Enumeration of Contour Correspondence

With the recent advances in computed tomography and magnetic resonance devices, cross-sectional images are now commonly used for diagnosis. However, how contours between cross-sections should be connected is often ambiguous. In this paper, we propose an algorithm that enumerates all possible cases of the correspondence of contours. This is useful for achieving fully automatic interpolation of contours, although our current implementation still requires some degree of manual interaction.

[1]  Eric Keppel,et al.  Approximating Complex Surfaces by Triangulation of Contour Lines , 1975, IBM J. Res. Dev..

[2]  Marc Levoy,et al.  Display of surfaces from volume data , 1988, IEEE Computer Graphics and Applications.

[3]  Carolyn A. Bucholtz,et al.  Shape-based interpolation , 1992, IEEE Computer Graphics and Applications.

[4]  A. B. Ekoule,et al.  A triangulation algorithm from arbitrary shaped multiple planar contours , 1991, TOGS.

[5]  Arthur W. Toga,et al.  Distance field manipulation of surface models , 1992, IEEE Computer Graphics and Applications.

[6]  Tosiyasu L. Kunii,et al.  Surface coding based on Morse theory , 1991, IEEE Computer Graphics and Applications.

[7]  Tony DeRose,et al.  Surface reconstruction from unorganized points , 1992, SIGGRAPH.

[8]  Andrew H. Gee,et al.  Surface interpolation from sparse cross sections using region correspondence , 2000, IEEE Transactions on Medical Imaging.

[9]  Tosiyasu L. Kunii,et al.  Constructing a Reeb graph automatically from cross sections , 1991, IEEE Computer Graphics and Applications.

[10]  Y. Attikiouzel,et al.  Border marriage : matching of contours of serial sections , 1991 .

[11]  Tosiyasu L. Kunii,et al.  The homotopy model: a generalized model for smooth surface generation from cross sectional data , 1991, The Visual Computer.

[12]  Bahram Parvin,et al.  A new regularized approach for contour morphing , 2000, Proceedings IEEE Conference on Computer Vision and Pattern Recognition. CVPR 2000 (Cat. No.PR00662).

[13]  Chandrajit L. Bajaj,et al.  Automatic reconstruction of surfaces and scalar fields from 3D scans , 1995, SIGGRAPH.

[14]  Thomas W. Sederberg,et al.  Conversion of complex contour line definitions into polygonal element mosaics , 1978, SIGGRAPH.

[15]  Gabriel Taubin,et al.  A signal processing approach to fair surface design , 1995, SIGGRAPH.

[16]  J. Udupa,et al.  Shape-based interpolation of multidimensional objects. , 1990, IEEE transactions on medical imaging.

[17]  Charles T. Loop,et al.  Smooth Subdivision Surfaces Based on Triangles , 1987 .

[18]  Andrew P. Witkin,et al.  Free-form shape design using triangulated surfaces , 1994, SIGGRAPH.

[19]  Pat Hanrahan,et al.  Volume Rendering , 2020, Definitions.

[20]  Jean-Daniel Boissonnat,et al.  Shape reconstruction from planar cross sections , 1988, Comput. Vis. Graph. Image Process..

[21]  Taku Komura,et al.  Topology matching for fully automatic similarity estimation of 3D shapes , 2001, SIGGRAPH.

[22]  Henk J. A. M. Heijmans.  Connected Morphological Operators for Binary Images , 1999, Comput. Vis. Image Underst..

[23]  Michael Shantz,et al.  Surface definition for branching, contour-defined objects , 1981, COMG.

[24]  Henry Fuchs,et al.  Optimal surface reconstruction from planar contours , 1977, CACM.