Automatic Reconstruction of B-Spline Surfaces of Arbitrary Topological Type
Matthias Eck, Hugues Hoppe.
Proceedings of SIGGRAPH 96. pp. 325-334. 1996.

Abstract
Creating freeform surfaces is a challenging task even with advanced geometric modeling systems. Laser range scanners offer a promising alternative for model acquisition - the 3D scanning of existing objects or clay maquettes. The problem of converting the dense point sets produced by laser scanners into useful geometric models is referred to as surface reconstruction. In this paper, we present a procedure for reconstructing a tensor product B-spline surface from a set of scanned 3D points. Unlike previous work which considers primarily the problem of fitting a single B-spline patch, our goal is to directly reconstruct a surface of arbitrary topological type. We must therefore define the surface as a network of B-spline patches. A key ingredient in our solution is a scheme for automatically constructing both a network of patches and a parametrization of the data points over these patches. In addition, we define the B-spline surface using a surface spline construction, and demonstrate that such an approach leads to an efficient procedure for fitting the surface while maintaining tangent plane continuity. We explore adaptive refinement of the patch network in order to satisfy user-specified error tolerances, and demonstrate our method on both synthetic and real data.

Spiraling Edge: Fast Surface Reconstruction from Partially Organized Sample Points
Patricia J. Crossno, Edward S. Angel.
IEEE Visualization '99. pp. 317-324. 1999.

Abstract
Many applications produce three-dimensional points that must be further processed to generate a surface. Surface reconstruction algorithms that start with a set of unorganized points are extremely time-consuming. Sometimes, however, points are generated such that there is additional information available to the reconstruction algorithm. We present Spiraling Edge, a specialized algorithm for surface reconstruction that is three orders of magnitude faster than algorithms for the general case. In addition to sample point locations, our algorithm starts with normal information and knowledge of each point's neighbors. Our algorithm produces a localized approximation to the surface by creating a star-shaped triangulation between a point and a subset of its nearest neighbors. This surface patch is extended by locally triangulating each of the points along the edge of the patch. As each edge point is triangulated, it is removed from the edge and new edge points along the patch's edge are inserted in its place. The updated edge spirals out over the surface until the edge encounters a surface boundary and stops growing in that direction, or until the edge reduces to a small hole that is filled by the final triangle.

Surface Reconstruction based on Lower Dimensional Localized Delaunay Triangulation
M. Gopi, S. Krishnan, C. T. Silva.
Computer Graphics Forum. 19 (3). 2000.

Abstract
We present a fast, memory efficient algorithm that generates a manifold triangular mesh S passing through a set of unorganized points P R³. 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 projection-based 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.

Parameterization for reconstruction of 3D freeform objects from laser-scanned data based on a PDE method
J. Barhak, A. Fischer.
The Visual Computer. 17 (6). pp. 353-369. 2001.

Abstract
In reverse engineering, laser scanners are commonly used since 3D data is sampled fast and accurately relative to other systems. However, they provide an enormous amount of irregular data that requires intensive reconstruction processing, based on the parameterization and surface fitting stages. Selection of an appropriate parameterization is essential for topology reconstruction as well as surface fitness. Current parameterization methods have topological problems, leading to undesired noisy self-intersecting surfaces. In this paper, a new adaptive parameterization PDE (partial differential equation) method is proposed for sculptured objects that were scanned from a single direction. The method is based on calculating a PDE non-self-intersecting parametric grid, and then fitting the base surface using CMA (control mesh approximation) and adaptive GDA (gradient descent approximation) methods.

High-quality texture reconstruction from multiple scans
Fausto Bernardini, Ioana M. Martin, Holly Rushmeier.
IEEE Transactions on Visualization and Computer Graphics. 7 (4). pp. 318-332. 2001.

Abstract
The creation of three-dimensional digital content by scanning real objects has become common practice in graphics applications for which visual quality is paramount, such as animation, e-commerce, and virtual museums. While a lot of attention has been devoted recently to the problem of accurately capturing the geometry of scanned objects, the acquisition of high-quality textures is equally important, but not as widely studied. In this paper, we focus on methods to construct accurate digital models of scanned objects by integrating high-quality texture and normal maps with geometric data. These methods are designed for use with inexpensive, electronic camera-based systems in which low-resolution range images and high-resolution intensity images are acquired. The resulting models are well-suited for interactive rendering on the latest-generation graphics hardware with support for bump mapping. Our contributions include new techniques for processing range, reflectance, and surface normal data, for image-based registration of scans, and for reconstructing high-quality textures for the output digital object.

Automatic surface reconstruction from point sets in space
Marco Attene, Michela Spagnuolo.
Computer Graphics Forum. 19 (3). 2000.

Abstract
In this paper an algorithm is proposed that takes as input a generic set of unorganized points, sampled on a real object, and returns a closed interpolating surface. Specifically, this method generates a closed 2-manifold surface made of triangular faces, without limitations on the shape or genus of the original solid. The reconstruction method is based on generation of the Delaunay tetrahedralization of the point set, followed by a sculpturing process constrained to particular criteria. The main applications of this tool are in medical analysis and in reverse engineering areas. It is possible, for example, to reconstruct anatomical parts starting from surveys based on TACs or magnetic resonance.

Surface Reconstruction and Display from Range and Color Data
Kari Pulli, Linda G. Shapiro.
Graphical Models. 62 (3). pp. 165-201. 2000.

Abstract
This paper addresses the problem of scanning both the color and geometry of real objects and displaying realistic images of the scanned objects from arbitrary viewpoints. We describe a complete system that uses a stereo camera setup with active lighting to scan the object surface geometry and color. Scans expressed in sensor coordinates are registered into a single object-centered coordinate system by aligning both the color and geometry where the scans overlap. The range data are integrated into a surface model using a robust hierarchical space carving method. The fit of the resulting approximate mesh to data is improved and the mesh structure is simplified using mesh optimization methods. In addition, a method for view-dependent texturing of the reconstructed surfaces is described. The method projects the color data from the input images onto the surface model and blends the various images depending on the location of the viewpoint and other factors such as surface orientation.

Reconstruction of B-spline Surfaces from Scattered Data Points
Benjamin F. Gregorski, Bernd Hamann, Kenneth I. Joy.
Computer Graphics International 2000. pp. 163-172. 2000.

Abstract
We present a new approach for reconstructing a smooth surface from a set of scattered points in three-dimensional (3D) space. Our algorithm first decomposes a given point set into a quadtree-like data structure known as a strip tree. The strip tree is used to fit a set of least squares quadratic surfaces to the data points. These quadratic surfaces are then degree-elevated to bi-cubic surfaces and blended together to form a set of B-spline surfaces that approximates the given point set.

New techniques for topologically correct surface reconstruction
U. Adamy, J. Giesen, M. John.
IEEE Visualization 2000. pp. 373-380. 2000.

Abstract
We present a novel approach to surface reconstruction based on the Delaunay complex. First we give a simple and fast algorithm that picks locally a surface at each vertex. For that, we introduce the concept of /spl lambda/-intervals. It turns out that for smooth regions of the surface this method works very well and at difficult parts of the surface yields an output well-suited for postprocessing. As a postprocessing step we propose a topological clean up and a new technique based on linear programming in order to establish a topologically correct surface. These techniques should be useful also for many other reconstruction schemes.