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Surface Reconstruction Via Contour Metamorphosis: An Eulerian Approach With Lagrangian Particle Tracking
Linköping University, Department of Science and Technology. Linköping University, The Institute of Technology.
Drexel University.
Linköping University, Department of Science and Technology, Digital Media. Linköping University, The Institute of Technology.
2005 (English)In: IEEE Visualization 05,2005, IEEE , 2005, 407-414 p.Conference paper (Refereed)
Abstract [en]

We present a robust method for 3D reconstruction of closed surfaces from sparsely sampled parallel contours. A solution to this problem is especially important for medical segmentation, where manual contouring of 2D imaging scans is still extensively used. Our proposed method is based on a morphing process applied to neighboring contours that sweeps out a 3D surface. Our method is guaranteed to produce closed surfaces that exactly pass through the input contours, regardless of the topology of the reconstruction.

Our general approach consecutively morphs between sets of input contours using an Eulerian formulation (i.e. fixed grid) augmented with Lagrangian particles (i.e. interface tracking). This is numerically accomplished by propagating the input contours as 2D level sets with carefully constructed continuous speed functions. Specifically this involves particle advection to estimate distances between the contours, monotonicity constrained spline interpolation to compute continuous speed functions without overshooting, and stateof- the-art numerical techniques for solving the level set equations. We demonstrate the robustness of our method on a variety of medical, topographic and synthetic data sets.

Place, publisher, year, edition, pages
IEEE , 2005. 407-414 p.
Keyword [en]
3D reconstruction, contours, level sets
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-36950Local ID: 33136ISBN: 0-7803-9462-3OAI: diva2:257799
16th IEEE Visualization 2005 (VIS 2005), October 23-28, Minneapolis, Minnesota, USA
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2010-10-20
In thesis
1. Level-set methods and geodesic distance functions
Open this publication in new window or tab >>Level-set methods and geodesic distance functions
2009 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The work in this thesis focuses on efficient implementations of level-set methods and geodesic distance functions. The level-set method is a grid based design that inherits many favorable traits from implicit geometry. It is connected to distance functions through its special way of representing geometry: in ìo each point in space stores the closest distance to the surface. To differentiate between the inside and outside of a closed object a signed distance is used. In the discrete form the representation keeps a box around the surface that stores regularly positioned samples of the distance function – i.e. a grid. These samples implicitly encode the surface as the zeroth level-set of the signed distance function, hence the name level-set methods. With this representation of geometry follows a toolbox of operations based on partial differential equations (PDE). The solution to these PDES allows for arbitrary motion and deformation of the surface.

This thesis focuses on two topics: 1) grid storage for level-set methods, and 2) geodesic distance functions and parameterization. These topics are covered in a series of in-depth articles.

Today, level-set methods are becoming widespread in both academia and industry. Data structures and highly accurate methods and numerical schemes are available that allow for efficient handling of topological changes of dynamic curves and surfaces. For some applications, such as the capturing of the air/water interface in free surface fluid simulations, it’s is the only realistic choice. In other areas level-set methods are emerging as a competitive candidate to triangle meshes and other explicit representations.

In particular this work introduces efficient level-set data-structures that allow for extremely detailed simulations and representations. It also presents a parameterization method based on geodesic distance that produces a unique coordinate system, the Riemannian normal coordinates (RNC). Amongst other interesting applications this parameterization can be used for decal compositing, and the translation of vector space algorithms to surfaces. The approximation of the RNC involves one or more distance functions. In this thesis, a method originally presented for triangle meshes is adopted. It is then and extended to compute accurate geodesic distance in anisotropic domains in two and three dimensions. The extension to higher dimensions is also outlined.

To motivate this work several applications based on these novel methods and data structures are presented showing rapid ray-tracing, shape morphing, segmentation, geodesic interpolation, texture mapping, and more.

Place, publisher, year, edition, pages
Linköping: Linköping Universisty Electronic Press, 2009. 92 p.
Linköping Studies in Science and Technology. Dissertations, ISSN 0345-7524 ; 1275
National Category
Engineering and Technology
urn:nbn:se:liu:diva-54830 (URN)978-91-7393-524-1 (ISBN)
Public defence
2009-11-19, K3. Kåkenhus, Campus Norrköping, Linköpings universitet, Norrköping, 13:00 (English)
Available from: 2010-04-15 Created: 2010-04-15 Last updated: 2010-06-21Bibliographically approved

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