Spherical harmonic surface representation with feedback control

Sarp Ertuerk; Tim J. Dennis

doi:10.1117/12.341058

8 March 1999 Spherical harmonic surface representation with feedback control

Sarp Ertuerk, Tim J. Dennis

Proceedings Volume 3640, Three-Dimensional Image Capture and Applications II; (1999) https://doi.org/10.1117/12.341058
Event: Electronic Imaging '99, 1999, San Jose, CA, United States

Abstract

Spherical harmonic (SH) surface representation is used commonly for modeling rigid and non-rigid object. SH parameters are evaluated by fitting a surface constructed from a sum of harmonics to the raw 3D object data. Least squares error fitting is used and parameters are computed in a sequential process. Residual error feedback is proposed to control fitting accuracy. The residual radial error is available at each sample point after the computation of each parameter and used in the computation process of the next harmonic parameter. The SH representation order can be incremented until the harmonic model is sufficiently close to the object surface, or the gain in accuracy is so small as to be worthless. In this way representation order is automated. The raw object surface data is likely to contain areas that have no sample data. Although small and moderate sized gaps are automatically limited during SH parameter computation, large areas can develop spurious high amplitude harmonics. The ability of the sample pattern to 'control' a particular basis function can be checked during the computation process and the coefficients of uncontrolled harmonics set to zero to eliminate spurious features. The model is reconstructed in wire-frame form using geodesic sampling of the harmonic representation.

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Sarp Ertuerk and Tim J. Dennis "Spherical harmonic surface representation with feedback control", Proc. SPIE 3640, Three-Dimensional Image Capture and Applications II, (8 March 1999); https://doi.org/10.1117/12.341058

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KEYWORDS

Spherical lenses

Error analysis

Feedback control

3D modeling

Data modeling

Optical spheres

Statistical modeling

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