Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
An implicit formulation for precise contact modeling between flexible solids
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
A variational level set approach to multiphase motion
Journal of Computational Physics
Multicategory Classification by Support Vector Machines
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Adaptively sampled distance fields: a general representation of shape for computer graphics
Proceedings of the 27th annual conference on Computer graphics and interactive techniques
A Generalization of Algebraic Surface Drawing
ACM Transactions on Graphics (TOG)
Reconstruction and representation of 3D objects with radial basis functions
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Non-Manifold Implicit Surfaces Based on Discontinuous Implicitization and Polygonization
GMP '02 Proceedings of the Geometric Modeling and Processing — Theory and Applications (GMP'02)
Multi-level partition of unity implicits
ACM SIGGRAPH 2003 Papers
Interpolating and approximating implicit surfaces from polygon soup
ACM SIGGRAPH 2004 Papers
ACM SIGGRAPH 2006 Papers
Shape reconstruction from unorganized cross-sections
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Piecewise multi-classification support vector machines
IJCNN'09 Proceedings of the 2009 international joint conference on Neural Networks
Smooth, Volume-Accurate Material Interface Reconstruction
IEEE Transactions on Visualization and Computer Graphics
Volumetric modeling with diffusion surfaces
ACM SIGGRAPH Asia 2010 papers
Proceedings of the 2011 SIGGRAPH Asia Conference
Piecewise tri-linear contouring for multi-material volumes
GMP'10 Proceedings of the 6th international conference on Advances in Geometric Modeling and Processing
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Implicit functions have a wide range of applications in entertainment, engineering and medical imaging. A standard two-phase implicit function only represents the interior and exterior of a single object. To facilitate solid modeling of heterogeneous objects with multiple internal regions, object-space multiphase implicit functions are much desired. Multiphase implicit functions have much potential in modeling natural organisms, heterogeneous mechanical parts and anatomical atlases. In this paper, we introduce a novel class of object-space multiphase implicit functions that are capable of accurately and compactly representing objects with multiple internal regions. Our proposed multiphase implicit functions facilitate true object-space geometric modeling of heterogeneous objects with non-manifold features. We present multiple methods to create object-space multiphase implicit functions from existing data, including meshes and segmented medical images. Our algorithms are inspired by machine learning algorithms for training multicategory max-margin classifiers. Comparisons demonstrate that our method achieves an error rate one order of magnitude smaller than alternative techniques.