Frequency Analysis of Gradient Estimators in Volume Rendering Nal Version

In volume rendering gradient information is used to classify and color samples along a ray. In this paper we present an analysis of the theoretically ideal gradient estimator and compare some commonly used gradient estimators with the ideal estimator. A new method is presented to calculate the gradient on an arbitrary position, 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. A comparison will be made showing the di erences with other methods. Computational e ciency can be realized since parts of the interpolation computation can be leveraged in the gradient estimation.