Localization of a robotic system within previously mapped environment is important for reducing estimation drift and reusing built maps. Existing techniques geometry-based localization have focused on the description local surface geometry, usually using pointclouds as underlying representation. We propose geometrybased that extracts features directly from an implicit representation: Signed Dis...

We present a surface compression method that stores surfaces as wavelet-compressed signed-distance volumes. Our approach enables the representation of surfaces with complex topology and arbitrary numbers of components within a single multiresolution data structure. This data structure elegantly handles topological modification at high compression rates. Our method does not require the costly an...

We propose displaced signed distance fields, an implicit shape representation to accurately, efficiently and robustly 3D-print finely detailed smoothly curved surfaces at native device resolution. As the resolution accuracy of 3D printers increase, accurate reproduction such becomes increasingly realizable from a hardware perspective. However, representing with polygonal meshes requires high po...

Traditionally variational level set model for image segmentation is solved by using gradient descent method, which has low computational efficiency and needs complex re-initialization of level set functions as signed distance functions. In this paper, we first reformulate the variational model as a constrained optimization problem. Then we present an augmented Lagrangian projection method to pr...

We propose a new method for the reconstruction of the signed distance function in the context of level set methods. The new method is a modification of the algorithm which makes use of the PDE equation for the distance function introduced by M. Sussman, P. Smereka, and S. Osher (1994, J. Comput. Phys. 119, 146). It is based mainly on the use of a truly upwind discretization near the interface. ...

A new redistancing method for piecewise polynomial finite element level set functions is introduced. The method directly computes the distance to the implicitly given discrete level set. Rigorous error bounds and numerical experiments are provided. Both show that, up to constants, the method is as good as the nodal interpolation of the computationally unavailable signed distance function of the...

We propose a technique that could significantly improve the accuracy of the levelset method and has the potential for fully conservative treatment. Level set method uses the levelset function, usually an approximate signed distance function Φ to indirectly represent the interface by the zero set of Φ. When Φ is advanced to the next time level by an advection equation, it is no longer a signed d...