Noise-corrupted signals and images can be reconstructed by minimization of a Hamiltonian. Often this Hamiltonian is a non-convex functional. The solution of minimum energy can then be approximated by the Graduated Non-Convexity (GNC) algorithm developed for the weak membrane by Blake and Zisserman. The GNC approximates the non-convex functional by a convex functional, and varies the solution sp...

Simple representation of complex 3D data sets is a fundamental problem in computer vision. From a quality control perspective, it is crucial to use efficient and simple techniques do define a reference model for further recognition or comparison tasks. In this paper, we focus on reverse engineering 3D data sets by recovering rational supershapes to build an implicit function to represent mechan...

Abstract. Surface reconstruction from a set of noisy point measurements has been a well studied problem for several decades. Recently, variational and discrete optimization approaches have been applied to solve it, demonstrating good robustness to outliers thanks to a global energy minimization scheme. In this work, we use a recent approach embedding several optimization algorithms into a commo...

This paper proposes a method called meshless parameterization for param eterizing and triangulating single patch unorganized point sets The points are mapped into a planar parameter domain by solving a sparse linear system By making a stan dard triangulation of the parameter points we obtain a corresponding triangulation of the original data set

We present a streaming method for reconstructing surfaces from large data sets generated by a laser range scanner using wavelets. Wavelets provide a localized, multiresolution representation of functions and this makes them ideal candidates for streaming surface reconstruction algorithms. We show how wavelets can be used to reconstruct the indicator function of a shape from a cloud of points wi...

The problem of reconstructing a shape from its sample appears in many scientific and engineering applications. Because of the variety in shapes and applications, many algorithms have been proposed over the last three decades, some of which exploit application-specific information and some of which are more general. We focus on techniques that apply to the general setting and have geometric and ...

This paper describes the application of a first order regularization technique to the problem of reconstruction of visible surfaces. Our approach is a computationally efficient first order method that simultaneously achieves approximate in\ nriance and preservation of discontinuities. Our reconstruction method is also robust with respect to the smoothing parameter The robustness property to I a...