Feature-Preserving Volume Filtering

Abstract

In this paper a feature-preserving volume filtering method is presented. The basic idea is to minimize a threecomponent global error function penalizing the density and gradient errors and the curvature of the unknown filtered function. The optimization problem leads to a large linear equation system defined by a sparse coefficient matrix. We will show that such an equation system can be efficiently solved in frequency domain using fast Fourier transformation (FFT). For the sake of clarity, first we illustrate our method on a 2D example which is a dedithering problem. Afterwards the 3D extension is discussed in detail since we propose our method mainly for volume filtering. We will show that the 3D version can be efficiently used for elimination of the typical staircase artifacts of direct volume rendering without losing fine details. Unlike local filtering techniques, our novel approach ensures a global smoothing effect. Previous global 3D methods are restricted to binary volumes or segmented iso-surfaces and they are based on area minimization of one single reconstructed surface. In contrast, our method is a general volume-filtering technique, implicitly smoothing all the iso-surfaces at the same time. Although the strength of the presented algorithm is demonstrated on a specific 2D and a specific 3D application, it is considered as a general mathematical tool for processing images and volumes.