We present a new method for adaptive surface meshing and triangulation which controls the local level-of-detail of the surface approximation by local spectral estimates. These estimates are determined by a wavelet representation of the surface data. The basic idea is to decompose the initial data set by means of an orthogonal or semi-orthogonal tensor product wavelet transform (WT) and to analyze the resulting coefficients. In surface regions, where the partial energy of the resulting coefficients is low, the polygonal approximation of the surface can be performed with larger triangles without loosing too much fine grain details. However, since the localization of the WT is bound by the Heisenberg principle the meshing method has to be controlled by the detail signals rather than directly by the coefficients. The dyadic scaling of the WT stimulated us to build an hierarchical meshing algorithm which transforms the initially regular data grid into a quadtree representation by rejection of unimportant mesh vertices. The optimum triangulation of the resulting quadtree cells is carried out by selection from a look-up table. The tree grows recursively as controlled by detail signals which are computed from a modified inverse WT. In order to control the local level-of-detail, we introduce a new class of wavelet space filters acting as “magnifying glasses ” on the data. We show that our algorithm performs a low algorithmic complexity, so that surface meshing can be achieved at interactive rates, such as required by flight simulators. However, other applications are possible as well, such as mesh reduction in complex data, FEM or radiosity meshing. The method is applied on different types of data comprising both digital terrain models and laser range scans. In addition, quantitative investigations on error analysis are carried out.

Results overview: First, a volumetric scalar data set of size 256 3 requiring 16 MB is shown. Second, the hierarchically encoded data set (0.78 MB) is directly rendered using programmable graphics hardware. Third, one time step (256 3) of a 1.4 GB shock wave simulation is shown. Fourth, the same time step is directly rendered out of a compressed sequence of 70 MB. Rendering the data sets to a 512 2 viewport runs at 11 and 24 fps, respectively, on an ATI 9700. A survey of graphics developers on the issue of texture mapping hardware for volume rendering would most likely find that the vast majority of them view limited texture memory as one of the most serious drawbacks of an otherwise fine technology. In this paper, we propose a compression scheme for static and time-varying volumetric data sets based on vector quantization that allows us to circumvent this limitation. We describe a hierarchical quantization scheme that is based on a multiresolution covariance analysis of the original field. This allows for the efficient encoding of large-scale data sets, yet providing a mechanism to exploit temporal coherence in non-stationary fields. We show, that decoding and rendering the compressed data stream can be done on the graphics chip using programmable hardware. In this way, data transfer between the CPU and the graphics processing unit (GPU) can be minimized thus enabling flexible and memory efficient real-time rendering options. We demonstrate the effectiveness of our approach by demonstrating interactive renditions of Gigabyte data sets at reasonable fidelity on commodity graphics hardware.

This paper presents a new 3D RGB image compression scheme designed for interactive real-time applications. In designing our compression method, we have compromised between two important goals: high compression ratio and fast random access ability, and have tried to minimize the overhead caused during runtime reconstruction. Our compression technique is suitable for applications wherein data are accessed in a somewhat unpredictable fashion, and real-time performance of decompression is necessary. The experimental results on three different kinds of 3D images from medical imaging, image-based rendering, and solid texture mapping suggest that the compression method can be used effectively in developing real-time applications that must handle large volume data, made of color samples taken in three- or higher-dimensional space.

Visualizing very large volume data has been recognized as a task requiring great effort in a variety of science and engineering fields. In particular, such data usually places considerable demands on run-time memory space. This paper describes an effective 3D compression scheme for very large volume data that exploits the power of wavelet theory. In designing our compression method, we have compromised between two important factors: high compression ratio and fast run-time random access. Our experimental results on the Visual Human data sets show that our method achieves fairly good compression ratios. In addition, it minimizes the overhead caused during run-time reconstruction of voxel values. This 3D compression scheme will be useful in developing many interactive visualization systems for huge volume data, and will make visualization technology accessible to a much wider range of users, as it can be based on personal computers or low-end workstations with limited memory. Keywords: ...

In this paper, we address the problem of the efficient visualization of large irregular volume data sets by exploiting a multiresolution model based on tetrahedral meshes.

Interactive visualization of very large volume data has been recognized as a task requiring great effort in a variety of science and engineering fields. In particular, such data usually places considerable demands on run-time memory space. In this paper, we present an effective 3D compression scheme for interactive visualization of very large volume data, that exploits the power of wavelet theory. In designing our method, we have compromised between two important factors: high compression ratio and fast run-time random access ability. Our experimental results on the Visual Human data sets show that our method achieves fairly good compression ratios. In addition, it minimizes the overhead caused during run-time reconstruction of voxel values. This 3D compression scheme will be useful in developing many interactive visualization systems for huge volume data, especially when they are based on personal computers or workstations with limited memory. Keywords: very large volume data, wavele...

Volume data sets resulting from, e.g., computerized tomography (CT) or magnetic resonance (MR) imaging modalities require enormous storage capacity even at moderate resolution levels. Such large files may require compression for processing in CPU memory which, however, comes at the cost of decoding times and some loss in reconstruction quality with respect to the original data. For many typical volume visualization applications (rendering of volume slices, subvolumes of interest, or isosurfaces) only a part of the volume data needs to be decoded. Thus, efficient compression techniques are needed that provide random access and rapid decompression of arbitrary parts the volume data. We propose a technique which is block based and operates in the wavelet transformed domain. We report performance results which compare favorably with previously published methods yielding large reconstruction quality gains from about 6 to 12 dB in PSNR for a 512 3-volume extracted from the Visible Human data set. In terms of compression our algorithm compressed the data 6 times as much as the previous state-of-theart block based coder for a given PSNR quality. 1.

These tutorial notes provide an introduction, review, and discussion of the state-of-the-art on simplification methods, Level Of Detail, and multiresolution models for surface meshes, and of their applications. The problem of approximating a surface with a triangular mesh is formally introduced, and major simplification techniques are classified, reviewed, and compared. A general framework is introduced next, which encompasses all multiresolution surface models based on decomposition, and major multiresolution meshes are classified, reviewed, and compared in the context of such a framework. Applications of simplification methods, LOD, and multiresolution to computer graphics, virtual reality, geographical information systems, flight simulation, and volume visualization are also reviewed.

In order to display, transform, and compare volumetric data, it is often convenient or necessary to use different representations derived from the original discrete voxel values; in particular, several methods have been proposed to compute and display an iso-surface defined by some threshold value. In this paper we describe a method to represent the volume enclosed by an iso-surface as the union of simple volume primitives. The needed properties (displayed image, volume, surface, etc.) are derived from this representation. A survey of properties that might be needed or useful for such representations shows that some important ones are lacking in the representations used so far. Basic properties include efficiency of computation, storage, and display. Some other properties of interest include stability (the fact that the representation changes little for a small change in the data, such as noise or small distortions), the ability to determine the similarities between two data sets, and ...

When interactive real-time applications are developed with very large volume data, the use of lossy compression is often inevitable. Lossy compression schemes generally encode data without consideration of the purpose of visualization that is actually performed, which often results in inefficient compression. In this paper, we present a new method for classifying voxels according to their importance in visualization, and assigning weights to them properly. The associated weight information can be combined with lossy compression schemes to reduce the visual degradation of reconstructed images, which, as a consequence, leads to higher compression rates and visual fidelity. Test results demonstrate that the proposed technique improves the quality of both compression and visualization significantly. 1