Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Journal of Mathematical Imaging and Vision
Inference of Surfaces, 3D Curves, and Junctions from Sparse, Noisy, 3D Data
IEEE Transactions on Pattern Analysis and Machine Intelligence
Dual contouring of hermite data
Proceedings of the 29th annual conference on Computer graphics and interactive techniques
ACM SIGGRAPH 2004 Papers
Ridge-valley lines on meshes via implicit surface fitting
ACM SIGGRAPH 2004 Papers
Topological Lines in 3D Tensor Fields
VIS '04 Proceedings of the conference on Visualization '04
Apparent ridges for line drawing
ACM SIGGRAPH 2007 papers
Ridge based curve and surface reconstruction
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Efficient Visualization of Lagrangian Coherent Structures by Filtered AMR Ridge Extraction
IEEE Transactions on Visualization and Computer Graphics
Crease Surfaces: From Theory to Extraction and Application to Diffusion Tensor MRI
IEEE Transactions on Visualization and Computer Graphics
The domain of a point set surface
SPBG'04 Proceedings of the First Eurographics conference on Point-Based Graphics
Fast extraction of high-quality crease surfaces for visual analysis
EuroVis'11 Proceedings of the 13th Eurographics / IEEE - VGTC conference on Visualization
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Extremal surfaces are a class of implicit surfaces that have been found useful in a variety of geometry reconstruction applications. Compared to iso-surfaces, extremal surfaces are particularly challenging to construct in part due to the presence of boundaries and the lack of a consistent orientation. We present a novel, grid-based algorithm for constructing polygonal approximations of extremal surfaces that may be open or unorientable. The algorithm is simple to implement and applicable to both uniform and adaptive grid structures. More importantly, the resulting discrete surface preserves the structural property of the extremal surface in a grid-independent manner. The algorithm is applied to extract ridge surfaces from intensity volumes and reconstruct surfaces from point sets with unoriented normals.