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Exact and Optimal Conversion of a Hole-free 2d Digital Object into a Union of Balls in Polynomial Time
This paper addresses the problem of converting a 2d digital object, i.e. a set S of points in...
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Average Curve of n Digital Curves
Building on [23], we investigate the problem of defining and computing the average of digital curves. Given n digital curves that satisfy...
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Representation of Imprecise Digital Objects
In this paper, we investigate a new framework to handle noisy digital objects. We consider digital closed simple 4-connected curves that are the...
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Algorithms for Fast Digital Straight Segments Union
Given two Digital Straight Segments (DSS for short) of known minimal characteristics, we investigate the union of these DSSs: is it still a DSS ? If...
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Optimal Covering of a Straight Line Applied to Discrete Convexity
The relation between a straight line and its digitization as a digital straight line is often expressed using a notion of proximity. In this...
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Walking in the Farey Fan to Compute the Characteristics of a Discrete Straight Line Subsegment
Given a Digital Straight Line (DSL) of known characteristics (a,b,μ), we address the problem of computing the characteristics of any of its...
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A Near-Linear Time Guaranteed Algorithm for Digital Curve Simplification under the Fréchet Distance
Given a digital curve and a maximum error, we propose an algorithm that computes a simplification of the curve such that the Fréchet distance between...
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Hierarchical Discrete Medial Axis for Sphere-Tree Construction
In discrete geometry, the Distance Transformation and the Medial Axis Extraction are classical tools for shape analysis. In this paper, we present a...
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What Does Digital Straightness Tell about Digital Convexity?
The paper studies local convexity properties of parts of digital boundaries. An online and linear-time algorithm is introduced for the decomposition...
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On Three Constrained Versions of the Digital Circular Arc Recognition Problem
In this paper, the problem of digital circular arcs recognition is investigated in a new way. The main contribution is a simple and linear-time...
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Duality and Geometry Straightness, Characterization and Envelope
Duality applied to geometrical problems is widely used in many applications in computer vision or computational geometry. A classical example is the...
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Minimal Decomposition of a Digital Surface into Digital Plane Segments Is NP-Hard
This paper deals with the complexity of the decomposition of a digital surface into digital plane segments (DPS for short). We prove that the...
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Optimization Schemes for the Reversible Discrete Volume Polyhedrization Using Marching Cubes Simplification
The aim of this article is to present a reversible and topologically correct construction of a polyhedron from a binary object. The proposed...
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Reversible Polygonalization of a 3D Planar Discrete Curve: Application on Discrete Surfaces
Reversible polyhedral modelling of discrete objects is an important issue to handle those objects. We propose a new algorithm to compute a polygonal...
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Discrete Surfaces Segmentation into Discrete Planes
This paper is composed of two parts. In the first one, we present an analysis of existing discrete surface segmentation algorithms. We show that two...
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Decomposition of a Three-Dimensional Discrete Object Surface into Discrete Plane Pieces
This paper deals with the polyhedrization of discrete volumes. The aim is to do a reversible transformation from a discrete volume to a Euclidean...
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Towards an Invertible Euclidean Reconstruction of a Discrete Object
An invertible Euclidean reconstruction method for a 2Dcurve is proposed. Hints on an extension to 3D are provided. The framework of this method is...
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From Digital Plane Segmentation to Polyhedral Representation
Many applications, manipulation or just visualization of discrete volumes are time consuming problems. The general idea to solve these difficulties...