Lossless Compression of Predicted Floating-Point Geometry

The sizeof geometric data sets in scientific and industrial applications is constantly increasing. Storing surfng or volume meshes in standard uncompressedf ormats results in large files that are expensive to store and slow to load and transmit. Scientists and engineersofne refeer ff using mesh compression because currently available schemes modif the mesh data. While connectivity is encoded in a lossless manner, the floating-point coordinates associated with the vertices are quantized onto aunif6: integer grid to enable e#cient predictive compression. Although a fine enough grid can usually represent the data with su#cient precision, the original floating-point values will change, regardless of grid resolution. In this paper we describe a methodf or compressing floating-point coordinates with predictive coding in a completely lossless manner. The initial quantization step is omitted and predictions are calculated in floating-point. The predicted and the actual floating-point values are broken up into sign, exponent, and mantissa and their corrections are compressed separately with context-based arithmetic coding. As the quality of the predictions varies with the exponent, we use the exponent to switch between di#erent arithmetic contexts. We report compression results using the popular parallelogram predictor, but our approach will work with any prediction scheme. The achieved bit-ratesf or lossless floating-point compression nicely complement those resultingfsu unifting quantizing with di#erent precisions

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

Compressing Polygon Mesh Connectivity with Degree Duality Prediction

In this paper we present a coder for polygon mesh connectivity that delivers the best connectivity compression rates meshes reported so far. Our coder is an extension of the vertex-based coder for triangle mesh connectivity by Touma and Gotsman [26]. We code polygonal connectivity as a sequence of face and vertex degrees and exploit the correlation between them for mutual predictive compression. Because low-degree vertices are likely to be surrounded by high-degree faces and vice versa, we predict vertex degrees based on neighboring face degrees and face degrees based on neighboring vertex degrees

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