done by using both geometric information represented by the reference curvature and gradient information contained in the source image. The application of this work is done in a medical application.

A Generic and Parallel Algorithm for 2D Image Discrete Contour Reconstruction

International audienceIn this paper, we present a generic topological and geometrical framework for the digital reconstruction of complex contours from labeled images. The proposed technique is based on combinatorial map simplifications guided by digital straight segments. We illustrate the genericity of the framework with a parallel contour reconstruction algorithm

Accurate curvature estimation along digital contours with maximal digital circular arcs

International audienceWe propose in this paper a new curvature estimator basedon the set of maximal digital circular arcs. For strictly convex shapeswith continuous curvature fields digitized on a grid of step h, we showthat this estimator is mutligrid convergent if the discrete length of themaximal digital circular arcs grows in Ω(h− 2 ). We indeed observed thisorder of magnitude. Moreover, experiments showed that our estimatoris at least as fast to compute as existing estimators and more accurateeven at low resolution

MIX STAR-AUTONOMOUS QUANTALES AND THE CONTINUOUS WEAK ORDER

International audienceThe set of permutations on a finite set can be given a lattice structure (known as the weak Bruhat order). The lattice structure is generalized to the set of words on a fixed alphabet Σ = { x, y, z,. .. }, where each letter has a fixed number of occurrences (these lattices are known as multinomial lattices and, in dimension 2, as lattices of lattice paths). By interpreting the letters x, y, z,. .. as axes, these words can be interpreted as discrete increasing paths on a grid of a d-dimensional cube, where d = card(Σ). We show in this paper how to extend this order to images of continuous monotone paths from the unit interval to a d-dimensional cube. The key tool used to realize this construction is the quantale L ∨ (I) of join-continuous functions from the unit interval to itself; the construction relies on a few algebraic properties of this quantale: it is-autonomous and it satisfies the mix rule. We begin developing a structural theory of these lattices by characterizing join-irreducible elements, and by proving these lattices are generated from their join-irreducible elements under infinite joins