David Coeurjolly

Bio: David Coeurjolly is an academic researcher from University of Lyon. The author has contributed to research in topics: Digital geometry & Discrete geometry. The author has an hindex of 24, co-authored 128 publications receiving 1900 citations. Previous affiliations of David Coeurjolly include Institut national des sciences Appliquées de Lyon & Lyon College.

Wasserstein Dictionary Learning: Optimal Transport-based unsupervised non-linear dictionary learning

Abstract: This article introduces a new non-linear dictionary learning method for histograms in the probability simplex. The method leverages optimal transport theory, in the sense that our aim is to reconstruct histograms using so called displacement interpolations (a.k.a. Wasserstein barycenters) between dictionary atoms; such atoms are themselves synthetic histograms in the probability simplex. Our method simultaneously estimates such atoms, and, for each datapoint, the vector of weights that can optimally reconstruct it as an optimal transport barycenter of such atoms. Our method is computationally tractable thanks to the addition of an entropic regularization to the usual optimal transportation problem, leading to an approximation scheme that is efficient, parallel and simple to differentiate. Both atoms and weights are learned using a gradient-based descent method. Gradients are obtained by automatic differentiation of the generalized Sinkhorn iterations that yield barycenters with entropic smoothing. Because of its formulation relying on Wasserstein barycenters instead of the usual matrix product between dictionary and codes, our method allows for non-linear relationships between atoms and the reconstruction of input data. We illustrate its application in several different image processing settings.

Optimal Separable Algorithms to Compute the Reverse Euclidean Distance Transformation and Discrete Medial Axis in Arbitrary Dimension

Abstract: In binary images, the distance transformation (DT) and the geometrical skeleton extraction are classic tools for shape analysis. In this paper, we present time optimal algorithms to solve the reverse Euclidean distance transformation and the reversible medial axis extraction problems for d-dimensional images. We also present a d-dimensional medial axis filtering process that allows us to control the quality of the reconstructed shape

A comparative evaluation of length estimators of digital curves

Abstract: This paper compares previously published length estimators in image analysis having digitized curves as input. The evaluation uses multigrid convergence (theoretical results and measured speed of convergence) and further measures as criteria. This paper also suggests a new gradient-based method for length estimation, and combines a previously proposed length estimator for straight segments with a polygonalization method.

A survey of content based 3D shape retrieval methods

Abstract: Recent developments in techniques for modeling, digitizing and visualizing 3D shapes has led to an explosion in the number of available 3D models on the Internet and in domain-specific databases. This has led to the development of 3D shape retrieval systems that, given a query object, retrieve similar 3D objects. For visualization, 3D shapes are often represented as a surface, in particular polygonal meshes, for example in VRML format. Often these models contain holes, intersecting polygons, are not manifold, and do not enclose a volume unambiguously. On the contrary, 3D volume models, such as solid models produced by CAD systems, or voxels models, enclose a volume properly. This paper surveys the literature on methods for content based 3D retrieval, taking into account the applicability to surface models as well as to volume models. The methods are evaluated with respect to several requirements of content based 3D shape retrieval, such as: (1) shape representation requirements, (2) properties of dissimilarity measures, (3) efficiency, (4) discrimination abilities, (5) ability to perform partial matching, (6) robustness, and (7) necessity of pose normalization. Finally, the advantages and limitations of the several approaches in content based 3D shape retrieval are discussed.

Graefe's archive for clinical and experimental ophthalmology

Abstract: "Graefe's Archive" is a distinguished international journal that presents original clinical reports and clinically relevant experimental studies. Founded in 1854 by Albrecht von Graefe to serve as a source of useful clinical information and a stimulus for discussion, the journal has published articles by leading ophthalmologists and vision research scientists for more than a century. With peer review by an international Editorial Board and prompt English-language publication, "Graefe's Archive" provides rapid dissemination of clinical and clinically related experimental information.

A Survey of Shape Feature Extraction Techniques

Abstract: "A picture is worth one thousand words". This proverb comes from Confucius a Chinese philosopher before about 2500 years ago. Now, the essence of these words is universally understood. A picture can be magical in its ability to quickly communicate a complex story or a set of ideas that can be recalled by the viewer later in time. Visual information plays an important role in our society, it will play an increasingly pervasive role in our lives, and there will be a growing need to have these sources processed further. The pictures or images are used in many application areas like architectural and engineering design, fashion, journalism, advertising, entertainment, etc. Thus it provides the necessary opportunity for us to use the abundance of images. However, the knowledge will be useless if one can't _nd it. In the face of the substantive and increasing apace images, how to search and to retrieve the images that we interested with facility is a fatal problem: it brings a necessity for image retrieval systems. As we know, visual features of the images provide a description of their content. Content-based image retrieval (CBIR), emerged as a promising mean for retrieving images and browsing large images databases. CBIR has been a topic of intensive research in recent years. It is the process of retrieving images from a collection based on automatically extracted features.