Hierarchical representation of 2D polygons based on approximate skeletons

No abstract availabl

An interactive analysis of harmonic and diffusion equations on discrete 3D shapes

AbstractRecent results in geometry processing have shown that shape segmentation, comparison, and analysis can be successfully addressed through the spectral properties of the Laplace–Beltrami operator, which is involved in the harmonic equation, the Laplacian eigenproblem, the heat diffusion equation, and the definition of spectral distances, such as the bi-harmonic, commute time, and diffusion distances. In this paper, we study the discretization and the main properties of the solutions to these equations on 3D surfaces and their applications to shape analysis. Among the main factors that influence their computation, as well as the corresponding distances, we focus our attention on the choice of different Laplacian matrices, initial boundary conditions, and input shapes. These degrees of freedom motivate our choice to address this study through the executable paper, which allows the user to perform a large set of experiments and select his/her own parameters. Finally, we represent these distances in a unified way and provide a simple procedure to generate new distances on 3D shapes

Metodologie di Morfologia Matematica per il filtraggio di immagini

No abstract availabl

Tailor: understanding 3D shapes using curvature

Tools for the automatic decomposition of a surface into shape features will facilitate the editing, matching, texturing, morphing, compression, and simplification of 3D shapes. Different features, such as flats, limbs, tips, pits, and various blending shapes that transition between them may be characterized in terms of local curvature and other differential properties of the surface or in terms of a global skeletal organization of the volume it encloses. Unfortunately, both solutions are extremely sensitive to small perturbations in the surface smoothness and to quantization effects when they operate on triangulated surfaces. Thus, we propose a multi-resolution approach, which not only estimates the curvature of a vertex over neighborhoods of variable size, but also takes into account the topology of the surface in that neighborhood. Our approach is based on blowing a spherical bubble at each vertex and studying how the intersection of that bubble with the surface evolves. For example, for a thin limb, that intersection will start simply connected and will rapidly split into two components. For a point on the tip of a limb, that intersection will usually simply remain connected, but the ratio of its length to the radius of the bubble will be decreasing. For a point on a blend, that ratio will exceed 2p. We describe an efficient approach for computing these characteristics for a sampled set of bubble radii and for using them to identify features, based on easily formulated f i lters, that may capture the needs of a particular application

Edge-Sharpener: A geometric filter for recovering sharp features in uniform triangulations

3D scanners, iso-surface extraction procedures, and several recent geometric compression schemes sample surfaces of 3D shapes in a regular fashion, without any attempt to align the samples with the sharp edges and corners of the original shape. Consequently, the interpolating triangle meshes chamfer these sharp features and thus exhibit significant errors. The new Edge-Sharpener filter introduced here identifies the chamfer edges and subdivides them and their incident triangles by inserting new vertices and by forcing these vertices to lie on intersections of planes that locally approximate the smooth surfaces that meet at these sharp features. This post-processing significantly reduces the error produced by the initial sampling process. For example, we have observed that the L2 error introduced by the SwingWrapper9 remeshing-based compressor can be reduced down to a fifth by executing Edge-Sharpener after decompression, with no additional information

Three-Dimensional Modelling of the Terra Nova Bay Sea Floor (Ross Sea - Antarctica)

The importance of gathering data on the Antarctic coastline and its adjacent waters has been widely recognised by the Antarctic Treaty Consultative Meeting (ATCM), the Council of Managers of National Antarctic Programs (COMNAP) and the Scientific Committee on Antarctic Research (SCAR). In particular, both for navigational safety and environmental monitoring, it is very desirable to increase hydrographic activity in those areas which have the most significant importance from a scientific or navigational point of view - such as in the continental shelf and continental slope areas of the western part of the Ross Sea. Quite apart from the safety of navigation requirements, knowledge of the seabed topography is necessary to study and understand the various phenomena taking place in the marine environment. For example, the movement of water masses and their mixing processes depend on the shape of the seabed and adjacent coastline. The sea area surrounding Antarctica is one of the least explored parts of the world’s oceans and the available bathymetric data is only sufficient to allow a very general analysis to be made. With the probable growth of tourism and fishing around Antarctica and with the increasing need to understand the effects on the world’s climate of Antarctic water patterns, it is necessary to consider powerful new techniques - such as threedimensional modelling of the sea floors - in order to build up more quickly an effective and reliable bathymetric data base of Antarctic waters

A multi-resolutive extraction of geometric descriptors for virtual shapes and humans

Tools for the automatic decomposition of a surface into shape features will facilitate and optimize the classification, matching, texturing, morphing, and simplification of 3D shapes. Different features, such as flats, limbs, tips, pits, and various blending shapes between them may be characterized in terms of local curvature and other differential properties of the surface, or in terms of a global skeletal organization of the volume it encloses. However, both solutions are extremely sensitive to small perturbations in the surface smoothness and to quantization effects when they operate on triangulated surfaces. The paper presents a shape characterization based on a multi-resolutive curvature computation where the vertices of a given triangle mesh are classified according to their curvature and shape behavior in neighborhoods of increasing size, and whose final goal is to segment 3D models into main bodies and tubular parts, and to code the tube/body connectivity with their geometric parameters. Last, we propose to apply the morphological analysis for the automatically extraction of the semantic of human body models for their representation, retrieval and applications to animation. We prove the efficacy of our tool in automatically extracting morphological shape parameters and locating feature points on the human body identifying fingertips, nose,armpits, ankles, umbilicus, and so on

Between Algorithm and Model: Different Molecular Surface Definitions for the Poisson-Boltzmann based Electrostatic Characterization of Biomolecules in Solution

The definition of a molecular surface which is physically sound and computationally efficient is a very interesting and long standing problem in the implicit solvent continuum modeling of biomolecular systems as well as in the molecular graphics field. In this work, two molecular surfaces are evaluated with respect to their suitability for electrostatic computation as alternatives to the widely used Connolly-Richards surface: the blobby surface, an implicit Gaussian atom centered surface, and the skin surface. As figures of merit, we considered surface differentiability and surface area continuity with respect to atom positions, and the agreement with explicit solvent simulations. Geometric analysis seems to privilege the skin to the blobby surface, and points to an unexpected relationship between the non connectedness of the surface, caused by interstices in the solute volume, and the surface area dependence on atomic centers. In order to assess the ability to reproduce explicit solvent results, specific software tools have been developed to enable the use of the skin surface in Poisson-Boltzmann calculations with the DelPhi solver. Results indicate that the skin and Connolly surfaces have a comparable performance from this last point of view