Multiresolution for curves and surfaces based on constraining wavelets

Olsen, Luke; Samavati, Faramarz; Bartels, Richard H.

doi:10.1016/j.cag.2007.01.033

Cited by 32 publications

(40 citation statements)

References 12 publications

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“…From Table 2 we can find the results by refined filters have marked improvement. The method by Olsen et al [15], based on cubic B-spline, is also an approximating scheme, however, it is binary. We take the original curves in Figures 11 and 12 as examples to compare our refined ternary method with the binary one.…”

Section: Some Examplesmentioning

confidence: 99%

“…Based on a four neighbouring details besidẽ v k i shown in Figure 2, unlike two details for binary subdivision schemes by Olsen and Samavati [14] and Olsen et al [15], the local error is denoted as…”

Section: Refinementmentioning

confidence: 99%

“…Samavati and Bartels [1,18] proposed reverse subdivision schemes for cubic B-splines and Dyn-Levin-Gregory (DLG) 4-point interpolating scheme [4] based on global and local least-square data fitting, respectively. Olsen et al [14,15] constructed MR representation for curves and surfaces based on constraining wavelets whose fundamental was also to build a biorthogonal wavelet system. By introducing curve and surface energy, Sadeghi et al [16,17] presented smooth reverse subdivision which also realized curves and surfaces MR representation, and the generated coarse results better preserved the overall structure of the fine objects.…”

Section: Introductionmentioning

confidence: 99%

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Multiresolution representation for curves based on ternary subdivision schemes

Guo

Zheng

Peng

2014

International Journal of Computer Mathematics

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Subdivision offers a way to increase the resolution of models, while reverse subdivision possesses the opposite ability. Combining the two theories could realize the multiresolution (MR) representation of models. Based on two ternary subdivision schemes, we present the trial and refined filters and an algorithm to realize MR representation for curves, which has some difference compared with the work relating to binary schemes. And the filters yield biorthogonal wavelet systems which are the underlying theory fundament of curves MR. By experiments and numerical calculations, we demonstrate that by using the ternary methods one can accomplish the MR representation for curves and the low-resolution results obtained by reverse subdivision can approximate the original curves well. Besides, ternary methods need smaller number of decomposition times than binary methods to get low-resolution results at similar levels of resolution for the same original curve.

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Section: Some Examplesmentioning

confidence: 99%

Section: Refinementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Multiresolution representation for curves based on ternary subdivision schemes

Guo

Zheng

Peng

2014

International Journal of Computer Mathematics

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“…The method is efficient, but it relies on shaders, which is impracticable, when targeting handheld devices. Olsen et al (2007) described a multiresolution method for curves and surfaces based on constraining wavelets. Then the constraint leads to an initial set of decomposition filters.…”

Section: Related Workmentioning

confidence: 99%

Transmission and visualization of large geographical maps

Zhang

Ren

et al. 2011

ISPRS Journal of Photogrammetry and Remote Sensing

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“…MR settings based on wavelets have been proposed for many curve and surface subdivision types -Bsplines [12], Doo-Sabin [24], Loop [2,18,22], and Catmull-Clark [3,14] surfaces. So while waveletbased approaches can indeed be used to construct MR systems, several related questions have not been addressed.…”

Section: Introductionmentioning

confidence: 99%

A Discrete Approach to Multiresolution Curves and Surfaces

Olsen

Samavati

2008

2008 International Conference on Computational Sciences and Its Applications

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Subdivision surfaces have been widely adopted in modeling in part because they introduce a separation between the surface and the underlying basis functions. Such a separation allows for simple schemes that work on general topology surfaces. Multiresolution representations based on subdivision, however, incongruently return to continuous functional spaces in their construction and analysis. In this paper, we investigate a discrete approach to multiresolution construction for a variety of subdivision schemes, based only on the subdivision rules. Noting that a compact representation can only afford to store a subset of the detail information, our construction enforces a constraint between locally adjacent detail terms. In this way, all detail information is recoverable for reconstruction, and a decomposition approach is implied by the constraint. The construction is demonstrated with case studies in DynLevin-Gregory curves and Catmull-Clark surfaces, each of which our method produces results as good as earlier methods. It is further shown that our construction can be interpreted as biorthogonal wavelet systems.

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Multiresolution for curves and surfaces based on constraining wavelets

Cited by 32 publications

References 12 publications

Multiresolution representation for curves based on ternary subdivision schemes

Multiresolution representation for curves based on ternary subdivision schemes

Transmission and visualization of large geographical maps

A Discrete Approach to Multiresolution Curves and Surfaces

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