Algorithms in combinatorial geometry
Algorithms in combinatorial geometry
Shape reconstruction from planar cross sections
Computer Vision, Graphics, and Image Processing
An upper bound for conforming Delaunay triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
Arbitrary topology shape reconstruction from planar cross sections
Graphical Models and Image Processing
Geometric structures for three-dimensional shape representation
ACM Transactions on Graphics (TOG)
Surface Reconstruction by Multiaxial Triangulation
IEEE Computer Graphics and Applications
On the combinatorial complexity of euclidean Voronoi cells and convex hulls of d-dimensional spheres
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Contour interpolation by straight skeletons
Graphical Models
Volume viewer: an interactive tool for fitting surfaces to volume data
Proceedings of the 6th Eurographics Symposium on Sketch-Based Interfaces and Modeling
Provably good 2D shape reconstruction from unorganized cross-sections
SGP '08 Proceedings of the Symposium on Geometry Processing
Reconstruction of multi-label domains from partial planar cross-sections
SGP '09 Proceedings of the Symposium on Geometry Processing
Technical Section: Shape approximation by differential properties of scalar functions
Computers and Graphics
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
SMI 2011: Full Paper: Freestyle: Sculpting meshes with self-adaptive topology
Computers and Graphics
Online reconstruction of 3D objects from arbitrary cross-sections
ACM Transactions on Graphics (TOG)
Shape reconstruction from unorganized set of points
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
Object-space multiphase implicit functions
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Topologically correct reconstruction of tortuous contour forests
Computer-Aided Design
An algorithm for triangulating multiple 3D polygons
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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In this paper, we consider the problem of reconstructing a shape from unorganized cross-sections. The main motivation for this problem comes from medical imaging applications where cross-sections of human organs are obtained by means of a free hand ultrasound apparatus. The position and orientation of the cutting planes may be freely chosen which makes the problem substantially more difficult than in the case of parallel cross-sections, for which a rich literature exists. The input data consist of the cutting planes and (an approximation of) their intersection with the object. Our approach consists of two main steps. First, we compute the arrangement of the cutting planes. Then, in each cell of the arrangement, we reconstruct an approximation of the object from its intersection with the boundary of the cell. Lastly, we glue the various pieces together. The method makes use of the Delaunay triangulation and generalizes the reconstruction method of Boissonnat and Geiger [BG93] for the case of parallel planes. The analysis provides a neat characterization of the topological properties of the result and, in particular, shows an interesting application of Moebius diagrams to compute the locus of the branching points. We have implemented our algorithm in C++, using the [CGAL] library. Experimental results show that the algorithm performs well and can handle complicated branching configurations.