A Comparative Study on Polygonal Mesh Simplification Algorithms

Polygonal meshes are a common way of representing three dimensional surface models in many different areas of computer graphics and geometry processing. However, with the evolution of the technology, polygonal models are becoming more and more complex. As the complexity of the models increase, the visual approximation to the real world objects get better but there is a trade-off between the cost of processing these models and better visual approximation. In order to reduce this cost, the number of polygons in a model can be reduced by mesh simplification algorithms. These algorithms are widely used such that nearly all of the popular mesh editing libraries include at least one of them. In this work, polygonal simplification algorithms that are embedded in open source libraries: CGAL, VTK and OpenMesh are compared with the Metro geometric error measuring tool. By this way we try to supply a guidance for developers for publicly available mesh libraries in order to implement polygonal mesh simplification

Efficient Decimation of Polygonal Models Using Normal Field Deviation

A simple and robust greedy algorithm has been proposed for efficient and quality decimation of polygonal models. The performance of a simplification algorithm depends on how the local geometric deviation caused by a local decimation operation is measured. As normal field of a surface plays key role in its visual appearance, exploiting the local normal field deviation in a novel way, a new measure of geometric fidelity has been introduced. This measure has the potential to identify and preserve the salient features of a surface model automatically. The resulting algorithm is simple to implement, produces approximations of better quality and is efficient in running time. Subjective and objective comparisons validate the assertion. It is suitable for applications where the focus is better speed-quality trade-off, and simplification is used as a processing step in other algorithms

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

High-Quality Simplification and Repair of Polygonal Models

Because of the rapid evolution of 3D acquisition and modelling methods, highly complex and detailed polygonal models with constantly increasing polygon count are used as three-dimensional geometric representations of objects in computer graphics and engineering applications. The fact that this particular representation is arguably the most widespread one is due to its simplicity, flexibility and rendering support by 3D graphics hardware. Polygonal models are used for rendering of objects in a broad range of disciplines like medical imaging, scientific visualization, computer aided design, film industry, etc. The handling of huge scenes composed of these high-resolution models rapidly approaches the computational capabilities of any graphics accelerator. In order to be able to cope with the complexity and to build level-of-detail representations, concentrated efforts were dedicated in the recent years to the development of new mesh simplification methods that produce high-quality approximations of complex models by reducing the number of polygons used in the surface while keeping the overall shape, volume and boundaries preserved as much as possible. Many well-established methods and applications require "well-behaved" models as input. Degenerate or incorectly oriented faces, T-joints, cracks and holes are just a few of the possible degenaracies that are often disallowed by various algorithms. Unfortunately, it is all too common to find polygonal models that contain, due to incorrect modelling or acquisition, such artefacts. Applications that may require "clean" models include finite element analysis, surface smoothing, model simplification, stereo lithography. Mesh repair is the task of removing artefacts from a polygonal model in order to produce an output model that is suitable for further processing by methods and applications that have certain quality requirements on their input. This thesis introduces a set of new algorithms that address several particular aspects of mesh repair and mesh simplification. One of the two mesh repair methods is dealing with the inconsistency of normal orientation, while another one, removes the inconsistency of vertex connectivity. Of the three mesh simplification approaches presented here, the first one attempts to simplify polygonal models with the highest possible quality, the second, applies the developed technique to out-of-core simplification, and the third, prevents self-intersections of the model surface that can occur during mesh simplification

Topology Preserving Simplification of 2D Non-Manifold Meshes with Embedded Structures

International audienceMesh simplification has received tremendous attention over the past years. Most of the previous works deal with a proper choice of error measures to guide the simplification. Preserving the topological characteristics of the mesh and possibly of data attached to the mesh is a more recent topic, the present paper is about.We introduce a new topology preserving simplification algorithm for triangular meshes, possibly non-manifold, with embedded polylines. In this context embedded means that the edges of the polylines are also edges of the mesh. The paper introduces a robust test to detect if the collapse of an edge in the mesh modifies either the topology of the mesh or the topology of the embedded polylines. This validity test is derived using combinatorial topology results. More precisely we define a so-called extended complex from the input mesh and the embedded polylines. We show that if an edge collapse of the mesh preserves the topology of this extended complex, then it also preserves both the topology of the mesh and the embedded polylines. Our validity test can be used for any 2-complex mesh, including non-manifold triangular meshes. It can be combined with any previously introduced error measure. Implementation of this validity test is described. We demonstrate the power and versatility of our method with scientific data sets from neuroscience, geology and CAD/CAM models from mechanical engineering

Structure-Aware Mesh Decimation

International audienceWe present a novel approach for the decimation of trian-gle surface meshes. Our algorithm takes as input a triangle surface mesh and a set of planar proxies detected in a pre-processing analysis step, and structured via an adjacency graph. It then performs greedy mesh decimation through a series of edge collapse, designed to approximate the local mesh geometry as well as the geometry and structure of proxies. Such structure-preserving approach is well suited to planar abstraction, i.e., extreme decimation approxi-mating well the planar parts while filtering out the others. Our experiments on a variety of inputs illustrate the po-tential of our approach in terms of improved accuracy and preservation of structure

Kolmiulotteisten tietokoneavusteisten mallien yksinkertaistaminen renderoinnin nopeuttamiseksi

Visualization of three-dimensional (3D) computer-aided design model is an integral part of the design process. Large assemblies such as plant or building designs contain a substantial amount of geometric data. New constraints for visualization performance and the amount of geometric data are set by the advent of mobile devices and virtual reality headsets. Our goal is to improve visualization performance and reduce memory consumption by simplifying 3D models while retaining the output simplification quality stable regardless of the geometric complexity of the input mesh. We research the current state of 3D mesh simplification methods that use geometry decimation. We design and implement our own data structure for geometry decimation. Based on the existing research, we select and use an edge decimation method for model simplification. In order to free the user from configuring edge decimation level per model by hand, and to retain a stable quality of the simplification output, we propose a threshold parameter, \textit{edge decimation cost threshold}. The threshold is calculated by multiplying the length of the model’s bounding box diagonal with a user-defined scale parameter. Our results show that the edge decimation cost threshold works as expected. The geometry decimation algorithm manages to simplify models with round surfaces with an excellent simplification rate. Based on the edge decimation cost threshold, the algorithm terminates the geometry decimation for models that have a large number of planar surfaces. Without the threshold, the simplification leads to large geometric errors quickly. The visualization performance improvement from the simplification scales almost at the same rate as the simplification rate

Proximity-aware multiple meshes decimation using quadric error metric

La décimation progressive de maillage par l'application successive d'opérateurs topologiques est un outil standard de traitement de la géométrie. Un élément clé de tels algorithmes est la métrique d'erreur, qui donne la priorité aux opérateurs minimisant l'erreur de décimation. La plupart des travaux précédents se concentrent sur la préservation des propriétés locales du maillage lors du processus de décimation, le plus notable étant la métrique d'erreur quadrique qui utilise l'opérateur d'effondrement d'arête. Toutefois, les maillages obtenus à partir de scènes issues de CAO et décrivant des systèmes complexes requièrent souvent une décimation significative pour la visualisation et l'interaction sur des terminaux bas de gamme. Par conséquent, la préservation de la disposition des objets est nécessaire dans de tels cas, afin de préserver la lisibilité globale du système pour des applications telles que la réparation sur site, l'inspection, la formation, les jeux sérieux, etc. Dans ce contexte, cette thèse a trait à préserver la lisibilité des relations de proximité entre maillages lors de la décimation, en introduisant une nouvelle approche pour la décimation conjointe de multiples maillages triangulaires présentant des proximités. Les travaux présentés dans cette thèse se décomposent en trois contributions. Tout d'abord, nous proposons un mécanisme pour la décimation simultanée de multiples maillages. Ensuite, nous introduisons une métrique d'erreur sensible à la proximité, combinant l'erreur locale de l'arête (i.e. la métrique d'erreur quadrique) avec une fonction pénalisant la proximité, ce qui augmente l'erreur des effondrements d'arête là où les maillages sont proches les uns des autres. Enfin, nous élaborons une détection automatique des zones de proximité. Pour finir, nous démontrons les performances de notre approche sur plusieurs modèles générés à partir de scènes issues de CAO.Progressive mesh decimation by successively applying topological operators is a standard tool in geometry processing. A key element of such algorithms is the error metric, which allows to prioritize operators minimizing the decimation error. Most previous work focus on preserving local properties of the mesh during the decimation process, with the most notable being the Quadric Error Metric which uses the edge collapse operator. However, meshes obtained from CAD scenes and describing complex systems often require significant decimation for visualization and interaction on low-end terminals. Hence preserving the arrangement of objects is required in such cases, in order to maintain the overall system readability for applications such as on-site repair, inspection, training, serious games, etc. In this context, this thesis focuses on preserving the readability of proximity relations between meshes during decimation, by introducing a novel approach for the joint decimation of multiple triangular meshes with proximities. The works presented in this thesis consist in three contributions. First, we propose a mechanism for the simultaneous decimation of multiple meshes. Second, we introduce a proximity-aware error metric, combining the local edge error (i.e. Quadric Error Metric) with a proximity penalty function, which increases the error of edge collapses modifying the geometry where meshes are close to each other. Last, we devise an automatic detection of proximity areas. Finally, we demonstrate the performances of our approach on several models generated from CAD scenes

Feature preserving decimation of urban meshes

1 online resource (vii, 72 pages) : illustrations (chiefly colour), charts (chiefly colour)Includes abstract.Includes bibliographical references (pages 65-72).Commercial buildings as well as residential houses represent core structures of any modern day urban or semi-urban areas. Consequently, 3D models of urban buildings are of paramount importance to a majority of digital urban applications such as city planning, 3D mapping and navigation, video games and movies, among others. However, current studies suggest that existing 3D modeling approaches often involve high computational cost and large storage volumes for processing the geometric details of the buildings. Therefore, it is essential to generate concise digital representations of urban buildings from the 3D measurements or images, so that the acquired information can be efficiently utilized for various urban applications. Such concise representations, often referred to as “lightweight” models, strive to capture the details of the physical objects with less computational storage. Furthermore, lightweight models consume less bandwidth for online applications and facilitate accelerated visualizations. In this thesis, we provide an assessment study on state-of-the-art data structures for storing lightweight urban buildings. Then we propose a method to generate lightweight yet highly detailed 3D building models from LiDAR scans. The lightweight modeling pipeline comprises the following stages: mesh reconstruction, feature points detection and mesh decimation through gradient structure tensors. The gradient of each vertex of the reconstructed mesh is obtained by estimating the vertex confidence through eigen analysis and further encoded into a 3 X 3 structure tensor. We analyze the eigenvalues of structure tensor representing gradient variations and use it to classify vertices into various feature classes, e.g., edges, and corners. While decimating the mesh, fea ture points are preserved through a mean cost-based edge collapse operation. The experiments on different building facade models show that our method is effective in generating simplified models with a trade-off between simplification and accuracy

Human perception-oriented segmentation for triangle meshes

A segmentação de malhas é um tópico importante de investigação em computação gráfica, em particular em modelação geométrica. Isto deve-se ao facto de as técnicas de segmentaçãodemalhasteremváriasaplicações,nomeadamentenaproduçãodefilmes, animaçãoporcomputador, realidadevirtual, compressãodemalhas, assimcomoemjogosdigitais. Emconcreto, asmalhastriangularessãoamplamenteusadasemaplicações interativas, visto que sua segmentação em partes significativas (também designada por segmentação significativa, segmentação perceptiva ou segmentação perceptualmente significativa ) é muitas vezes vista como uma forma de acelerar a interação com o utilizador ou a deteção de colisões entre esses objetos 3D definidos por uma malha, bem como animar uma ou mais partes significativas (por exemplo, a cabeça de uma personagem) de um dado objeto, independentemente das restantes partes. Acontece que não se conhece nenhuma técnica capaz de segmentar correctamente malhas arbitrárias −ainda que restritas aos domínios de formas livres e não-livres− em partes significativas. Algumas técnicas são mais adequadas para objetos de forma não-livre (por exemplo, peças mecânicas definidas geometricamente por quádricas), enquanto outras são mais talhadas para o domínio dos objectos de forma livre. Só na literatura recente surgem umas poucas técnicas que se aplicam a todo o universo de objetos de forma livre e não-livre. Pior ainda é o facto de que a maioria das técnicas de segmentação não serem totalmente automáticas, no sentido de que quase todas elas exigem algum tipo de pré-requisitos e assistência do utilizador. Resumindo, estes três desafios relacionados com a proximidade perceptual, generalidade e automação estão no cerne do trabalho descrito nesta tese. Para enfrentar estes desafios, esta tese introduz o primeiro algoritmo de segmentação baseada nos contornos ou fronteiras dos segmentos, cuja técnica se inspira nas técnicas de segmentação baseada em arestas, tão comuns em análise e processamento de imagem,porcontraposiçãoàstécnicasesegmentaçãobaseadaemregiões. Aideiaprincipal é a de encontrar em primeiro lugar a fronteira de cada região para, em seguida, identificar e agrupar todos os seus triângulos internos. As regiões da malha encontradas correspondem a saliências e reentrâncias, que não precisam de ser estritamente convexas, nem estritamente côncavas, respectivamente. Estas regiões, designadas regiões relaxadamenteconvexas(ousaliências)eregiõesrelaxadamentecôncavas(oureentrâncias), produzem segmentações que são menos sensíveis ao ruído e, ao mesmo tempo, são mais intuitivas do ponto de vista da perceção humana; por isso, é designada por segmentação orientada à perceção humana (ou, human perception- oriented (HPO), do inglês). Além disso, e ao contrário do atual estado-da-arte da segmentação de malhas, a existência destas regiões relaxadas torna o algoritmo capaz de segmentar de maneira bastante plausível tanto objectos de forma não-livre como objectos de forma livre. Nesta tese, enfrentou-se também um quarto desafio, que está relacionado com a fusão de segmentação e multi-resolução de malhas. Em boa verdade, já existe na literatura uma variedade grande de técnicas de segmentação, bem como um número significativo de técnicas de multi-resolução, para malhas triangulares. No entanto, não é assim tão comum encontrar estruturas de dados e algoritmos que façam a fusão ou a simbiose destes dois conceitos, multi-resolução e segmentação, num único esquema multi-resolução que sirva os propósitos das aplicações que lidam com malhas simples e segmentadas, sendo que neste contexto se entende que uma malha simples é uma malha com um único segmento. Sendo assim, nesta tese descreve-se um novo esquema (entenda-seestruturasdedadosealgoritmos)demulti-resoluçãoesegmentação,designado por extended Ghost Cell (xGC). Este esquema preserva a forma das malhas, tanto em termos globais como locais, ou seja, os segmentos da malha e as suas fronteiras, bem como os seus vincos e ápices são preservados, não importa o nível de resolução que usamos durante a/o simplificação/refinamento da malha. Além disso, ao contrário de outros esquemas de segmentação, tornou-se possível ter segmentos adjacentes com dois ou mais níveis de resolução de diferença. Isto é particularmente útil em animação por computador, compressão e transmissão de malhas, operações de modelação geométrica, visualização científica e computação gráfica. Em suma, esta tese apresenta um esquema genérico, automático, e orientado à percepção humana, que torna possível a simbiose dos conceitos de segmentação e multiresolução de malhas trianguladas que sejam representativas de objectos 3D.The mesh segmentation is an important topic in computer graphics, in particular in geometric computing. This is so because mesh segmentation techniques find many applications in movies, computer animation, virtual reality, mesh compression, and games. Infact, trianglemeshesarewidelyusedininteractiveapplications, sothattheir segmentation in meaningful parts (i.e., human-perceptually segmentation, perceptive segmentationormeaningfulsegmentation)isoftenseenasawayofspeedinguptheuser interaction, detecting collisions between these mesh-covered objects in a 3D scene, as well as animating one or more meaningful parts (e.g., the head of a humanoid) independently of the other parts of a given object. It happens that there is no known technique capable of correctly segmenting any mesh into meaningful parts. Some techniques are more adequate for non-freeform objects (e.g., quadricmechanicalparts), whileothersperformbetterinthedomainoffreeform objects. Only recently, some techniques have been developed for the entire universe of objects and shapes. Even worse it is the fact that most segmentation techniques are not entirely automated in the sense that almost all techniques require some sort of pre-requisites and user assistance. Summing up, these three challenges related to perceptual proximity, generality and automation are at the core of the work described in this thesis. In order to face these challenges, we have developed the first contour-based mesh segmentation algorithm that we may find in the literature, which is inspired in the edgebased segmentation techniques used in image analysis, as opposite to region-based segmentation techniques. Its leading idea is to firstly find the contour of each region, and then to identify and collect all of its inner triangles. The encountered mesh regions correspond to ups and downs, which do not need to be strictly convex nor strictly concave, respectively. These regions, called relaxedly convex regions (or saliences) and relaxedly concave regions (or recesses), produce segmentations that are less-sensitive to noise and, at the same time, are more intuitive from the human point of view; hence it is called human perception- oriented (HPO) segmentation. Besides, and unlike the current state-of-the-art in mesh segmentation, the existence of these relaxed regions makes the algorithm suited to both non-freeform and freeform objects. In this thesis, we have also tackled a fourth challenge, which is related with the fusion of mesh segmentation and multi-resolution. Truly speaking, a plethora of segmentation techniques, as well as a number of multiresolution techniques, for triangle meshes already exist in the literature. However, it is not so common to find algorithms and data structures that fuse these two concepts, multiresolution and segmentation, into a symbiotic multi-resolution scheme for both plain and segmented meshes, in which a plainmeshisunderstoodasameshwithasinglesegment. So, weintroducesuchanovel multiresolution segmentation scheme, called extended Ghost Cell (xGC) scheme. This scheme preserves the shape of the meshes in both global and local terms, i.e., mesh segments and their boundaries, as well as creases and apices are preserved, no matter the level of resolution we use for simplification/refinement of the mesh. Moreover, unlike other segmentation schemes, it was made possible to have adjacent segments with two or more resolution levels of difference. This is particularly useful in computer animation, mesh compression and transmission, geometric computing, scientific visualization, and computer graphics. In short, this thesis presents a fully automatic, general, and human perception-oriented scheme that symbiotically integrates the concepts of mesh segmentation and multiresolution