Anne Vialard

Fast, accurate and convergent tangent estimation on digital contours

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 multigrid convergence) is proved in the case of convex shapes with C^3 boundary.

Analysis and comparative evaluation of discrete tangent estimators

This paper presents a comparative evaluation of tangent estimators 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, asymptotic convergence. We further propose a new estimator mixing the qualities of existing ones and outperforming them on most mentioned points.

Geometrical parameters extraction from discrete paths

We present in this paper the advantages of using the model of Euclidean paths for the geometrical analysis of a discrete curve. The Euclidean paths are a semi-continuous representation of a discrete path providing a good approximation of the underlying real curve. We describe the use of this model to obtain accurate estimations of lenght, tangent orientation and curvature.

Euclidean paths: a new representation of boundary of discrete regions

The aim of this work is to provide a means to approximate the real boundary underlying the discrete boundary of a digitized 2D region. We require that the sampling of the reconstructed boundary be exactly the discrete one. To this end, we propose a new representation of the boundary of a discrete region that we call Euclidean paths. This paper fully describes the method used to build a Euclidean path and gives several examples of applications both for image analysis and image synthesis.

Quality Evaluation of Ancient Digitized Documents for Binarization Prediction

This article proposes an approach to predict the result of binarization algorithms on a given document image according to its state of degradation. Indeed, historical documents suffer from different types of degradation which result in binarization errors. We intend to characterize the degradation of a document image by using different features based on the intensity, quantity and location of the degradation. These features allow us to build prediction models of binarization algorithms that are very accurate according to R2 values and p-values. The prediction models are used to select the best binarization algorithm for a given document image. Obviously, this image-by-image strategy improves the binarization of the entire dataset.

Discrete Deformable Boundaries for the Segmentation of Multidimensional Images

Energy-minimizing techniques are an interesting approach to the segmentation problem. They extract image components by deforming a geometric model according to energy constraints. This paper proposes an extension to these works, which can segment arbitrarily complex image components in any dimension. The geometric model is a digital surface with which an energy is associated. The model grows inside the component to segment by following minimal energy paths. The segmentation result is obtained a posteriori by examining the energies of the successive model shapes. We validate our approach on several 2D images.

A new antialiasing approach for image compositing

In this paper we describe a new antialiasing technique for discrete regions. We propose the use of a new model of contours, called euclidean paths, which provides an approximation of the underlying real boundary of a discrete region. Euclidean paths are used to compute the blending coefficients of the frontier pixels. This method allows us to superimpose a discrete region on a background while avoiding the well-known staircase effect.

Inter-pixel Euclidean paths for image analysis

Inter-pixel boundaries provide a robust and consistent description of segmented images but have a poor visual aspect, especially when being enlarged. Approximation curve are sometimes used to smooth discrete boundaries but they do not provide error free reconstruction and may be uneasy to use in this context. In this paper we show the advantages of using Euclidean paths in order to smooth inter-pixel boundaries and we demonstrate the interest of inter-pixel Euclidean paths for the purpose of image segmentation and analysis.

Centerlines of Tubular Volumes Based on Orthogonal Plane Estimation

In this article we present a new method to compute a centerline on tubular volumes. The curve-skeleton is central to many applications in discrete geometry, since it captures interesting geometrical and topological properties with respect to the initial volume. Although there are numerous algorithms for skeleton computation, they are not necessarily well-suited for tubular volume specificities, and can lead to unexpected results faulty branches, not complete. Our method works on tubular-like volumes with junctions tree structures and varying diameter. It is based on the center of mass of cross-sections computed using a Voronoi covariance measure on the volume. Our method adapts its parameters to the shape of the tube. The results on both synthetic and real tubular structures with non-constant diameter illustrate the methods efficiency.

Precise Cross-Section Estimation on Tubular Organs

In this article we present a new method to estimate precisely the cross-section of tubular organs. Obtaining a precise cross-section is the critical step to perform quantitative analysis of those organs, for which diameter or area are often correlated to pathologies. Our estimation method, based on a covariance measure from the Voronoi cells of the set of studied points, can be computed either from the skeleton representation, or from the whole set of voxels of the segmented tubular organ. This estimator can give a cross-section estimation from any point of the organ, and is both more accurate and more robust to segmentation errors than state-of-the-art methods.