Three-dimensional distance field metamorphosis
ACM Transactions on Graphics (TOG)
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Reducing aliasing artifacts in iso-surfaces of binary volumes
VVS '00 Proceedings of the 2000 IEEE symposium on Volume visualization
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Matching: Similarity Measures and Algorithms
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
Contour interpolation by straight skeletons
Graphical Models
Nonlinear interpolation between slices
Proceedings of the 2007 ACM symposium on Solid and physical modeling
A 4-point interpolatory subdivision scheme for curve design
Computer Aided Geometric Design
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Reconstruction of 3D objects from 2D cross-sections is an intriguing problem with many potential applications. We approach this problem through a novel multi-resolution method based on iterative refinement of the sets representing the cross-sections. To that end, we introduce a new geometric weighted average of two sets, defined for positive weights (corresponding to interpolation) and when one weight is negative (corresponding to extrapolation). This new average can be used to interpolate between cross-sections of a 3D object in a piecewise way. To obtain a smoother reconstruction of the 3D object, we adapt to sets the 4-point interpolatory subdivision scheme using the new average with both positive and negative weights. The effectiveness of the new method is demonstrated by several examples.