Highly detailed geometric models are rapidly becoming commonplace in computer graphics. These models, often represented as complex triangle meshes, challenge rendering performance, transmission bandwidth, and storage capacities. This paper introduces the progressive mesh (PM) representation, a new scheme for storing and transmitting arbitrary triangle meshes. This efficient, lossless, continuous-resolution representation addresses several practical problems in graphics: smooth geomorphing of level-of-detail approximations, progressive transmission, mesh compression, and selective refinement. In addition, we present a new mesh simplification procedure for constructing a PM representation from an arbitrary mesh. The goal of this optimization procedure is to preserve not just the geometry of the original mesh, but more importantly its overall appearance as defined by its discrete and scalar appearance attributes such as material identifiers, color values, normals, and texture coordinates. We demonstrate construction of the PM representation and its applications using several practical models.

In this paper, we introduce the progressive simplicial complex (PSC) representation, a new format for storing and transmitting triangulated geometric models. Like the earlier progressive mesh (PM) representation, it captures a given model as a coarse base model together with a sequence of refinement transformations that progressively recover detail. The PSC representation makes use of a more general refinement transformation, allowing the given model to be an arbitrary triangulation (e.g. any dimension, non-orientable, non-manifold, non-regular), and the base model to always consist of a single vertex. Indeed, the sequence of refinement transformations encodes both the geometry and the topology of the model in a unified multiresolution framework. The PSC representation retains the advantages of PM's. It defines a continuous sequence of approximating models for runtime level-of-detail control, allows smooth transitions between any pair of models in the sequence, supports progressive transmission, and offers a space-efficient representation. Moreover, by allowing changes to topology, the PSC sequence of approximations achieves better fidelity than the corresponding PM sequence.

In this paper we introduce the Progressive Forest Split (PFS) representation, a new adaptive refinement scheme for storing and transmitting manifold triangular meshes in progressive and highly compressed form. As in the Progressive Mesh (PM) method of Hoppe, a triangular mesh is represented as a low resolution polygonal model followed by a sequence of refinement operations, each one specifying how to add triangles and vertices to the previous level of detail to obtain a new level. The PFS format shares with PM and other refinement schemes the ability to smoothly interpolate between consecutive levels of detail. However, it achieves much higher compression ratios than PM by using a more complex refinement operation which can, at the expense of reduced granularity, be encoded more efficiently. A forest split operation doubling the number n of triangles of a mesh requires a maximum of approximately 3:5n bits to represent the connectivity changes, as opposed to approximately #5 + log 2 #n## n bits in PM. We describe

In earlier work, we introduced the progressive mesh (PM) representation, a new format for storing and transmitting arbitrary triangle meshes. For a given mesh, the PM representation defines a continuous sequence of level-of-detail approximations, allows smooth visual transitions (geomorphs) between these approximations, supports progressive transmission, and makes an effective compression scheme. In this paper, we present data structures and algorithms for efficient implementation of the PM representation and its applications. Also, we report quantitative results using a variety of computer graphics models.

The Virtual Reality Modeling Language (VRML) is rapidly becoming the standard file format for transmitting 3D virtual worlds across the Internet. Static and dynamic descriptions of 3D objects, multimedia content, and a variety of hyperlinks can be represented in VRML files. Both VRML browsers and authoring tools for the creation of VRML files are widely available for several different platforms. In this paper we describe the topologically-assisted geometric compression technology included in our proposal for the VRML Compressed Binary Format. This technology produces significant reduction of file sizes and, subsequently, of the time required for transmission of such files across the Internet. Compression ratios of up to 50:1 or more are achieved for large models. The proposal also includes combines a binary encoding to create compact, rapidly-parsable binary VRML files. The proposal is currently being evaluated by the Compressed Binary Format Working Group of the VRML Consortium as a ...

We present a method for compressing non-manifold polygonal meshes, i.e., polygonal meshes with singularities, which occur very frequently in the real-world. Most efficient polygonal compression methods currently available are restricted to a manifold mesh: they require converting a non-manifold mesh to a manifold mesh, and fail to retrieve the original model connectivity after decompression. The present method works by converting the original model to a manifold model, encoding the manifold model using an existing mesh compression technique, and clustering, or stitching together during the decompression process vertices that were duplicated earlier to faithfully recover the original connectivity. This paper focuses on efficiently encoding and decoding the stitching information. Using a naive method, the stitching information would incur a prohibitive cost, while our methods guarantee a worst case cost of O(logm) bits per vertex replication, where m is the number of non-manifold vertices. Furthermore, when exploiting the adjacency between vertex replications, many replications can be encoded with an insignificant cost. By interleaving the connectivity, stitching information, geometry and properties, we can avoid encoding repeated vertices (and properties bound to vertices) multiple times; thus a reduction of the size of the bit-stream of about 10% is obtained compared with encoding the model as a manifold.

Some of the largest and most intricate surfaces result from isosurface extraction of volume data produced by 3D imaging modalities and scientific simulations. Such surfaces often possess both complicated geometry and topology (i.e., many connected components and high genus). Because of their sheer size, efficient compression algorithms, in particular progressive encodings, are critical in working with these surfaces. Most standard mesh compression algorithms have been designed to deal with generally smooth surfaces of low topologic complexity. Much better results can be achieved with algorithms which are specifically designed for isosurfaces arising from volumetric datasets.

Current coding techniques for 3-D graphic models mainly focus on coding efficiency, which makes them extremely sensitive to channel errors due to the irregular mesh structure. In this paper, we introduce a new approach for error-resilient coding of arbitrary 3-D graphic models by extending the error-free constructive traversal compression scheme proposed by Li and Kuo. A 3-D mesh of an arbitrary structure is partitioned into pieces of a smaller uniform size with joint boundaries. The size of a piece is determined adaptively based on the channel error rate. The topology and geometry information of each joint boundary and each piece of a connected component is coded independently. The coded topology and first several important bit-planes of the joint-boundary data are protected against channel errors by using the Bose--Chaudhuri--Hocquenghem error-correcting code. At the decoder, each piece is decoded and checked for channel errors. The decoded joint-boundary information is used to perform data recovery and error concealment on the corrupted piece data. All decoded pieces are combined together according to their configuration to reconstruct all connected components of the complete 3-D model. Our experiments demonstrate that the proposed approach has excellent error resiliency at a reasonable bit-rate overhead. The techniques is also capable of incrementally rendering one connected component of the 3-D model at a time.

294,018 vertices, compressed to 0.7437 bits per face. C: UNC CThead data set, level 1160, 312,488 faces, 312,287 vertices, compressed to 0.8081 bits per face. In this paper we introduce a new and simple algorithm to compress isosurface data. This is the data extracted by isosurface algorithms from scalar functions defined on volume grids, and used to generate polygon meshes or alternative representations. In this algorithm the mesh connectivity and a substantial proportion of the geometric information are encoded to a fraction of a bit per Marching Cubes vertex with a context based arithmetic coder closely related to the JBIG binary image compression standard. The remaining optional geometric information that specifies the location of each Marching Cubes vertex more precisely along its supporting intersecting grid edge, is efficiently encoded in scan-order with the same mechanism. Vertex normals can optionally be computed as normalized gradient vectors by the encoder and included in the bitstream after quantization and entropy encoding, or computed by the decoder in a postprocessing smoothing step. These choices are determined by trade-offs associated with an in-core vs. out-of-core decoder structure. The main features of our algorithm are its extreme simplicity and high compression rates.

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. In this report we describe several schemes that have been recently introduced to represent single and multi-resolution polygonal meshes in compressed form, and to progressively transmit polygonal mesh data. The progressive transmission of polygonal meshes allows the decoder process to make part of a single-resolution mesh, or the low resolution levels of detail of a multi-resolution mesh, available to the rendering system before the whole bitstream is fully received and decoded. It is desirable to combine compression and progressive transmission, but not all the existing methods exhibit both features. These progressive transmission schemes are closely related to surface simplification or decimation methods, which change the surface topology while approximating the geometry, and can be regarded as lossy compression schemes as well. Finally, we describe in more detail the Topological Surgery and Progressive Forest Split schemes that are currently part of the MPEG-4 multimedia standard. 1.