Marching Cubes in an Unsigned Distance Field for Surface Reconstruction from Unorganized Point Sets (original) (raw)
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Implicit Surface Reconstruction and uniform Sampling by Striped Marching Triangles
2003
The synthesis of computer models from real objects is a usual procedure in medical image processing and reverse engineering. In both cases, the main issues are to reach a topologically consistent and geometrically precise object reconstruction. Implicit surfaces provide a solution to this problem. They define a smooth surface surrounding objects which must be polygonized for an efficient visualization. Due to the increasing size of the application generated data, it becomes necessary to use precise and efficient methods. This work presents a modified method of implicit surface polygonization based on “Marching Triangles”. This modification assures the topological consistency with the initial dataset during the progressive reconstruction of the surface, avoiding overlapping triangles. In addition, a comparison of our method with the marching cubes and the adaptive skeleton climbing algorithms is provided.
Marching Triangle Polygonization for Efficient Surface Reconstruction from Its Distance Transform
Lecture Notes in Computer Science, 2009
In this paper we propose a new polygonization method based on the classic Marching Triangle algorithm. It is an improved and efficient version of the basic algorithm which produces a complete mesh without any cracks. Our method is useful in the surface reconstruction process of scanned objects. It works over the scalar field distance transform of the object to produce the resulting triangle mesh. First we improve the original algorithm in finding new potential vertices in the mesh growing process. Second we modify the Delaunay sphere test on the new triangles. Third we consider new triangles configuration to obtain a more complete mesh. Finally we introduce an edge processing sequence to improve the overall Marching Triangle algorithm. We use a relevant error metric tool to compare results and show our new method is more accurate than Marching Cube which is the most widely used triangulation algorithm in the surface reconstruction process of scanned objects.
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14th International Conference on Image Analysis and Processing (ICIAP 2007), 2007
The well-known marching cubes algorithm is modified to apply to the face-centered cubic (fcc) grid. Thus, the local configurations that are considered when extracting the local surface patches are not cubic anymore. This paper presents three different partitionings of the fcc grid to be used for the local configurations. The three candidates are evaluated theoretically and experimentally and compared with the original marching cubes algorithm. It is proved that the reconstructed surface is topologically equivalent to the surface of the original object when the surface of the original object that is digitized is smooth and a sufficiently dense fcc grid is used.
A Generalized Marching Cubes Algorithm Based On Non-Binary Classifications
We present a new technique for generating surface meshes from a uniform set of discrete samples. Our method extends the well-known marching cubes algorithm used for computing polygonal isosurfaces. While in marching cubes each vertex of a cubic grid cell is binary classified as lying above or below an isosurface, in our approach an arbitrary number of vertex classes can be specified. Consequently the resulting surfaces consist of patches separating volumes of two different classes each.
Marching cubes: A high resolution 3D surface construction algorithm
ACM Siggraph Computer Graphics, 1987
We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.
Smooth signed distance surface reconstruction and applications
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2012
We describe a new and simple variational formulation to reconstruct the surface geometry, topology, and color map of a 3D scene from a finite set of colored oriented points. Point clouds are nowadays obtained using a variety of techniques, including structured lighting systems, pasive multi-view stereo algorithms, and 3D laser scanning. In our formulation the implicit function is forced to be a smooth approximation of the signed distance function to the surface. The formulation allows for a number of different efficient discretizations, reduces to a finite dimensional least squares problem for all linearly parameterized families of functions, does not require the specification of boundary conditions, and it is particularly good at extrapolating missing and/or irregularly sampled data. The resulting algorithms are significantly simpler and easier to implement than alternative methods. In particular, our implementation based on a primal-graph octree-based hybrid finite element-finite difference discretization, and the Dual Marching Cubes isosurface extraction algorithm is very efficient, and produces high quality crack-free adaptive manifold polygon meshes. After the geometry and topology are reconstructed, the color information from the points is smoothly extrapolated to the surface by solving a second variational problem which also reduces to a finite dimensional least squares problem. The resulting method produces high quality polygon meshes with smooth color maps, which accurately approximate the source colored oriented points. An open source implementation of this method is available for download. We describe applications to digital archaeology, 3D forensics, and 3D broadcasting.
Surface generation from datasets using triangulation algorithms cubes require large amounts of computati generation and interpolation of vertices. a templated method of generating triangl less computation involved and saves on memory. Each cube orientation corres boundary cases in the original algorith prebuilt table of templated triangles. The using binary input may be further smoot functions related to input image data.
IEEE Transactions on Visualization and Computer Graphics, 2003
A characterization and classification of the isosurfaces of trilinear functions is presented. Based upon these results, a new algorithm for computing a triangular mesh approximation to isosurfaces for data given on a 3D rectilinear grid is presented. The original marching cubes algorithm is based upon linear interpolation along edges of the voxels. The asymptotic decider method is based upon bilinear interpolation on faces of the voxels. The algorithm of this paper carries this theme forward to using trilinear interpolation on the interior of voxels. The algorithm described here will produce a triangular mesh surface approximation to an isosurface which preserves the same connectivity/separation of vertices as given by the isosurface of trilinear interpolation.
Space subdivision for fast polygonization of implicit surfaces
2002
This paper presents the basic principles for the visualization of objects which are defined by implicit functions and CSG trees. The basic principles (Marching cubes, Marching tetrahedra and Marching triangles) for iso-surfaces rendering of such objects are compared. A new fast modification of the Marching triangles algorithm is presented and compared with others algorithms. It is based on the space subdivision technique that enabled a significant speed-up of the Marching triangles algorithm. The speed-up grows with the grid resolution in which the object is represented. The presented algorithm is convenient for objects with large smooth and complex surfaces. The method produces a triangular mesh that consists of well-shaped triangles.
Surface Reconstruction from Unorganized Points
We describe and demonstrate an algorithm that takes as input an unorganized set of points {xl, . . . . x.} c IR3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance -all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from two-dimensional slices, and interactive surface sketching.