Connectivity Compression for Irregular Quadrilateral Meshes

Applications that require Internet access to remote 3D datasets are often limited by the storage costs of 3D models. Several compression methods are available to address these limits for objects represented by triangle meshes. Many CAD and VRML models, however, are represented as quadrilateral meshes or mixed triangle/quadrilateral meshes, and these models may also require compression. We present an algorithm for encoding the connectivity of such quadrilateral meshes, and we demonstrate that by preserving and exploiting the original quad structure, our approach achieves encodings 30 - 80% smaller than an approach based on randomly splitting quads into triangles. We present both a code with a proven worst-case cost of 3 bits per vertex (or 2.75 bits per vertex for meshes without valence-two vertices) and entropy-coding results for typical meshes ranging from 0.3 to 0.9 bits per vertex, depending on the regularity of the mesh. Our method may be implemented by a rule for a particular splitting of quads into triangles and by using the compression and decompression algorithms introduced in [Rossignac99] and [Rossignac&Szymczak99]. We also present extensions to the algorithm to compress meshes with holes and handles and meshes containing triangles and other polygons as well as quads

Static 3D Triangle Mesh Compression Overview

3D triangle meshes are extremely used to model discrete surfaces, and almost always represented with two tables: one for geometry and another for connectivity. While the raw size of a triangle mesh is of around 200 bits per vertex, by coding cleverly (and separately) those two distinct kinds of information it is possible to achieve compression ratios of 15:1 or more. Different techniques must be used depending on whether single-rate vs. progressive bitstreams are sought; and, in the latter case, on whether or not hierarchically nested meshes are desirable during reconstructio

A new method for simplification and compression of 3D meshes

We focus on the lossy compression of manifold triangle meshes. Our SwingWrapper approach partitions the surface of an original mesh M into simply-connected regions, called triangloids. We compute a new mesh M\u27. Each triangle of M\u27 is a close approximation of a pseudo-triangle of M. By construction, the connectivity of M\u27 is fairly regular and can be compressed to less than a bit per triangle using EdgeBreaker or one of the other recently developed schemes. The locations of the vertices of M\u27 are compactly encoded with our new prediction scheme, which uses a single correction parameter per vertex. For example, a variety of popular models retiled with our approach yield 10 times fewer triangles without exceeding an error of 1% of the radius of the bounding ball. Vertices of M\u27 are encoded with an average of 6 bits, which results in a total storage of 0.4 bits per triangle of the original mesh. The proposed solution may also be used to encode crude meshes for adaptive transmission and for controlling subdivision surfaces

Mesh compression: Theory and practice.

Three-dimensional meshes (3D meshes, for short) are fast becoming an emerging media type, used in a variety of application domains such as engineering design, manufacture, architecture, bio-informatics, medicine, entertainment, commerce, science, defense, etc. The volume of data of this media type that is being circulated on the internet is increasing very rapidly and is being used as frequently as other media types like text, audio (1D), images and video (2D). Hence, 3D meshes need good processing and visualization methods. Also, the sizes of these meshes are much greater than the other media types mentioned above and often exceeds the memory and bandwidth available for their storage and transmission. Compression schemes for such large 3D meshes have become a subject of intense study lately. Meshes are either made up of triangles or quadrilaterals. Meshes made up of only triangles are called triangle meshes and meshes made up of quadrilaterals are called quadrilateral meshes (quad meshes, for short). A mesh is described by specifying its geometry (vertex coordinates) and its connectivity (adjacencies of the triangles or quadrilaterals). Previous research on mesh compression has been mostly for triangle meshes. Quad meshes were traditionally handled by first triangulating them and then applying triangle mesh compression techniques. In order to avoid this additional triangulation step, a direct technique is proposed for compressing and decompressing the connectivity of quad meshes. This technique takes a quad mesh as input and encodes its connectivity as a sequence of opcodes which can be restored back to the quad mesh, using the decompression technique. A data structure called EdgeTable is introduced to aid in the traversal of a quad mesh during compression. Also, a technique based on constrained Delaunay triangulation for reconstructing the connectivity of a 2D mesh from its geometry and a minimum set of edges is proposed. Source: Masters Abstracts International, Volume: 44-03, page: 1393. Thesis (M.Sc.)--University of Windsor (Canada), 2005

Mesh Compression

Die Kompression von Netzen ist eine weitgefächerte Forschungsrichtung mit Anwendungen in den verschiedensten Bereichen, wie zum Beispiel im Bereich der Handhabung extrem großer Modelle, beim Austausch von dreidimensionalem Inhalt über das Internet, im elektronischen Handel, als anpassungsfähige Repräsentation für Volumendatensätze usw. In dieser Arbeit wird das Verfahren der Cut-Border Machine beschrieben. Die Cut-Border Machine kodiert Netze, indem ein Teilbereich durch das Netz wächst (region growing). Kodiert wird die Art und Weise, wie neue Netzelemente dem wachsenden Teilbereich einverleibt werden. Das Verfahren der Cut-Border Machine kann sowohl auf Dreiecksnetze als auch auf Tetraedernetze angewendet werden. Trotz der einfachen Struktur des Verfahrens kann eine sehr hohe Kompressionsrate erzielt werden. Im Falle von Tetraedernetzen erreicht die Cut-Border Machine die beste Kompressionsrate von allen bekannten Verfahren. Die einfache Struktur der Cut-Border Machine ermöglicht einerseits die Realisierung direkt in Hardware und ist auch als Implementierung in Software extrem schnell. Auf der anderen Seite erlaubt die Einfachheit eine theoretische Analyse des Algorithmus. Gezeigt werden konnte, dass für ebene Triangulierungen eine leicht modifizierte Version der Cut-Border Machine lineare Laufzeiten in der Zahl der Knoten erzielt und dass die komprimierte Darstellung nur linearen Speicherbedarf benötigt, d.h. nicht mehr als fünf Bits pro Knoten. Neben der detaillierten Beschreibung der Cut-Border Machine mit mehreren Verbesserungen und Optimierungen, enthält die Arbeit eine Einführung zu Netzen und geeigneten Datenstrukturen und entwickelt mehrere Kodierungsverfahren, die im Bereich der Netzkompression Anwendung finden. Eine breite Übersicht verwandter Arbeiten gibt Einblick in des Forschungsgebiet. Weiterhin wird die Effizienz mehrerer in der Literatur beschriebener Verfahren verbessert. Insbesondere konnte die algorithmisch erzielte obere Schranke für die KodiMesh Compression is a broad research area with applications in a lot of different areas, such as the handling of very large models, the exchange of three dimensional content over the internet, electronic commerce, the flexible representation of volumetric data and so on. In this thesis the mesh compression method of the Cut-Border Machine is described. The Cut-Border Machine encodes meshes by growing a region through the mesh and encoding the way, in which the mesh elements are incorporated into the growing region. The Cut-Border Machine can be applied to triangular and tetrahedral meshes. Although the method is not too complicated, it achieves very good compression rates. In the tetrahedral case the Cut-Border Machine performs best among all known methods. The simple nature of the Cut-Border Machine allows on the one hand for a hardware implementation and performs also as software implementation extremely well. On the other hand the simplicity allows for a theoretical analysis of the Cut-Border Machine. It could be shown, that for planar triangulations a slightly modified version of the Cut-Border Machine runs in linear time in the number of vertices and that the compressed representation only consumes linear storage space, i.e. no more than five bits per vertex. Besides the detailed description of the Cut-Border Machine with several improvements and optimizations, the thesis gives an introduction to meshes and appropriate data structures, develops several coding techniques useful for mesh compression and gives a broad overview of related work. Furthermore the author improves the encoding efficiency of several other compression techniques. In particular could the algorithmically achieved upper bound for the encoding of planar triangulations be improved to ten percent above the theoretical limit, what is the best known result up to now

Robust and Scalable Transmission of Arbitrary 3D Models over Wireless Networks

We describe transmission of 3D objects represented by texture and mesh over unreliable networks, extending our earlier work for regular mesh structure to arbitrary meshes and considering linear versus cubic interpolation. Our approach to arbitrary meshes considers stripification of the mesh and distributing nearby vertices into different packets, combined with a strategy that does not need texture or mesh packets to be retransmitted. Only the valence (connectivity) packets need to be retransmitted; however, storage of valence information requires only 10% space compared to vertices and even less compared to photorealistic texture. Thus, less than 5% of the packets may need to be retransmitted in the worst case to allow our algorithm to successfully reconstruct an acceptable object under severe packet loss. Even though packet loss during transmission has received limited research attention in the past, this topic is important for improving quality under lossy conditions created by shadowing and interference. Results showing the implementation of the proposed approach using linear, cubic, and Laplacian interpolation are described, and the mesh reconstruction strategy is compared with other methods

Compact connectivity representation for triangle meshes

Many digital models used in entertainment, medical visualization, material science, architecture, Geographic Information Systems (GIS), and mechanical Computer Aided Design (CAD) are defined in terms of their boundaries. These boundaries are often approximated using triangle meshes. The complexity of models, which can be measured by triangle count, increases rapidly with the precision of scanning technologies and with the need for higher resolution. An increase in mesh complexity results in an increase of storage requirement, which in turn increases the frequency of disk access or cache misses during mesh processing, and hence decreases performance. For example, in a test application involving a mesh with 55 million triangles in a machine with 4GB of memory versus a machine with 1GB of memory, performance decreases by a factor of about 6000 because of memory thrashing. To help reduce memory thrashing, we focus on decreasing the average storage requirement per triangle measured in 32-bit integer references per triangle (rpt). This thesis covers compact connectivity representation for triangle meshes and discusses four data structures: 1. Sorted Opposite Table (SOT), which uses 3 rpt and has been extended to support tetrahedral meshes. 2. Sorted Quad (SQuad), which uses about 2 rpt and has been extended to support streaming. 3. Laced Ring (LR), which uses about 1 rpt and offers an excellent compromise between storage compactness and performance of mesh traversal operators. 4. Zipper, an extension of LR, which uses about 6 bits per triangle (equivalently 0.19 rpt), therefore is the most compact representation. The triangle mesh data structures proposed in this thesis support the standard set of mesh connectivity operators introduced by the previously proposed Corner Table at an amortized constant time complexity. They can be constructed in linear time and space from the Corner Table or any equivalent representation. If geometry is stored as 16-bit coordinates, using Zipper instead of the Corner Table increases the size of the mesh that can be stored in core memory by a factor of about 8.PhDCommittee Chair: Rossignac, Jarek; Committee Co-Chair: Frost, David; Committee Member: Lindstrom, Peter; Committee Member: Liu, C. Karen; Committee Member: Turk, Gre

A New 3D Representation and Compression Algorithm for Non-Rigid Moving Objects using Affine-Octree

This paper presents a new 3D representation for non-rigid objects using motion vectors between two consecutive frames. Our method relies on an Octree to recursively partition the object into smaller parts for which a small number of motion parameters can accurately represent that portion of the object. The partitioning continues as long as the respective motion parameters are insufficiently accurate to describe the object. Unlike other Octree methods, our method employs an affine transformation for the motion description part, which greatly reduces the storage. Finally, an adaptive thresholding, a singular value decomposition for dealing with singularities, and a quantization and arithmetic coding further enhance our proposed method by increasing the compression while maintaining very good signal-noise ratio. Compared with other methods like trilinear interpolation or Principle Component Analysis (PCA) based algorithm, the Affine-Octree method is easy to compute and highly compact. As the results demonstrate, our method has a better performance in terms of compression ratio and PSNR, while it remains simple

Compression of 3D models with NURBS

With recent progress in computing, algorithmics and telecommunications, 3D models are increasingly used in various multimedia applications. Examples include visualization, gaming, entertainment and virtual reality. In the multimedia domain 3D models have been traditionally represented as polygonal meshes. This piecewise planar representation can be thought of as the analogy of bitmap images for 3D surfaces. As bitmap images, they enjoy great flexibility and are particularly well suited to describing information captured from the real world, through, for instance, scanning processes. They suffer, however, from the same shortcomings, namely limited resolution and large storage size. The compression of polygonal meshes has been a very active field of research in the last decade and rather efficient compression algorithms have been proposed in the literature that greatly mitigate the high storage costs. However, such a low level description of a 3D shape has a bounded performance. More efficient compression should be reachable through the use of higher level primitives. This idea has been explored to a great extent in the context of model based coding of visual information. In such an approach, when compressing the visual information a higher level representation (e.g., 3D model of a talking head) is obtained through analysis methods. This can be seen as an inverse projection problem. Once this task is fullled, the resulting parameters of the model are coded instead of the original information. It is believed that if the analysis module is efficient enough, the total cost of coding (in a rate distortion sense) will be greatly reduced. The relatively poor performance and high complexity of currently available analysis methods (except for specific cases where a priori knowledge about the nature of the objects is available), has refrained a large deployment of coding techniques based on such an approach. Progress in computer graphics has however changed this situation. In fact, nowadays, an increasing number of pictures, video and 3D content are generated by synthesis processing rather than coming from a capture device such as a camera or a scanner. This means that the underlying model in the synthesis stage can be used for their efficient coding without the need for a complex analysis module. In other words it would be a mistake to attempt to compress a low level description (e.g., a polygonal mesh) when a higher level one is available from the synthesis process (e.g., a parametric surface). This is, however, what is usually done in the multimedia domain, where higher level 3D model descriptions are converted to polygonal meshes, if anything by the lack of standard coded formats for the former. On a parallel but related path, the way we consume audio-visual information is changing. As opposed to recent past and a large part of today's applications, interactivity is becoming a key element in the way we consume information. In the context of interest in this dissertation, this means that when coding visual information (an image or a video for instance), previously obvious considerations such as decision on sampling parameters are not so obvious anymore. In fact, as in an interactive environment the effective display resolution can be controlled by the user through zooming, there is no clear optimal setting for the sampling period. This means that because of interactivity, the representation used to code the scene should allow the display of objects in a variety of resolutions, and ideally up to infinity. One way to resolve this problem would be by extensive over-sampling. But this approach is unrealistic and too expensive to implement in many situations. The alternative would be to use a resolution independent representation. In the realm of 3D modeling, such representations are usually available when the models are created by an artist on a computer. The scope of this dissertation is precisely the compression of 3D models in higher level forms. The direct coding in such a form should yield improved rate-distortion performance while providing a large degree of resolution independence. There has not been, so far, any major attempt to efficiently compress these representations, such as parametric surfaces. This thesis proposes a solution to overcome this gap. A variety of higher level 3D representations exist, of which parametric surfaces are a popular choice among designers. Within parametric surfaces, Non-Uniform Rational B-Splines (NURBS) enjoy great popularity as a wide range of NURBS based modeling tools are readily available. Recently, NURBS has been included in the Virtual Reality Modeling Language (VRML) and its next generation descendant eXtensible 3D (X3D). The nice properties of NURBS and their widespread use has lead us to choose them as the form we use for the coded representation. The primary goal of this dissertation is the definition of a system for coding 3D NURBS models with guaranteed distortion. The basis of the system is entropy coded differential pulse coded modulation (DPCM). In the case of NURBS, guaranteeing the distortion is not trivial, as some of its parameters (e.g., knots) have a complicated influence on the overall surface distortion. To this end, a detailed distortion analysis is performed. In particular, previously unknown relations between the distortion of knots and the resulting surface distortion are demonstrated. Compression efficiency is pursued at every stage and simple yet efficient entropy coder realizations are defined. The special case of degenerate and closed surfaces with duplicate control points is addressed and an efficient yet simple coding is proposed to compress the duplicate relationships. Encoder aspects are also analyzed. Optimal predictors are found that perform well across a wide class of models. Simplification techniques are also considered for improved compression efficiency at negligible distortion cost. Transmission over error prone channels is also considered and an error resilient extension defined. The data stream is partitioned by independently coding small groups of surfaces and inserting the necessary resynchronization markers. Simple strategies for achieving the desired level of protection are proposed. The same extension also serves the purpose of random access and on-the-fly reordering of the data stream

3D Point Cloud Data and Triangle Face Compression by a Novel Geometry Minimization Algorithm and Comparison with other 3D Formats

Polygonal meshes remain the primary representation for visualization of 3D data in a wide range of industries including manufacturing, architecture, geographic information systems, medical imaging, robotics, entertainment, and military applications. Because of its widespread use, it is desirable to compress polygonal meshes stored in file servers and exchanged over computer networks to reduce storage and transmission time requirements. 3D files encoded by OBJ format are commonly used to share models due to its clear simple design. Normally each OBJ file contains a large amount of data (e.g. vertices and triangulated faces) describing the mesh surface. In this research we introduce a novel algorithm to compress vertices and triangle faces called Geometry Minimization Algorithm (GM-Algorithm). First, each vertex consists of (x, y, z) coordinates that are encoded into a single value by the GM-Algorithm. Second, triangle faces are encoded by computing the differences between two adjacent vertex locations, and then coded by the GM-Algorithm followed by arithmetic coding. We tested the method on large data sets achieving high compression ratios over 90% while keeping the same number of vertices and triangle faces as the original mesh. The decompression step is based on a Parallel Fast Matching Search Algorithm (Parallel-FMS) to recover the structure of the 3D mesh. A comparative analysis of compression ratios is provided with a number of commonly used 3D file formats such as MATLAB, VRML, OpenCTM and STL showing the advantages and effectiveness of our approach