Computational geometry

http://research.engr.oregonstate.edu/immiscibles/sites/research.engr.oregonstate.edu.immiscibles/files/Papers/Wildenschild_Sheppard_AWR_2012.pdf

X-ray imaging and analysis techniques for quantifying pore-scale structure and processes in subsurface porous medium systems

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.

/pdf/a-survey-of-content-based-3d-shape-retrieval-methods-1p1e9hurpn.pdf

A survey of content based 3D shape retrieval methods

"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.

Graefe's archive for clinical and experimental ophthalmology

"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.

/pdf/a-survey-of-shape-feature-extraction-techniques-3qmkhziio7.pdf

A Survey of Shape Feature Extraction Techniques

We present, in details, a generic tool to estimate differential geometric quantities on digital shapes, which are subsets of Z^d. This tool, called digital integral invariant, simply places a ball at the point of interest, and then examines the intersection of this ball with input data to infer local geometric information. Just counting the number of input points within the intersection provides curvature estimation in 2D and mean curvature estimation in 3D. The covariance matrix of the same point set allows to recover principal curvatures, principal directions and normal direction estimates in 3D. We show the multigrid convergence of all these estimators, which means that their estimations tend toward the exact geometric quantities on — smooth enough— Euclidean shapes digitized with finer and finer gridsteps. During the course of the chapter, we establish several multigrid convergence results of digital volume and moments estimators in arbitrary dimensions. Afterwards, we show how to set automatically the radius parameter while keeping multigrid convergence properties. Our estimators are then demonstrated to be accurate in practice, with extensive comparisons with state-of-the-art methods. To conclude the exposition, we discuss their robustness to perturbations and noise in input data and we show how such estimators can detect features using scale-space arguments.

/pdf/robust-and-convergent-curvature-and-normal-estimators-with-5fc9m1ru3z.pdf

Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants

Optimal transport (OT) distances between probability distributions are parameterized by the ground metric they use between observations. Their relevance for real-life applications strongly hinges on whether that ground metric parameter is suitably chosen. The challenge of selecting it adaptively and algorithmically from prior knowledge, the so-called ground metric learning (GML) problem, has therefore appeared in various settings. In this paper, we consider the GML problem when the learned metric is constrained to be a geodesic distance on a graph that supports the measures of interest. This imposes a rich structure for candidate metrics, but also enables far more efficient learning procedures when compared to a direct optimization over the space of all metric matrices. We use this setting to tackle an inverse problem stemming from the observation of a density evolving with time; we seek a graph ground metric such that the OT interpolation between the starting and ending densities that result from that ground metric agrees with the observed evolution. This OT dynamic framework is relevant to model natural phenomena exhibiting displacements of mass, such as the evolution of the color palette induced by the modification of lighting and materials.

Ground Metric Learning on Graphs

This article presents a novel discretization of the Laplace–Beltrami operator on digital surfaces.We adapt an existing convolution technique proposed by Belkin et al. [5] for triangular meshes to topological border of subsets of Z n. The core of the method relies on first-order estimation of measures associated with our discrete elements (such as length, area etc.). We show strong consistency (i.e. pointwise convergence) of the operator and compare it against various other discretizations.

/pdf/laplace-beltrami-operator-on-digital-surfaces-ojw2s8ftsk.pdf

Laplace–Beltrami Operator on Digital Surfaces

This paper presents a new three-dimensional shape descriptor: 3D angular radial transform. It is an extension of the 2D region based shape descriptor proposed by MPEG-7, the angular radial transform (ART). We propose to generalize the ART to index 3D models.

/pdf/art-extension-for-description-indexing-and-retrieval-of-3d-4avndh87kw.pdf

ART extension for description, indexing and retrieval of 3D objects

On the classical discrete grid, the analysis of digital straight lines (DSL for short) has been intensively studied for nearly half a century. In this article, we are interested in a discrete geometry on irregular grids. More precisely, our goal is to define geometrical properties on irregular isothetic grids that are tilings of the Euclidean plane with different sized axis parallel rectangles.

/pdf/supercover-model-and-digital-straight-line-recognition-on-4c3uezg07g.pdf

David Coeurjolly

Papers

Robust and Convergent Curvature and Normal Estimators with Digital Integral Invariants

Ground Metric Learning on Graphs

Laplace–Beltrami Operator on Digital Surfaces

ART extension for description, indexing and retrieval of 3D objects

Supercover model and digital straight line recognition on irregular isothetic grids