Spherical wavelets: Efficiently representing functions on a sphere

Schröder, Peter; Sweldens, Wim

doi:10.1007/bfb0011096

Cited by 265 publications

(419 citation statements)

References 28 publications

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“…Other researchers proposed the use of the lifting scheme to decompose the surfaces. Schroder and Swelden have proposed an extension of the lifting scheme to decompose spherical surfaces [32,33].…”

Section: -Multi-scales Analysis On Surfaces Represented By Triangulamentioning

confidence: 99%

Multi-scale freeform surface texture filtering using a mesh relaxation scheme

Jiang

Abdul-Rahman

Scott

2013

Meas. Sci. Technol.

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Surface filtering algorithms using Fourier, Gaussian, wavelets … etc., are well-established for simple Euclidean geometries. However, these filtration techniques cannot be applied to today's complex freeform surfaces, which have non-Euclidean geometries, without distortion of the results. This paper proposes a new multi-scale filtering algorithm for freeform surfaces that are represented by triangular meshes based on a mesh relaxation scheme. The proposed algorithm is capable of decomposing a freeform surface into different scales and to separate surface roughness, waviness and form from each other as will be demonstrated throughout the paper. Results of applying the proposed algorithm to computer-generated as well as real surfaces are represented and compared with a lifting wavelet filtering algorithm.

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Section: -Multi-scales Analysis On Surfaces Represented By Triangulamentioning

confidence: 99%

Multi-scale freeform surface texture filtering using a mesh relaxation scheme

Jiang

Abdul-Rahman

Scott

2013

Meas. Sci. Technol.

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“…Schröder and W. Sweldens [11] wanted to extend the discrete wavelet transform to any manifolds and in particular to the sphere. They have used a subdivision grid on the sphere (see Fig.…”

Section: Extension Of the Multifractal Analysis To The Spherementioning

confidence: 99%

Multifractal Analysis on the Sphere

Koenig

Chainais

2008

Lecture Notes in Computer Science

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Abstract.A new generation of instruments in astrophysics or vision now provide spherical data. These spherical data may present a selfsimilarity property while no spherical analysis tool is yet available to characterize this property. In this paper we present a first numerical study of the extension of multifractal analysis onto the sphere using spherical wavelet transforms. We use a model of multifractal spherical textures as a reference to test this approach. The results of the spherical analysis appear qualitatively satisfactory but not as accurate as those of the usual 2D multifractal analysis.

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“…Schroeder et al [31] extended wavelets to spherical domain to efficiently represent spherical functions. They used these spherical wavelets to represent a 2D slice of BRDF by keeping the viewing direction constant.…”

Section: Spherical Waveletsmentioning

confidence: 99%

BRDF Acquisition with Basis Illumination

Ghosh

Achutha

Heidrich

et al. 2007

2007 IEEE 11th International Conference on Computer Vision

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To create a realistic image we need to characterize how light reflects off a surface.In optics terminology, the complete Bidirectional Reflectance Distribution Function is needed. At a given point on a surface the BRDF is a function of two directions, one toward the light and one toward the viewer. Any device for measuring the 4D reflectance data has to obtain measurements over the hemisphere of incident and exitant directions which can be quite tedious if done using the brute-force approach.In this thesis, we describe an efficient image-based acquisition setup that has no moving parts and can acquire reflectance data in a matter of a few minutes. We make this possible by using curved reflective surfaces that eliminate the need to move either the camera or the light source. The acquisition speedup mostly comes from the way we optically sample the BRDF data into a suitable basis. This also saves us the postprocess compression of data. We then encode the data into a compact form that is suitable for use in various rendering systems. ContentsAbstract .

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Spherical wavelets: Efficiently representing functions on a sphere

Cited by 265 publications

References 28 publications

Multi-scale freeform surface texture filtering using a mesh relaxation scheme

Multi-scale freeform surface texture filtering using a mesh relaxation scheme

Multifractal Analysis on the Sphere

BRDF Acquisition with Basis Illumination

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