Automatic reconstruction of surfaces and scalar fields from 3D scans

By Chandrajit L. Bajaj, Fausto Bernardini, Guoliang Xu. 1995

We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. A possible application is the rapid computer model reconstruction of an existing part or prototype from a three dimensional (3D) points scan of its surface. Color, texture or some scalar material property of the physical part, define natural scalar fields over the surface of the CAD model. Our reconstruction algorithm does not impose any convexity or differentiability restrictions on the surface of the original physical part or the scalar field function, except that it assumes that there is a sufficient sampling of the input point data to unambiguously reconstruct the CAD model. Compared to earlier methods our algorithm has the advantages of simplicity, efficiency and uniformity (both CAD model and scalar field reconstruction). The simplicity and efficiency of our approach is based on several novel uses of appropriate sub-structures (alpha shapes) of a three-dimensional Delaunay Triangulation, its dual the three-dimensional Voronoi diagram, and dual uses of trivariate Bernstein-Bezier forms. The boundary of the CAD model is modeled using implicit cubic Bernstein-Bezier patches, while the scalar field is reconstructed with functional cubic Bernstein-Bezier patches. CR

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Citations in the corpus

Computing and Rendering Point Set Surfaces (2003, methodology): “There are several efficient triangulation techniques, such as [2], [3], [5], [7], [17].”
The ball-pivoting algorithm for surface reconstruction (1999, methodology): “Given data satisfying the conditions of the reconstruction theorem of section III, one seed per connected component is enough to reconstruct the entire manifold (function find seedtriangleat line 10 in figure 5).”
State-of-The-Art and Applications of 3D Imaging Sensors in Industry, Cultural Heritage, Medicine, and Criminal Investigation (2009, methodology): “Volumetric methods [64, 65], mesh stitching [66, 67], region growing techniques [68, 69], and sculpting based methods [70] are of outmost importance in this field.”
A volumetric method for building complex models from range images (1996, methodology): “More recently, Bajaj, et al [1] used alpha-shapes to construct a signed distance function to which they fit implicit polynomials.”
The 3D Model Acquisition Pipeline (2002, background): “Bajaj et al. [44,47] use a binary search on the parameter α to ﬁnd a subcomplex that deﬁnes a closed surface containing all the data points.”
Fast surface reconstruction using the level set method (2001, methodology): “The second approach uses the data set to define a signed distance function on rectangular grids and denotes the zero isocontour of the signed distance function as the reconstructed implicit surface [6, 9, 16].”
Tight cocone: a water-tight surface reconstructor (2003, background): “This leads to undesired holes and other artifacts in the output surface.”
Point set surfaces (2001, methodology): “There are several efficient triangulation techniques, such as [1, 2, 4, 6, 12].”
Parallel Poisson Surface Reconstruction (2009, methodology): “When noise is present in the data, the resulting surface is often jagged and must be refit to the samples [7] or smoothed [5] in post-processing.”