All-frequency precomputed radiance transfer using spherical radial basis functions and clustered tensor approximation

2006 ◽  
Author(s):  
Yu-Ting Tsai ◽  
Zen-Chung Shih
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Spherical Radial Basis Functions ◽  
Tensor Approximation ◽  
Precomputed Radiance Transfer

PDF-to-ODF Inversion by Approximation with Spherical Radial Basis Functions

2005 ◽  
pp. 313-318 ◽  
Author(s):  
Ralf Hielscher ◽  
Swanhild Bernstein ◽  
Helmut Schaeben ◽  
K.Gerald van den Boogaart ◽  
Judith Beckmann ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Spherical Radial Basis Functions

The combination and contribution of different gravity measurements in regional quasi-geoid determination based on spherical radial basis functions

2021 ◽  
Author(s):  
Qing Liu ◽  
Michael Schmidt ◽  
Laura Sánchez
Keyword(s):  
Radial Basis Functions ◽  
Gravity Data ◽  
Basis Functions ◽  
Airborne Gravity ◽  
Frequency Noise ◽  
Geoid Model ◽  
Topographic Model ◽  
Radial Basis ◽  
Spherical Radial Basis Functions ◽  
Terrestrial Data

<p>In this study, we investigate the optimal combination of local gravity observations and their contributions to the regional quasi-geoid model. The study area is located in Colorado, USA, with two types of regional data sets, namely terrestrial gravity data and airborne gravity data, available within the “1 cm geoid experiment”. The approach based on series expansions in terms of spherical radial basis functions (SRBF) is applied, which has been developed at DGFI-TUM in the last two decades. We use two different types of basis functions covering the same spectral domain separately for the terrestrial and the airborne measurements. The Shannon function is applied to the terrestrial data, and the Cubic Polynomial (CuP) function which has smoothing features is applied to the airborne data for filtering their high-frequency noise.</p><p>To assess the contributions of the regional terrestrial and airborne gravity data to the final quasi-geoid model, four solutions are compared, namely the combined solution, the terrestrial only, the airborne only, and finally the model only solution, i.e., only the global gravity model and the topographic model are used without any gravity data from regional measurements. By adding the terrestrial data to the GGM and the topographic model, the RMS error of the quasi-geoid model w.r.t the validation data (the mean solution of independent computations delivered by fourteen institutions from all over the world) drops from 4 to 1.8 cm, and it is further reduced to 1 cm by including the airborne data.</p>

All-Frequency Lighting with Multiscale Spherical Radial Basis Functions

2010 ◽  
Vol 16 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Ping-Man Lam ◽  
Tze-Yiu Ho ◽  
Chi-Sing Leung ◽  
Tien-Tsin Wong
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Spherical Radial Basis Functions

PDF-to-ODF Inversion by Approximation with Spherical Radial Basis Functions

2005 ◽  
Vol 495-497 ◽  
pp. 313-318
Author(s):  
Ralf Hielscher ◽  
Swanhild Bernstein ◽  
Helmut Schaeben ◽  
K.Gerald van den Boogaart ◽  
Judith Beckmann ◽  
...  
Keyword(s):  
Radial Basis Functions ◽  
Basis Functions ◽  
Radial Basis ◽  
Spherical Radial Basis Functions
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