Surface Recovery from 3D Point Data Using a Combined Parametric and Geometric Flow Approach

Abstract

Abstract. This paper presents a novel method for surface recovery from discrete 3D point data sets. In order to produce improved reconstruction results, the algorithm presented in this paper combines the advantages of a parametric approach to model local surface structure, with the generality and the topological adaptability of a geometric flow approach. This hybrid method is specifically designed to preserve discontinuities in 3D, to be robust to noise, and to reconstruct objects with arbitrary topologies. The key ideas are to tailor a curvature consistency algorithm to the case of a set of points in 3D and to then incorporate a flux maximizing geometric flow for surface reconstruction. The approach is illustrated with experimental results on a variety of data sets. IntroductionSurface reconstruction from incomplete data sets is a classical problem in computer vision. The problem consists of finding a surface S that approximates a physical surface P by using a set of point coordinates sampled from the surface P. These point coordinates may be corrupted with noise, due to imperfections in the acquisition of the data. Like many other problems in computer vision, the problem of surface reconstruction is ill-posed. Prior knowledge about the world and the data acquisition process must therefore be used in order to make it solvable. A good algorithm for surface reconstruction should be robust to noise and result in smooth surfaces, while recovering important structural information from the data, such as edges, ridges and holes. The presence of such structural information in the reconstructed 3D model is very important for further, higher-level processing tasks, such as shape segmentation into parts, object recognition, etc. It should impose as little restrictions on the topology of the reconstructed object as possible. These issues are taken into consideration in the research presented in this paper. The approach to surface reconstruction presented in this article combines two different philosophies, namely that of a parametric reconstruction approach, and that of a geometric flow reconstruction approach. Many algorithms for surface recovery are based on either one of the two types of approaches, but few have attempted to

Global Optimization for Shape Fitting

“…While explicit mesh-based representations are very common, e.g. [5], to avoid mesh-related numerical problems, many methods represent surfaces implicitly using level-sets [6,21,22,18]. Both meshes and level-sets can be locally optimized via gradient descent.…”

“…Savadjiev et al [18] formulate surface fitting as a problem of estimating a dense vector field {v p } of surface normals from sparse data. Then, a continuous surface can be recovered from a dense field {v p } by optimizing a flux functional…”

“…However, a lack of global surface orientation in [18] results in ±180 degree ambiguity of the estimated vectors {v p }. Then, they use some heuristics deviating from (3) and causing geometric artifacts (e.g.…”

Kernel based method for surface estimation using Laser scanner data

“…Several methods have been suggested for implicit surface modeling. One popular method is to use local nature for deducing the implicit functions, such as level set models [7,8], local surface models [9], geometric flow [10] or implicit surfaces interpolated from polygon data [11]. Because of the use of the local nature of terrain analysis, most of the above mentioned methods often need normal information about the destination surface in order to produce the implicit surfaces correctly.…”

An Efficient Algorithm for Level Set Method Preserving Distance Function

“…Secondly, our algorithm preserves the LSM as an SDF, avoiding the classical re-distancing problem and providing desirable properties for some applications. For example, this makes an important difference in surface reconstruction, where surface normals can be fast and reliably estimated during the surface evolution instead of being required as input data s.a. [34,22], and in medical image segmentation, where the distance information can be exploited to include topology restrictions into the problem. Finally, our algorithm is easy to implement because the iterative scheme is based on standard minimization problems.…”