Multilevel Solvers for Unstructured Surface Meshes

Parameterization of unstructured surface meshes is of fundamental importance in many applications of digital geometry processing. Such parameterization approaches give rise to large and exceedingly ill-conditioned systems which are difficult or impossible to solve without the use of sophisticated multilevel preconditioning strategies. Since the underlying meshes are very fine to begin with, such multilevel preconditioners require mesh coarsening to build an appropriate hierarchy. In this paper we consider several strategies for the construction of hierarchies using ideas from mesh simplification algorithms used in the computer graphics literature. We introduce two novel hierarchy construction schemes and demonstrate their superior performance when used in conjunction with a multigrid preconditioner

A perception and manipulation system for collecting rock samples

An important part of a planetary exploration mission is to collect and analyze surface samples. As part of the Carnegie Mellon University Ambler Project, researchers are investigating techniques for collecting samples using a robot arm and a range sensor. The aim of this work is to make the sample collection operation fully autonomous. Described here are the components of the experimental system, including a perception module that extracts objects of interest from range images and produces models of their shapes, and a manipulation module that enables the system to pick up the objects identified by the perception module. The system was tested on a small testbed using natural terrain

Subset Warping: Rubber Sheeting with Cuts

Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself

Fast and deep deformation approximations

Character rigs are procedural systems that compute the shape of an animated character for a given pose. They can be highly complex and must account for bulges, wrinkles, and other aspects of a character's appearance. When comparing film-quality character rigs with those designed for real-time applications, there is typically a substantial and readily apparent difference in the quality of the mesh deformations. Real-time rigs are limited by a computational budget and often trade realism for performance. Rigs for film do not have this same limitation, and character riggers can make the rig as complicated as necessary to achieve realistic deformations. However, increasing the rig complexity slows rig evaluation, and the animators working with it can become less efficient and may experience frustration. In this paper, we present a method to reduce the time required to compute mesh deformations for film-quality rigs, allowing better interactivity during animation authoring and use in real-time games and applications. Our approach learns the deformations from an existing rig by splitting the mesh deformation into linear and nonlinear portions. The linear deformations are computed directly from the transformations of the rig's underlying skeleton. We use deep learning methods to approximate the remaining nonlinear portion. In the examples we show from production rigs used to animate lead characters, our approach reduces the computational time spent on evaluating deformations by a factor of 5×-10×. This significant savings allows us to run the complex, film-quality rigs in real-time even when using a CPU-only implementation on a mobile device

2D and 3D surface image processing algorithms and their applications

This doctoral dissertation work aims to develop algorithms for 2D image segmentation application of solar filament disappearance detection, 3D mesh simplification, and 3D image warping in pre-surgery simulation. Filament area detection in solar images is an image segmentation problem. A thresholding and region growing combined method is proposed and applied in this application. Based on the filament area detection results, filament disappearances are reported in real time. The solar images in 1999 are processed with this proposed system and three statistical results of filaments are presented. 3D images can be obtained by passive and active range sensing. An image registration process finds the transformation between each pair of range views. To model an object, a common reference frame in which all views can be transformed must be defined. After the registration, the range views should be integrated into a non-redundant model. Optimization is necessary to obtain a complete 3D model. One single surface representation can better fit to the data. It may be further simplified for rendering, storing and transmitting efficiently, or the representation can be converted to some other formats. This work proposes an efficient algorithm for solving the mesh simplification problem, approximating an arbitrary mesh by a simplified mesh. The algorithm uses Root Mean Square distance error metric to decide the facet curvature. Two vertices of one edge and the surrounding vertices decide the average plane. The simplification results are excellent and the computation speed is fast. The algorithm is compared with six other major simplification algorithms. Image morphing is used for all methods that gradually and continuously deform a source image into a target image, while producing the in-between models. Image warping is a continuous deformation of a: graphical object. A morphing process is usually composed of warping and interpolation. This work develops a direct-manipulation-of-free-form-deformation-based method and application for pre-surgical planning. The developed user interface provides a friendly interactive tool in the plastic surgery. Nose augmentation surgery is presented as an example. Displacement vector and lattices resulting in different resolution are used to obtain various deformation results. During the deformation, the volume change of the model is also considered based on a simplified skin-muscle model

3D Mesh Simplification. A survey of algorithms and CAD model simplification tests

Simplification of highly detailed CAD models is an important step when CAD models are visualized or by other means utilized in augmented reality applications. Without simplification, CAD models may cause severe processing and storage is- sues especially in mobile devices. In addition, simplified models may have other advantages like better visual clarity or improved reliability when used for visual pose tracking. The geometry of CAD models is invariably presented in form of a 3D mesh. In this paper, we survey mesh simplification algorithms in general and focus especially to algorithms that can be used to simplify CAD models. We test some commonly known algorithms with real world CAD data and characterize some new CAD related simplification algorithms that have not been surveyed in previous mesh simplification reviews.Siirretty Doriast

Coarse-to-fine approximation of range images with bounded error adaptive triangular meshes

Copyright 2007 Society of Photo-Optical Instrumentation Engineers. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper are prohibitedA new technique for approximating range images with adaptive triangular meshes ensuring a user-defined approximation error is presented. This technique is based on an efficient coarse-to-fine refinement algorithm that avoids iterative optimization stages. The algorithm first maps the pixels of the given range image to 3D points defined in a curvature space. Those points are then tetrahedralized with a 3D Delaunay algorithm. Finally, an iterative process starts digging up the convex hull of the obtained tetrahedralization, progressively removing the triangles that do not fulfill the specified approximation error. This error is assessed in the original 3D space. The introduction of the aforementioned curvature space makes it possible for both convex and nonconvex object surfaces to be approximated with adaptive triangular meshes, improving thus the behavior of previous coarse-to-fine sculpturing techniques. The proposed technique is evaluated on real range images and compared to two simplification techniques that also ensure a user-defined approximation error: a fine-to-coarse approximation algorithm based on iterative optimization (Jade) and an optimization-free, fine-to-coarse algorithm (Simplification Envelopes).This work has been partially supported by the Spanish Ministry of Education and Science under projects TRA2004- 06702/AUT and DPI2004-07993-C03-03. The first author was supported by The Ramón y Cajal Program

Surveying and Three-Dimensional Modeling for Preservation and Structural Analysis of Cultural Heritage

Dense point clouds can be used for three important steps in structural analysis, in the field of cultural heritage, regardless of which instrument it was used for acquisition data. Firstly, they allow deriving the geometric part of a finite element (FE) model automatically or semi-automatically. User input is mainly required to complement invisible parts and boundaries of the structure, and to assign meaningful approximate physical parameters. Secondly, FE model obtained from point clouds can be used to estimate better and more precise parameters of the structural analysis, i.e., to train the FE model. Finally, the definition of a correct Level of Detail about the three-dimensional model, deriving from the initial point cloud, can be used to define the limit beyond which the structural analysis is compromised, or anyway less precise. In this work of research, this will be demonstrated using three different case studies of buildings, consisting mainly of masonry, measured through terrestrial laser scanning and photogrammetric acquisitions. This approach is not a typical study for geomatics analysis, but its challenges allow studying benefits and limitations. The results and the proposed approaches could represent a step towards a multidisciplinary approach where Geomatics can play a critical role in the monitoring and civil engineering field. Furthermore, through a geometrical reconstruction, different analyses and comparisons are possible, in order to evaluate how the numerical model is accurate. In fact, the discrepancies between the different results allow to evaluate how, from a geometric and simplified modeling, important details can be lost. This causes, for example, modifications in terms of mass and volume of the structure

From 3D Models to 3D Prints: an Overview of the Processing Pipeline

Due to the wide diffusion of 3D printing technologies, geometric algorithms for Additive Manufacturing are being invented at an impressive speed. Each single step, in particular along the Process Planning pipeline, can now count on dozens of methods that prepare the 3D model for fabrication, while analysing and optimizing geometry and machine instructions for various objectives. This report provides a classification of this huge state of the art, and elicits the relation between each single algorithm and a list of desirable objectives during Process Planning. The objectives themselves are listed and discussed, along with possible needs for tradeoffs. Additive Manufacturing technologies are broadly categorized to explicitly relate classes of devices and supported features. Finally, this report offers an analysis of the state of the art while discussing open and challenging problems from both an academic and an industrial perspective.Comment: European Union (EU); Horizon 2020; H2020-FoF-2015; RIA - Research and Innovation action; Grant agreement N. 68044