Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
ACM Transactions on Graphics (TOG)
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
Arbitrary topology shape reconstruction from planar cross sections
Graphical Models and Image Processing
Shape transformation using variational implicit functions
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Computational Geometry: Theory and Applications
IEEE Computer Graphics and Applications
Contour interpolation by straight skeletons
Graphical Models
Approximating complex surfaces by triangulation of contour lines
IBM Journal of Research and Development
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This paper presents a practical solution for three-dimensional shape reconstruction from sparsely sampled two-dimensional data, represented as contours on a set of parallel slices. Our method separates the solution for contour correspondence from the surface tiling, and is guaranteed to produce non-self-intersecting surfaces regardless of the contours' geometry, complexity, and the computed correspondence. Though our algorithm is fully automatic, human intervention is also possible for refinement. First, we apply a method based on object recognition techniques to find contour correspondence. Next, we use Voronoi diagrams and operations on a planar map to create a partition, which guarantees a correct reconstruction. Finally, a surface-interpolation algorithm is applied to the contours translated according to both their correspondence and the created partition to produce the actual surface. Experimental results demonstrate the good performance of our algorithm and improvement in the quality of reconstruction for sparsely-sampled inputs.