Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations
Journal of Computational Physics
Surface reconstruction from unorganized points
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
The NURBS book
International Journal of Computer Vision
Minimal Surfaces Based Object Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Physica D
Computer Vision and Image Understanding
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Motion of curves in three spatial dimensions using a level set approach
Journal of Computational Physics
Dynamic Shapes of Arbitrary Dimension: The Vector Distance Functions
Proceedings of the 9th IMA Conference on the Mathematics of Surfaces
How To Deal with Point Correspondences and Tangential Velocities in the Level Set Framework
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
Surface Reconstruction by Integrating 3D and 2D Data of Multiple Views
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
A Variational Analysis of Shape from Specularities using Sparse Data
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Surface Reconstruction from the Projection of Points, Curves and Contours
3DPVT '04 Proceedings of the 3D Data Processing, Visualization, and Transmission, 2nd International Symposium
Modelling Dynamic Scenes by Registering Multi-View Image Sequences
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Reconstructing open surfaces from unorganized data points
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
A geometric formulation of gradient descent for variational problems with moving surfaces
Scale-Space'05 Proceedings of the 5th international conference on Scale Space and PDE Methods in Computer Vision
Variational principles, surface evolution, PDEs, level set methods, and the stereo problem
IEEE Transactions on Image Processing
A grid based particle method for evolution of open curves and surfaces
Journal of Computational Physics
International Journal of Computer Vision
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In this paper a method for fitting open surfaces to data obtained from images is presented using a level set representation of the surface. This is done by tracking a curve, representing the boundary, on the implicitly defined surface. This curve is given as the intersection of the level set describing the surface and an auxiliary level set. These two level sets are propagated using the same motion vector field. Special care has to be taken in order for the surfaces not to intersect at other places than at the desired boundary. Methods for accomplishing this are presented and a fast scheme for finding initial values is proposed. This method gives a piecewise linear approximation of the initial surface boundary using a partition of the convex hull of the recovered 3D data. With the approach described in this paper, open surfaces can be fitted to e.g. point clouds obtained using structure from motion techniques. This paper solves an important practical problem since in many cases the surfaces in the scene are open or can only be viewed from certain directions. Experiments on several data sets support the method.