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176
Filling Holes In Complex Surfaces Using Volumetric Diffusion
, 2001
"... We address the problem of building watertight 3D models from surfaces that contain holesfor example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation al ..."
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Cited by 172 (2 self)
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We address the problem of building watertight 3D models from surfaces that contain holesfor example, sets of range scans that observe most but not all of a surface. We specifically address situations in which the holes are too geometrically and topologically complex to fill using triangulation algorithms. Our solution begins by constructing a signed distance function, the zero set of which defines the surface. Initially, this function is defined only in the vicinity of observed surfaces. We then apply a diffusion process to extend this function through the volume until its zero set bridges whatever holes may be present. If additional information is available, such as knownempty regions of space inferred from the lines of sight to a 3D scanner, it can be incorporated into the diffusion process. Our algorithm is simple to implement, is guaranteed to produce manifold noninterpenetrating surfaces, and is efficient to run on large datasets because computation is limited to areas near holes. By showing results for complex range scans, we demonstrate that our algorithm produces holefree surfaces that are plausible, visually acceptable, and usually close to the intended geometry.
Fast surface reconstruction using the level set method
 In VLSM ’01: Proceedings of the IEEE Workshop on Variational and Level Set Methods
, 2001
"... In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data ..."
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Cited by 151 (12 self)
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In this paper we describe new formulations and develop fast algorithms for implicit surface reconstruction based on variational and partial differential equation (PDE) methods. In particular we use the level set method and fast sweeping and tagging methods to reconstruct surfaces from scattered data set. The data set might consist of points, curves and/or surface patches. A weighted minimal surfacelike model is constructed and its variational level set formulation is implemented with optimal efficiency. The reconstructed surface is smoother than piecewise linear and has a natural scaling in the regularization that allows varying flexibility according to the local sampling density. As is usual with the level set method we can handle complicated topology and deformations, as well as noisy or highly nonuniform data sets easily. The method is based on a simple rectangular grid, although adaptive and triangular grids are also possible. Some consequences, such as hole filling capability, are demonstrated, as well as the viability and convergence of our new fast tagging algorithm.
Smooth Surface Reconstruction via Natural Neighbour Interpolation of Distance Functions
, 2000
"... We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through ..."
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Cited by 143 (8 self)
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We present an algorithm to reconstruct smooth surfaces of arbitrary topology from unorganised sample points and normals. The method uses natural neighbour interpolation, works in any dimension and allows to deal with non uniform samples. The reconstructed surface is a smooth manifold passing through all the sample points. This surface is implicitly represented as the zeroset of some pseudodistance function. It can be meshed so as to satisfy a userdefined error bound. Experimental results are presented for surfaces in R³.
Registration and Integration of Textured 3D Data
 IMAGE AND VISION COMPUTING
, 1996
"... In general, multiple views are required to create a complete 3D model of an object or a multiroomed indoor scene. In this work, we address the problem of merging multiple textured 3D data sets, each of which corresponding to a different view of a scene or object. There are two steps to the merging ..."
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Cited by 106 (3 self)
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In general, multiple views are required to create a complete 3D model of an object or a multiroomed indoor scene. In this work, we address the problem of merging multiple textured 3D data sets, each of which corresponding to a different view of a scene or object. There are two steps to the merging process: registration and integration. Registration is the process by which data sets are brought into alignment. To this end, we use a modified version of the Iterative Closest Point algorithm (ICP); our version, which we call color ICP, considers not only 3D information, but color as well. This has shown to have resulted in improved performance. Once the 3D data sets have been registered, we then integrate them to produce a seamless, composite 3D textured model. Our approach to integration uses a 3D occupancy grid to represent likelihood of spatial occupancy through voting. The occupancy grid representation allows the incorporation of sensor modeling. The surface of the merged model i...
Level set surface editing operators
 SIGGRAPH
, 2002
"... Figure 1: Surfaces edited with level set operators. Left: A damaged Greek bust model is repaired with a new nose, chin and sharpened hair. Right: A new model is constructed from models of a griffin and dragon (small figures), producing a twoheaded, winged dragon. We present a level set framework fo ..."
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Cited by 103 (10 self)
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Figure 1: Surfaces edited with level set operators. Left: A damaged Greek bust model is repaired with a new nose, chin and sharpened hair. Right: A new model is constructed from models of a griffin and dragon (small figures), producing a twoheaded, winged dragon. We present a level set framework for implementing editing operators for surfaces. Level set models are deformable implicit surfaces where the deformation of the surface is controlled by a speed function in the level set partial differential equation. In this paper we define a collection of speed functions that produce a set of surface editing operators. The speed functions describe the velocity at each point on the evolving surface in the direction of the surface normal. All of the information needed to deform a surface is encapsulated in the speed function, providing a simple, unified computational framework. The user combines predefined building blocks to create the desired speed function. The surface editing operators are quickly computed and may be applied both regionally and globally. The level set framework offers several advantages. 1) By construction, selfintersection cannot occur, which guarantees the generation of physicallyrealizable, simple, closed surfaces. 2) Level set models easily change topological genus, and 3) are free of the edge connectivity and mesh quality problems associated with mesh models. We present five examples of surface editing operators: blending, smoothing, sharpening, openings/closings and embossing. We demonstrate their effectiveness on several scanned objects and scanconverted models.
Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation
, 2000
"... We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P #R 3 . Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The spe ..."
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Cited by 81 (5 self)
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We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P #R 3 . Nothing is assumed about the geometry, topology or presence of boundaries in the data set except that P is sampled from a real manifold surface. The speed of our algorithm is derived from a projectionbased approach we use to determine the incident faces on a point. We define our sampling criteria to sample the surface and guarantee a topologically correct mesh after surface reconstruction for such a sampled surface. We also present a new algorithm to find the normal at a vertex, when the surface is sampled according our given criteria. We also present results of our surface reconstruction using our algorithm on unorganized point clouds of various models. 1. Introduction The problem of surface reconstruction from unorganized point clouds has been, and continues to be, an important topic of research. The problem can be loosely stated ...
Contextbased surface completion
 ACM Transactions on Graphics
"... Figure 1: Completing a hole in a pointbased model. In the darker colored region we removed sample points to demonstrate the surface completion technique. In the middle right the region is filled with a smooth patch conforming with the densely sampled areas, and the result of our contextbased surfa ..."
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Cited by 77 (4 self)
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Figure 1: Completing a hole in a pointbased model. In the darker colored region we removed sample points to demonstrate the surface completion technique. In the middle right the region is filled with a smooth patch conforming with the densely sampled areas, and the result of our contextbased surface completion is on the right. Sampling complex, realworld geometry with range scanning devices almost always yields imperfect surface samplings. These “holes ” in the surface are commonly filled with a smooth patch that conforms with the boundary. We introduce a contextbased method: the characteristics of the given surface are analyzed, and the hole is iteratively filled by copying patches from valid regions of the given surface. In particular, the method needs to determine best matching patches, and then, fit imported patches by aligning them with the surrounding surface. The completion process works top down, where details refine intermediate coarser approximations. To align an imported patch with the existing surface, we apply a rigid transformation followed by an iterative closest point procedure with nonrigid transformations. The surface is essentially treated as a point set, and local implicit approximations aid in measuring the similarity between two point set patches. We demonstrate the method at several pointsampled surfaces, where the holes either result from imperfect sampling during range scanning or manual removal.
Delaunay Based Shape Reconstruction from Large Data
, 2001
"... Surface reconstruction provides a powerful paradigm for modeling shapes from samples. For point cloud data with only geometric coordinates as input, Delaunay based surface reconstruction algorithms have been shown to be quite effective both in theory and practice. However, a major complaint against ..."
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Cited by 64 (5 self)
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Surface reconstruction provides a powerful paradigm for modeling shapes from samples. For point cloud data with only geometric coordinates as input, Delaunay based surface reconstruction algorithms have been shown to be quite effective both in theory and practice. However, a major complaint against Delaunay based methods is that they are slow and cannot handle large data. We extend the COCONE algorithm to handle supersize data. This is the first reported Delaunay based surface reconstruction algorithm that can handle data containing more than a million sample points on a modest machine.
Sampling and Reconstructing Manifolds Using AlphaShapes
 In Proc. 9th Canad. Conf. Comput. Geom
, 1997
"... There is a growing interest for the problem of reconstructing the shape of an object from multiple range images. Several methods, based on heuristics, have been described in the literature. We propose the use of alphashapes, which allow us to give a formal characterization of the reconstruction pro ..."
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Cited by 59 (7 self)
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There is a growing interest for the problem of reconstructing the shape of an object from multiple range images. Several methods, based on heuristics, have been described in the literature. We propose the use of alphashapes, which allow us to give a formal characterization of the reconstruction problem and to prove that, when certain sampling requirements are satisfied, the reconstructed alphashape is homeomorphic to the original object and approximate it within a fixed error bound. In a companion paper, we describe practical methods to automatically select an optimal alpha value, to deal with lessthanideal scans, and to fit smooth piecewise algebraic surface to the data points. 1 Introduction Cheaper, easiertouse 3D digitizers are fostering a growing interest for the problem of shapereconstruction. Automatic methods for reconstructing an accurate geometric model of an object from a set of digital scans have applications in reverse engineering, shape analysis, virtual worlds aut...