We consider applications of clustering techniques, Mean Shift and Self-Organizing Maps, to surface reconstruction (meshing) from scattered point data and review a novel kernel-based clustering method.

By now it is moderately well understood how to take as input a set of points that lie on an unknown manifold, and produce as output a piecewise linear approximation to the manifold. The question I explore here is: how fast can we do it? Previous solutions achieve a sequential runtime of O(n log n) in low ambient dimensions. I show that if the points are specified in floating point coordinates, ...

We propose a method to reconstruct surfaces from oriented point clouds corrupted by errors arising from range imaging sensors. The core of this technique is the formulation of the problem as a convex minimization that reconstructs the indicator function of the surface’s interior and substitutes the usual least-squares fidelity terms by Huber penalties to be robust to outliers, recover sharp cor...

We propose a method to reconstruct surfaces from oriented point clouds with non-uniform sampling and noise by formulating the problem as a convex minimization that reconstructs the indicator function of the surface’s interior. Compared to previous models, our reconstruction is robust to noise and outliers because it substitutes the leastsquares fidelity term by a robust Huber penalty; this allo...

In this chapter we introduce some of the properties of surfaces and their samples in three dimensions. The results developed in this chapter are used in later chapters to design algorithms for surface reconstruction and prove their guarantees. Before we talk about these results, let us explain what we mean by smooth surfaces. Consider a map π : U → V where U and V are the open sets in R2 and R3...

This report surveys recent techniques for reconstructing surfaces from points. We describe four main ideas in the graphics literature: signed distance estimation, Voronoi-based reconstruction, implicit surface fitting, and moving least squares surfaces. The main challenges include reconstruction without surface normals, robustness to noise, accuracy to sharp features, and provable reconstructio...

The paper presents a practical approach to measuring liver motion, both respiratory and laparoscopic, with a tool guided in the operating room. The presented method is based on standard operating room equipment, i.e. rigid laparoscopic cameras and a single incision laparoscopic surgery trocar. The triangulation algorithm is used and stereo correspondence points are marked manually by two indepe...

Given a finite sampling P ⊂ R of an unknown surface S, surface reconstruction is concerned with the calculation of a model of S from P . The model can be represented as a smooth or a triangulated surface, and is expected to match S from a topological and geometric standpoints. In this survey, we focus on the recent developments of Delaunay based surface reconstruction methods, which were the fi...

The area of surface reconstruction has seen substantial progress in the past two decades. The traditional problem addressed by surface reconstruction is to recover the digital representation of a physical shape that has been scanned, where the scanned data contains a wide variety of defects. While much of the earlier work has been focused on reconstructing a piece-wise smooth representation of ...