### BibTeX

@MISC{Guskov_topologicalnoise,

author = {Igor Guskov and et al.},

title = {Topological Noise Removal},

year = {}

}

### Years of Citing Articles

### OpenURL

### Abstract

Meshes obtained from laser scanner data often contain topological noise due to inaccuracies in the scanning and merging process. This topological noise complicates subsequent operations such as remeshing, parameterization and smoothing. We introduce an approach that removes unnecessary nontrivial topology from meshes. Using a local wave front traversal, we discover the local topologies of the mesh and identify features such as small tunnels. We then identify non-separating cuts along which we cut and seal the mesh, reducing the genus and thus the topological complexity of the mesh.

### Citations

1136 | Progressive meshes
- HOPPE
- 1996
(Show Context)
Citation Context ...ring acquisition, a complex model is often built from several scans. Each scanning pass produces a grid of points in space possibly with holes. A number of popular mesh reconstruction methods [9][31] =-=[19]-=- combine several range maps using an auxiliary volumetric representation: a signed distance volume constructed from a collection of scans. An isosurface is then extracted using the Marching Cubes algo... |

973 | Surface simplification using quadric error metrics - Garland, Heckbert - 1997 |

812 | A volumetric method for building complex models from range images
- Curless, Levoy
- 1996
(Show Context)
Citation Context ...ning. During acquisition, a complex model is often built from several scans. Each scanning pass produces a grid of points in space possibly with holes. A number of popular mesh reconstruction methods =-=[9]-=-[31] [19] combine several range maps using an auxiliary volumetric representation: a signed distance volume constructed from a collection of scans. An isosurface is then extracted using the Marching C... |

666 | Surface reconstruction from unorganized points
- Hoppe, Rose, et al.
- 1992
(Show Context)
Citation Context ...o a more efficient and “regular” representation such as NURBS or other spline/subdivisionbased multiresolution surface representations. This process is called remeshing in the graphics literature [22]=-=[18]-=- [21][25][24]. Several remeshing methods use simplification hierarchies of the initial irregular mesh in order to build efficient computational procedures. However, raw irregular meshes extracted from... |

444 | Implicit fairing of irregular meshes using diffusion and curvature flow
- Desbrun, Meyer, et al.
- 1999
(Show Context)
Citation Context ...ill produces topological artifacts such as tiny handles. It is often important to remove these handles so that they do not encumber later processing, such as simplification [20], smoothing, denoising =-=[10]-=-, and remeshing. Figure 8 shows the result of applying a smoothing procedure to a mesh with handles. While most of the surface gets smoother, the areas containing handles have visible artifacts. The e... |

422 | Triangle: Engineering a 2d quality mesh generator and delaunay triangulator - Shewchuk - 1996 |

256 | Parametrization and smooth approximation of surface triangulations
- FLOATER
- 1997
(Show Context)
Citation Context ...s. The Figure 7 shows the parameterized mesh region of the David’s ear. The texture coordinates are assigned with the (u, v)-coordinates computed with the shape-preserving parameterization of Floater =-=[14]-=-. The original unfiltered region of this mesh contained twelve tunnels and could not be properly parameterized onto the unit square. Our algorithm removes all of these tunnels in fifteen seconds, and ... |

232 | Maps: Multiresolution adaptive parameterization of surfaces - Lee, Sweldens, et al. - 1998 |

220 | Marching Cubes: A High Resolution 3D Surface Reconstruction Algorithm - Lorenen, Cline |

217 | Multiresolution signal processing for meshes
- Guskov, Sweldens, et al.
- 1999
(Show Context)
Citation Context ... will potentially wipe out other features of the model (thin tubes and connected components could be broken apart and the finer detailed geometry will disappear). Recent work by Gerstner and Pajarola =-=[16]-=- on topology preserving volume simplification is one potential solution to try to control the effect of the downsampling, however, presently this work offers no method to distinguish important topolog... |

213 | Fitting smooth surfaces to dense polygon meshes
- KRISHNAMURTHY, LEVOY
- 1996
(Show Context)
Citation Context ...ore efficient and “regular” representation such as NURBS or other spline/subdivisionbased multiresolution surface representations. This process is called remeshing in the graphics literature [22][18] =-=[21]-=-[25][24]. Several remeshing methods use simplification hierarchies of the initial irregular mesh in order to build efficient computational procedures. However, raw irregular meshes extracted from nois... |

160 | Progressive simplicial complexes
- POPOVIC, HOPPE
- 1997
(Show Context)
Citation Context ...efficient and “regular” representation such as NURBS or other spline/subdivisionbased multiresolution surface representations. This process is called remeshing in the graphics literature [22][18] [21]=-=[25]-=-[24]. Several remeshing methods use simplification hierarchies of the initial irregular mesh in order to build efficient computational procedures. However, raw irregular meshes extracted from noisy vo... |

140 | Appearancepreserving simplification - COHEN, OLANO, et al. - 1998 |

136 | Munkres, Elements of Algebraic Topology - R - 1984 |

135 | Displaced subdivision surfaces
- LEE, MORETON, et al.
(Show Context)
Citation Context ... and incomplete, hence the noise in the signed distance volume. While the manifold property of the extracted surface can be guaranteed with small modifications to the original Marching Cubes algorithm=-=[23]-=-, we observe that for noisy data it still produces topological artifacts such as tiny handles. It is often important to remove these handles so that they do not encumber later processing, such as simp... |

129 | F.: Progressive forest split compression
- Taubin, Guéziec, et al.
- 1998
(Show Context)
Citation Context ...n Section 3. The simplification algorithms of the second class (e.g. [15]) do not assume the mani-fold property and will therefore simplify the given mesh (or polygon/edge soup, or simplicial complex=-=[30]-=-) with out noticing small tunnels and handles. However, these algorithms are useful only for simplification per se, and despite starting with a proper manifold they cannot guarantee that the manifold ... |

117 | Normal meshes - GUSKOV, VIDIMCE, et al. - 2000 |

99 | Guaranteeing the topology of an implicit surface polygonization for interactive modeling
- Stander, Hart
- 1997
(Show Context)
Citation Context ...dges, and faces, correspondingly), and x : V → R 3 is the coordinate function that gives the coordinates of every vertex of V. x can be extended to the polytope |K| of K using barycentric coordinates =-=[28]-=-. In this paper the focus is on meshes extracted as isosurfaces of certain volumetric functions, and therefore, such meshes are guaranteed to be oriented manifolds. Thus, all meshes considered in this... |

93 | Semi-regular mesh extraction from volumes
- WOOD, DESBRUN, et al.
- 2000
(Show Context)
Citation Context ...rating curve. This operation does not change the connectedness of the surface but does reduce its genus introducing two new holes (boundaries), which are later triangulated using methods described in =-=[32]-=-[25], or commercial packages [1][2]. (Figure 2 illustrates this process.) In this way, we remove the small handles one by one, filtering the local topology of the mesh. 2 Algorithm We consider a trian... |

76 | A shrink wrapping approach to remeshing polygonal surfaces
- Kobbelt, Vorsatz, et al.
- 1999
(Show Context)
Citation Context ...e that for noisy data it still produces topological artifacts such as tiny handles. It is often important to remove these handles so that they do not encumber later processing, such as simplification =-=[20]-=-, smoothing, denoising [10], and remeshing. Figure 8 shows the result of applying a smoothing procedure to a mesh with handles. While most of the surface gets smoother, the areas containing handles ha... |

63 | Topology preserving edge contraction
- Dey, Edelsbrunner, et al.
- 1998
(Show Context)
Citation Context ...nifold property will be maintained for coarser levels of the hierarchy. 1.2 Related work A variety of researchers have relied on coding or matching the topology of a given mesh to a new configuration =-=[29]-=-[3][4]. Most recently a lot of attention has been directed towards general simplicial complexes. Specifically, the problem of preserving the topology of simplicial complexes while applying edge contra... |

57 | Topology preserving and controlled topology simplifying multiresolution isosurface extraction
- Gerstner, Pajarola
- 2000
(Show Context)
Citation Context ...d of simplification algorithm will clearly benefit from topological noise removal – we show several examples of such improvements in Section 3. The simplification algorithms of the second class (e.g. =-=[15]-=-) do not assume the mani-fold property and will therefore simplify the given mesh (or polygon/edge soup, or simplicial complex[30]) with out noticing small tunnels and handles. However, these algorit... |

51 | The digital Michelangelo Project, in - Levoy - 1999 |

50 |
Afra Zomorodian. Topological persistence and simplification
- Edelsbrunner, Letscher
(Show Context)
Citation Context ...icial complexes. Specifically, the problem of preserving the topology of simplicial complexes while applying edge contractions was considered by Dey et al [34]. The recent paper by Edelsbrunner et al.=-=[11]-=- considers topological simplification in the context of alpha complexes. It is worth noting that topological simplification of simplicial complexes in R3 is a much harder and less intuitive problem th... |

47 | Controlled simplification of genus for polygonal models
- EL-SANA, VARSHNEY
- 1997
(Show Context)
Citation Context ...context of alpha complexes. It is worth noting that topological simplification of simplicial complexes in R3 is a much harder and less intuitive problem than the one we consider. El-Sana and Varshney =-=[12]-=-[13] address a similar problem of controlled topology simplification for polygonal models. Their approach identifies removable tunnels by rolling a sphere of small radius over the object and filling t... |

44 | Robust meshes from multiple range maps
- Pulli, Duchamp, et al.
- 1997
(Show Context)
Citation Context ...demonstrate our approach we apply our technique to a variety of the Stanford laser range finder datasets. For example, we consider the dataset of the David’s head from Stanford’s Michelangelo project =-=[26]-=-. The original irregular mesh has genus 340. Obviously, none of these 340 tiny tunnels are actually present in the original sculpture, therefore all these tunnels (or handles) can be removed to facili... |

25 | Topology Simplification for Polygonal Virtual Environments
- El-Sana, Varshney
- 1998
(Show Context)
Citation Context ...ext of alpha complexes. It is worth noting that topological simplification of simplicial complexes in R3 is a much harder and less intuitive problem than the one we consider. El-Sana and Varshney [12]=-=[13]-=- address a similar problem of controlled topology simplification for polygonal models. Their approach identifies removable tunnels by rolling a sphere of small radius over the object and filling the t... |

22 | Auditory morse analysis of triangulated manifolds
- AXEN, EDELSBRUNNER
- 1998
(Show Context)
Citation Context ...ies but is generalized to the mesh setting with optimizations to discover small local topology and with optimizations to identify topological events. This work is closely related to work done by Axen =-=[7]-=- which relates a discrete wavefront traversal and critical points from Morse theory. It is worth noting that there is another way to potentially “filter” or smooth the noisy topology of scanned data b... |

6 |
Guaranteeing 2-manifold property for meshes
- Akleman, Chen
- 1998
(Show Context)
Citation Context ...ld property will be maintained for coarser levels of the hierarchy. 1.2 Related work A variety of researchers have relied on coding or matching the topology of a given mesh to a new configuration [29]=-=[3]-=-[4]. Most recently a lot of attention has been directed towards general simplicial complexes. Specifically, the problem of preserving the topology of simplicial complexes while applying edge contracti... |

6 | Computing morse functions on triangulated manifolds
- AXEN
- 1999
(Show Context)
Citation Context ...orse theory to guarantee the topology of the polygonization of an implicit surface. It is difficult to generalize this work tothe irregular mesh setting without becoming computational intensive (see =-=[6]-=- for a potential solution). We focus on discrete methods that can rapidly discover the topology. Recent work by Wood et al [37] presented an algorithm to quickly identify and reconstruct the topology ... |

3 | A new paradigm for changing topology of 2manifold polygonal meshes
- Akleman, Chen, et al.
- 2000
(Show Context)
Citation Context ...property will be maintained for coarser levels of the hierarchy. 1.2 Related work A variety of researchers have relied on coding or matching the topology of a given mesh to a new configuration [29][3]=-=[4]-=-. Most recently a lot of attention has been directed towards general simplicial complexes. Specifically, the problem of preserving the topology of simplicial complexes while applying edge contractions... |

2 |
Topologically Defined Iso-surfaces. Research Report 96-20, Laboratoire de l’Informatique du Parall´elisme
- Lachaud
- 1996
(Show Context)
Citation Context ... into a more efficient and “regular” representation such as NURBS or other spline/subdivisionbased multiresolution surface representations. This process is called remeshing in the graphics literature =-=[22]-=-[18] [21][25][24]. Several remeshing methods use simplification hierarchies of the initial irregular mesh in order to build efficient computational procedures. However, raw irregular meshes extracted ... |

2 |
Finite surfaces: a study of finite 2 complexes
- Whittlesey
- 1960
(Show Context)
Citation Context ...g. During acquisition, a complex model is often built from several scans. Each scanning pass produces a grid of points in space possibly with holes. A number of popular mesh reconstruction methods [9]=-=[31]-=- [19] combine several range maps using an auxiliary volumetric representation: a signed distance volume constructed from a collection of scans. An isosurface is then extracted using the Marching Cubes... |

1 |
Sunghee Choi and Naveen Leekha. A simple algorithm for homeomorphic surface reconstruction
- Amenta
- 2000
(Show Context)
Citation Context ...cient and “regular” representation such as NURBS or other spline/subdivisionbased multiresolution surface representations. This process is called remeshing in the graphics literature [22][18] [21][25]=-=[24]-=-. Several remeshing methods use simplification hierarchies of the initial irregular mesh in order to build efficient computational procedures. However, raw irregular meshes extracted from noisy volume... |