Reconstruction of Smooth Surfaces with Arbitrary Topology Adaptive Splines

We present a novel method for fitting a smooth G 1 continuous spline to point sets. It is based on an iterative conjugate gradient optimisation scheme. Unlike traditional tensor product based splines we can fit arbitrary topology surfaces with locally adaptive meshing. For this reason we call the surface “slime”.

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

[2]  Adrian Hilton,et al.  SLIME: A new deformable surface , 1994, BMVC.

[3]  Dimitris N. Metaxas,et al.  Adaptive shape evolution using blending , 1995, Proceedings of IEEE International Conference on Computer Vision.

[4]  Tony DeRose,et al.  A multisided generalization of Bézier surfaces , 1989, TOGS.

[5]  Adrian Hilton,et al.  Progress in arbitrary topology deformable surfaces , 1997, BMVC.

[6]  Matthias Eck,et al.  Automatic reconstruction of B-spline surfaces of arbitrary topological type , 1996, SIGGRAPH.

[7]  Andrew S. Glassner,et al.  Graphics Gems , 1990 .

[8]  Andrew Blake,et al.  Dynamic contours: real-time active splines , 1993 .

[9]  Gerald Farin,et al.  Curves and surfaces for computer aided geometric design , 1990 .

[10]  Adrian Hilton,et al.  Reliable Surface Reconstructiuon from Multiple Range Images , 1996, ECCV.

[11]  Paul J. Besl,et al.  A Method for Registration of 3-D Shapes , 1992, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  Tony DeRose,et al.  Generalized B-spline surfaces of arbitrary topology , 1990, SIGGRAPH.

[13]  Adrian Hilton,et al.  Marching triangles: range image fusion for complex object modelling , 1996, Proceedings of 3rd IEEE International Conference on Image Processing.

[14]  Marc Levoy,et al.  Fitting smooth surfaces to dense polygon meshes , 1996, SIGGRAPH.

[15]  Gene H. Golub,et al.  Matrix computations , 1983 .

[16]  Demetri Terzopoulos,et al.  Deformable models in medical image analysis: a survey , 1996, Medical Image Anal..

[17]  Akshay K. Singh,et al.  Deformable models in medical image analysis , 1996, Proceedings of the Workshop on Mathematical Methods in Biomedical Image Analysis.

[18]  Tony DeRose,et al.  Mesh optimization , 1993, SIGGRAPH.

[19]  Demetri Terzopoulos,et al.  Topologically adaptable snakes , 1995, Proceedings of IEEE International Conference on Computer Vision.