Surface reconstruction and representation of 3-D scenes
Pattern Recognition
A syntactic/semantic technique for surface reconstruction from cross-sectional contours
Computer Vision, Graphics, and Image Processing
A framework for surface reconstruction from 3D contours
Computer Vision, Graphics, and Image Processing
Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
Pessimal Guesses may be Optimal: A Counterintuitive Search Result
IEEE Transactions on Pattern Analysis and Machine Intelligence
A triangulation algorithm from arbitrary shaped multiple planar contours
ACM Transactions on Graphics (TOG)
ACM Transactions on Graphics (TOG)
Surface reconstruction between simple polygons via angle criteria
Journal of Symbolic Computation - Special issue on “algorithms: implementation, libraries and use”
A signal processing approach to fair surface design
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
Arbitrary topology shape reconstruction from planar cross sections
Graphical Models and Image Processing
Multiresolution banded refinement to accelerate surface reconstruction from polygons
Proceedings of the fourteenth annual symposium on Computational geometry
Interactive multi-resolution modeling on arbitrary meshes
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Improved constructions of Delaunay based contour surfaces
Proceedings of the fifth ACM symposium on Solid modeling and applications
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Optimal surface reconstruction from planar contours
Communications of the ACM
A new general triangulation method for planar contours
SIGGRAPH '82 Proceedings of the 9th annual conference on Computer graphics and interactive techniques
Conversion of complex contour line definitions into polygonal element mosaics
SIGGRAPH '78 Proceedings of the 5th annual conference on Computer graphics and interactive techniques
Surface definition for branching, contour-defined objects
ACM SIGGRAPH Computer Graphics
3D Object Reconstruction from Non-Parallel Cross-Sections
ICPR '04 Proceedings of the Pattern Recognition, 17th International Conference on (ICPR'04) Volume 3 - Volume 03
Contour interpolation by straight skeletons
Graphical Models
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
A generic software design for Delaunay refinement meshing
Computational Geometry: Theory and Applications
Poisson surface reconstruction
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
Shape reconstruction from unorganized cross-sections
SGP '07 Proceedings of the fifth Eurographics symposium on Geometry processing
Straight Skeletons of Three-Dimensional Polyhedra
ESA '08 Proceedings of the 16th annual European symposium on Algorithms
Transfinite mean value interpolation
Computer Aided Geometric Design
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Approximating complex surfaces by triangulation of contour lines
IBM Journal of Research and Development
Reconstruction of multi-label domains from partial planar cross-sections
SGP '09 Proceedings of the Symposium on Geometry Processing
Geometric tomography with topological guarantees
Proceedings of the twenty-sixth annual symposium on Computational geometry
Topologically correct reconstruction of tortuous contour forests
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
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We describe a simple algorithm to reconstruct the surface of smooth three-dimensional multilabeled objects from sampled planar cross-sections of arbitrary orientation. The algorithm has the unique ability to handle cross-sections in which regions are classified as being inside the object, outside the object, or unknown. This is achieved by constructing a scalar function on R3, whose zero set is the desired surface. The function is constructed independently inside every cell of the arrangement of the cross-section planes using transfinite interpolation techniques based on barycentric coordinates. These guarantee that the function is smooth, and its zero set interpolates the cross-sections. The algorithm is highly parallelizable and may be implemented as an incremental update as each new cross-section is introduced. This leads to an efficient online version, performed on a GPU, which is suitable for interactive medical applications.