Multiresolution signal processing for meshes

By Igor Guskov, Wim Sweldens, Peter Schröder. 1999

We generalize basic signal processing tools such as downsampling, upsampling, and filters to irregular connectivity triangle meshes. This is accomplished through the design of a non-uniform relaxation procedure whose weights depend on the geometry and we show its superiority over existing schemes whose weights depend only on connectivity. This is combined with known mesh simplification methods to build subdivision and pyramid algorithms. We demonstrate the power of these algorithms through a number of application examples including smoothing, enhancement, editing, and texture mapping.

Subfields: Speech & Audio

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Citations in the corpus

Spectral Networks and Locally Connected Networks on Graphs (2013, background): “There is a large literature on building wavelets on graphs, see for example [21, 7, 4, 5, 9].”
The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains (2012, background): “…as a smoothing operation to enhance the overall shape of an object [18], transform coding based on spectral decompositions for the compression of geometry data [19], and multiresolution representations of large meshes by decomposing one surface into multiple levels with different details [20].”
Mesh parameterization: theory and practice (2007, methodology): “This representation facilitates defining hierarchical representations and implementing multiresolution processing tools on top of it [Guskov et al., 1999].”
Texture synthesis on surfaces (2001, methodology): “Here we borrow techniques from mesh smoothing [22, 3, 7].”
Interactive geometry remeshing (2002, background): “The majority of previous work has proposed semi-regular remeshing techniques [24, 20, 21, 22], based on an initial phase of simplification which could be used in itself for remeshing [14, 27] since it performs the aforementioned edge operations and vertex shifting.”
Linear rotation-invariant coordinates for meshes (2005, methodology): “Multiresolution approaches [Zorin et al. 1997; Kobbelt et al. 1998; Guskov et al. 1999; Botsch and Kobbelt 2004] enable detailpreserving deformations by decomposing the surface into several frequency bands.”
On Linear Variational Surface Deformation Methods (2008, methodology): “A straightforward approach is to restrict S and B to have the same connectivity and to encode their geometric differenceD by per-vertex displacement vectors hi [29], [34], [74]:”
Progressive geometry compression (2000, background): “An important feature of MAPS is its ability to automatically align iso-parameter lines of the semiregular mesh with sharp features of the original input surface helping to avoid large wavelet coefficients near creases.”
Diffusion Wavelets (2004, background): “denoising of the point set, and in this respect it is most similar to [80].”
Interactive and anisotropic geometry processing using the screened Poisson equation (2011, methodology): “From Homogeneity to Anisotropy While methods such as [Taubin 1995; Kobbelt et al. 1998; Desbrun et al. 1999; Guskov et al. 1999; Ohtake et al. 2000] perform mesh fairing by solving a homogenous system of equations, there has also been significant research in the use of anisotropic diffusion for…”
Spectral compression of mesh geometry (2000, methodology): “Recent years have seen an increase of interest in signal processing approaches [20,6] to 3D mesh manipulation, and their extension to multiresolution analyses [15,9].”
Differential coordinates for interactive mesh editing (2004, background): “[11] use local frames attached to vertices and normal displacements that pierce the original surface and thus lead to resampling.”
Laplace-Beltrami eigenfunctions for deformation invariant shape representation (2007, unknown): “Afterwards, several versions were proposed in [DMSB99], [GSS99], [Tau00], [MDSB02], [Xu04b].”
Graph Signal Processing: Overview, Challenges, and Applications (2017, background): “and graph based filtering, processing and multi-resolution representations [74], [75], [76].”