This paper addresses the problem of removing the noise from noisy points clouds in the context of surface reconstruction. We introduce a new smoothing operator Q inspired by the moving least-squares method and robust statistics theory. Our method can be seen as an improvement of the moving least-squares method to preserve sharp features. We also present effective numerical optimization algorith...

In vector field analysis, saddle points have two different types of invariant manifolds, namely stable ones and unstable ones. The invariant manifolds represent separatrices that partition the domain of trajectories into invariant regions of different dynamics. In this work, we analyze the basins of attraction of two different stable nodes by reconstructing the separatrices of a saddle point. T...

Sharp features in manufactured and designed objects require particular attention when reconstructing surfaces from unorganized scan point sets using moving least squares (MLS) fitting. It’s an inherent property of MLS fitting that sharp features are smoothed out. Instead of searching for appropriate new fitting functions our approach computes a modified local point neighborhood so that a standa...

Moving least squares (MLS) is a very attractive tool to design effective meshless surface representations. However, as long as approximations are performed in a least square sense, the resulting definitions remain sensitive to outliers, and smooth-out small or sharp features. In this paper, we address these major issues, and present a novel point based surface definition combining the simplicit...

We study the performance of various agent strategies in an artificial investment scenario. Agents are equipped with a budget, $x(t)$, and at each time step invest a particular fraction, $q(t)$, of their budget. The return on investment (RoI), $r(t)$, is characterized by a periodic function with different types and levels of noise. Risk-avoiding agents choose their fraction $q(t)$ proportional t...

Creating models of real scenes is a complex task for which the use of traditional modelling techniques is inappropriate. For this task, laser rangefinders are frequently used to sample the scene from several viewpoints, with the resulting range images integrated into a final model. In practice, due to surface reflectance properties, occlusions and accessibility limitations, certain areas of the...

We develop and analyze a least squares procedure for approximating the homogeneous Dirichlet problem for the wave equation in a bounded domain SI in R . This procedure is based on the pure implicit scheme for time differencing. Surprisingly, it is the normal derivative of u rather than u itself which must be included in the boundary functional. This normal derivative is an unknown quantity. We ...

Creating models of real scenes is a complex task for which the use of traditional modeling techniques is inappropriate. For this task, laser rangefinders are frequently used to sample the scene from several viewpoints, with the resulting range images integrated into a final model. In practice, due to surface reflectance properties, occlusions and accessibility limitations, certain areas of the ...

Multiview reconstruction aims at computing the geometry of a scene observed by a set of cameras. Accurate 3D reconstruction of dynamic scenes is a key component in a large variety of applications, ranging from special effects to telepresence and medical imaging. In this paper we propose a method based on Moving Least Squares surfaces which robustly and efficiently reconstructs dynamic scenes ca...

We introduce a novel method for the generation of fully adaptive streak surfaces in time-varying flow fields based on particle advection and adaptive mesh refinement. Moving least squares approximation plays an important role in multiple stages of the proposed algorithm, which adaptively refines the surface based on curvature approximation and circumradius properties of the underlying Delaunay ...