Polygonization of implicit surfaces
Computer Aided Geometric Design
Principal Warps: Thin-Plate Splines and the Decomposition of Deformations
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-dimensional alpha shapes
ACM Transactions on Graphics (TOG)
SIGGRAPH '93 Proceedings of the 20th annual conference on Computer graphics and interactive techniques
Zippered polygon meshes from range images
SIGGRAPH '94 Proceedings of the 21st annual conference on Computer graphics and interactive techniques
Piecewise-linear interpolation between polygonal slices
Computer Vision and Image Understanding
A volumetric method for building complex models from range images
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Arbitrary topology shape reconstruction from planar cross sections
Graphical Models and Image Processing
Introduction to Implicit Surfaces
Introduction to Implicit Surfaces
Modelling with implicit surfaces that interpolate
ACM Transactions on Graphics (TOG)
Surface Coding Based on Morse Theory
IEEE Computer Graphics and Applications
Constructing a Reeb graph automatically from cross sections
IEEE Computer Graphics and Applications
SMI '01 Proceedings of the International Conference on Shape Modeling & Applications
A Mathematical Theory of Communication
A Mathematical Theory of Communication
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In surface reconstruction from planar cross sections it is necessary to build surfaces between 2D contours in consecutive cross sections. This problem has been traditionally attacked by (i) direct reconstruction based on local geometric proximity between the contours, and (ii) classification of topological events between the cross sections. These approaches have been separately applied with limited success. In case (i), the resulting surfaces may have overstretched or unnatural branches. These arise from local contour proximity which does not reflect global similarity between the contours. In case (ii), the topological events are identified but are not translated into the actual construction of a surface. This article presents an integration of the approaches (i) and (ii). Similarity between the composite 2D regions bounded by the contours in consecutive cross sections is used to: (a) decide whether a surface should actually relate two composite 2D regions, (b) identify the type and location of topological transitions between cross sections and (c) drive the surface construction for the regions found to be related in step (a). The implemented method avoids overstretched or unnatural branches, rendering a surface which is both geometrically intuitive and topologically faithful to the cross sections of the original object. The presented method is a good alternative in cases in which correct reproduction of the topology of the surface (e.g. simulation of flow in conduits) is more important than its geometry (e.g. assessment of tumor mass in radiation planning).