Frequency Analysis of Gradient Estimators in Volume Rendering

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 lter as the basis for the new gradient lter. As an example we will discuss the use of the derivative of the cubic spline. Comparisons with several other methods are demonstrated. Computational e ciency can be realized since parts of the interpolation computation can be leveraged in the gradient estimation.