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Hypermap Specification and Certified Linked Implementation Using Orbits
We propose a revised constructive specification and a certified hierarchized linked implementation of combinatorial hypermaps using a general notion...
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Formal Proof in Coq and Derivation of an Imperative Program to Compute Convex Hulls
This article deals with a method to build programs in computational geometry from their specifications. It focuses on a case study namely computing...
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Frequent Submap Discovery
Combinatorial maps are nice data structures for modeling the topology of nD objects subdivided in cells (e.g., vertices, edges, faces, volumes, ...)...
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Extracting Plane Graphs from Images
In order to use structural techniques from graph-based pattern recognition, a first necessary step consists in extracting a graph in an automatic way...
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Formal Study of Plane Delaunay Triangulation
This article presents the formal proof of correctness for a plane Delaunay triangulation algorithm. It consists in repeating a sequence of edge...
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Signatures of Combinatorial Maps
In this paper, we address the problem of computing a canonical representation of an n-dimensional combinatorial map. To do so, we define two...
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A Polynomial Algorithm for Submap Isomorphism
In this paper, we address the problem of searching for a pattern in a plane graph, i.e., a planar drawing of a planar graph. To do that, we propose...
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An Intuitionistic Proof of a Discrete Form of the Jordan Curve Theorem Formalized in Coq with Combinatorial Hypermaps
This paper presents a completely formalized proof of a discrete form of the Jordan Curve Theorem. It is based on a hypermap model of planar...
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Representation of Planar Hypergraphs by Contacts of Triangles
Many representation theorems extend from planar graphs to planar hypergraphs. The authors proved in [10] that every planar graph has a representation...
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A New Contour Filling Algorithm Based on 2D Topological Map
In this paper, we present a topological algorithm which allows to fill contours images. The filling problem has been widely treated and it recently...
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Topological Map: An Efficient Tool to Compute Incrementally Topological Features on 3D Images
In this paper, we show how to use the three dimensional topological map in order to compute efficiently topological features on objects contained in...
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How to Tile by Dominoes the Boundary of a Polycube
We prove that the boundary of a polycube (finite union of integer unit cubes) has always a tiling by foldable dominoes (two edge-adjacent unit...
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Using 2D Topological Map Information in a Markovian Image Segmentation
Topological map is a mathematical model of labeled image representation which contains both topological and geometrical information. In this work, we...
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Comparison and Convergence of Two Topological Models for 3D Image Segmentation
In this paper we compare two topological models of 3D segmented images representation. These models are based on a collaboration between a...
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Removal and Contraction for n-Dimensional Generalized Maps
Removal and contraction are basic operations for several methods conceived in order to handle irregular image pyramids, for multi-level image...
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Functional Modeling of Structured Images
Functional Graphical Models (FGM) describe functional dependence between variables by means of implicit equations. They offer a convenient way to...
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Topological Map Based Algorithms for 3D Image Segmentation
One of the most commonly used approach to segment a 2D image is the split and merge approach. In this paper, we are defining these two operations in...
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Introduction to Combinatorial Pyramids
A pyramid is a stack of image representations with decreasing resolution. Many image processing algorithms run on this hierarchical structure in...
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Topological Encoding of 3D Segmented Images
In this paper we define the 3d topological map and give an optimal algorithm which computes it from a segmented image. This data structure encodes...
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Orthogonal drawings of graphs for the automation of VLSI circuit design
This article shows the recent developments on orthogonal drawings of graphs which have applications for the automation of VLSI circuit design....