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Mark J. Bentum, Barthold B.A. Lichtenbelt, Tom Malzbender, "Frequency Analysis of Gradient Estimators in Volume Rendering," IEEE Transactions on Visualization and Computer Graphics, vol. 2, no. 3, pp. 242254, September, 1996.  
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@article{ 10.1109/2945.537307, author = {Mark J. Bentum and Barthold B.A. Lichtenbelt and Tom Malzbender}, title = {Frequency Analysis of Gradient Estimators in Volume Rendering}, journal ={IEEE Transactions on Visualization and Computer Graphics}, volume = {2}, number = {3}, issn = {10772626}, year = {1996}, pages = {242254}, doi = {http://doi.ieeecomputersociety.org/10.1109/2945.537307}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Visualization and Computer Graphics TI  Frequency Analysis of Gradient Estimators in Volume Rendering IS  3 SN  10772626 SP242 EP254 EPD  242254 A1  Mark J. Bentum, A1  Barthold B.A. Lichtenbelt, A1  Tom Malzbender, PY  1996 KW  Volume rendering KW  volume visualization KW  gradient filters. VL  2 JA  IEEE Transactions on Visualization and Computer Graphics ER   
Abstract—Gradient information is used in volume rendering to classify and color samples along a ray. In this paper, we present an analysis of the theoretically ideal gradient estimator and compare it to some commonly used gradient estimators. A new method is presented to calculate the gradient at arbitrary sample positions, using the derivative of the interpolation filter as the basis for the new gradient filter. As an example, we will discuss the use of the derivative of the cubic spline. Comparisons with several other methods are demonstrated. Computational efficiency can be realized since parts of the interpolation computation can be leveraged in the gradient estimation.
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