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This work presents a generic deformable model for extracting objects from volumetric data with a coarse-to-fine approach. This model is based on a dynamic triangulated surface which alters its geometry according to internal and external constraints to perform shape recovery. A new framework for topology changes is proposed to extract complex objects: within(More)
The Minimum Length Polygon (MLP) is an interesting first order approximation of a digital contour. For instance, the convexity of the MLP is characteristic of the digital convexity of the shape, its perimeter is a good estimate of the perimeter of the digitized shape. We present here two novel equivalent definitions of MLP, one arithmetic, one(More)
This paper presents a new tangent estimator to digitized curves based on digital line recognition. It outperforms existing ones on important criteria while keeping the same computation time: accuracy on smooth or polygonal shapes, isotropy, preservation of inflexion points and convexity, asymptotic behaviour. Its asymptotic convergence (sometimes called(More)
This paper presents a comparative evaluation of tangent es-timators based on digital line recognition on digital curves. The comparison is carried out with a comprehensive set of criteria: accuracy on smooth or polygonal shapes, behaviour on convex/concave parts, computation time, isotropy, aymptotic convergence. We further propose a new estimator mixing(More)
Deformable Model with Adaptive Mesh and Automated Topology Changes – p.1/21 Outline 1. Motivations 2. Description of the deformable model 2.1 Resolution adaptation by changing metrics 2.2 Topology adaptation 2.3 Dynamics 3. Defining metrics with respect to images 3.1 Required properties 3.2 Building metrics from images 4. Results 5. Conclusion and(More)
Discrete geometry redefines notions borrowed from Euclidean geometry creating a need for new algorithmical tools. The notion of convexity does not translate trivially, and detecting if a discrete region of the plane is convex requires a deeper analysis. To the many different approaches of digital convexity, we propose the combinatorics on words point of(More)
We propose in this paper a new curvature estimator based on the set of maximal digital circular arcs. For strictly convex shapes with continuous curvature fields digitized on a grid of step h, we show that this estimator is mutligrid convergent if the discrete length of the maximal digital circular arcs grows in Ω(h − 1 2). We indeed observed this order of(More)
Topological invariants are extremely useful in many applications related to digital imaging and geometric modeling, and homology is a classical one, which has not yet been fully explored in image applications. We present an algorithm that computes the whole homology of an object of arbitrary dimension: Betti numbers, torsion coefficients and generators.(More)