A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Singularity Theory and Phantom Edges in Scale Space
IEEE Transactions on Pattern Analysis and Machine Intelligence
Simulation of simplicity: a technique to cope with degenerate cases in geometric algorithms
ACM Transactions on Graphics (TOG)
Efficient ray tracing of volume data
ACM Transactions on Graphics (TOG)
Footprint evaluation for volume rendering
SIGGRAPH '90 Proceedings of the 17th annual conference on Computer graphics and interactive techniques
Area and volume coherence for efficient visualization of 3D scalar functions
VVS '90 Proceedings of the 1990 workshop on Volume visualization
A polygonal approximation to direct scalar volume rendering
VVS '90 Proceedings of the 1990 workshop on Volume visualization
Hierarchical splatting: a progressive refinement algorithm for volume rendering
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
A coherent projection approach for direct volume rendering
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Edge representation from wavelet transform maxima
Edge representation from wavelet transform maxima
Ten lectures on wavelets
Octrees for faster isosurface generation
ACM Transactions on Graphics (TOG)
Visibility-ordering meshed polyhedra
ACM Transactions on Graphics (TOG)
Characterization of Signals from Multiscale Edges
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
An introduction to wavelets
Frequency domain volume rendering
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
ACM Transactions on Graphics (TOG)
Fast volume rendering using a shear-warp factorization of the viewing transformation
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Multiscale 3D edge representation of volume data by a DOG wavelet
VVS '94 Proceedings of the 1994 symposium on Volume visualization
A multiresolution framework for volume rendering
VVS '94 Proceedings of the 1994 symposium on Volume visualization
Sorting and hardware assisted rendering for volume visualization
VVS '94 Proceedings of the 1994 symposium on Volume visualization
Topological modeling with simplicial complexes
Topological modeling with simplicial complexes
SIGGRAPH '88 Proceedings of the 15th annual conference on Computer graphics and interactive techniques
Volume Data and Wavelet Transforms
IEEE Computer Graphics and Applications
An Evaluation of Implicit Surface Tilers
IEEE Computer Graphics and Applications
Interval Set: A Volume Rendering Technique Generalizing Isosurface Extraction
VIS '95 Proceedings of the 6th conference on Visualization '95
Interactive splatting of nonrectilinear volumes
VIS '92 Proceedings of the 3rd conference on Visualization '92
The multilevel finite element method for adaptive mesh optimization and visualization of volume data
VIS '97 Proceedings of the 8th conference on Visualization '97
Advanced algorithmic approaches to medical image segmentation
Multiresolution Representation and Visualization of Volume Data
IEEE Transactions on Visualization and Computer Graphics
Structure-Significant Representation of Structured Datasets
IEEE Transactions on Visualization and Computer Graphics
Spatial Domain Wavelet Design for Feature Preservation in Computational Data Sets
IEEE Transactions on Visualization and Computer Graphics
Fast multiresolution extraction of multiple transparent isosurfaces
EGVISSYM'01 Proceedings of the 3rd Joint Eurographics - IEEE TCVG conference on Visualization
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A scalar volume V={(x, f(x)) | x 驴R} is described by a function f(x) defined over some region R of the 3D space. In this paper, we present a simple technique for rendering multiscale interval sets of the form ${\cal I}_{\mbi s}$(a, b) = {(x, fs(x)) |a驴gs(x) 驴b}, where a and b are either real numbers or infinities, and fs(x) is a smoothed version of f(x). At each scale s, the constraint a驴gs (x) 驴b identifies a subvolume in which the most significant variations of V are found. We use dyadic wavelet transform to construct gs(x) from f(x) and derive subvolumes with the following attractive properties: 1) the information contained in the subvolumes are sufficient for reconstructing the entire V, and 2) the shapes of the subvolumes provide a hierarchical description of the geometric structures of V. Numerically, the reconstruction in 1) is only an approximation, but it is visually accurate as errors reside at fine scales where our visual sensitivity is not so acute. We triangulate interval sets as 驴-shapes, which can be efficiently rendered as semi-transparent clouds. Because interval sets are extracted in the object space, their visual display can respond to changes of the view point or transfer function quite fast. The result is a volume rendering technique that provides faster, more effective user interaction with practically no loss of information from the original data. The hierarchical nature of multiscale interval sets also makes it easier to understand the usual complicated structures in scalar volumes.