EWA Volume Splatting

We present a novel framework for direct volume rendering using a splatting approach based on elliptical Gaussian kernels. To avoid aliasing artifacts, we introduce the concept of a resampling filter combining a reconstruction with a low-pass kernel. Because of the similarity to Heckbert's EWA (elliptical weighted average) filter for texture mapping we call our technique EWA volume splatting. It provides high image quality without aliasing artifacts or excessive blurring even with non-spherical kernels. Hence it is suitable for regular, rectilinear, and irregular volume data sets. Moreover, our framework introduces a novel approach to compute the footprint function. It facilitates efficient perspective projection of arbitrary elliptical kernels at very little additional cost. Finally, we show that EWA volume reconstruction kernels can be reduced to surface reconstruction kernels. This makes our splat primitive universal in reconstructing surface and volume data.

Authors

Matthias Zwicker
Markus Gross
Computer Graphics Lab, ETH Zürich, Switzerland

Hanspeter Pfister
Jeroen van Baar
MERL - Mitsubishi Electric Research Laboratories

Introduction

Volume rendering is an important technique in visualizing acquired and simulated data sets in scientific and engineering applications. The ideal volume rendering algorithm reconstructs a continuous function in 3D, transforms this 3D function into screen space, and then evaluates opacity integrals along line-of-sights. In 1989, Westover introduced splatting for interactive volume rendering, which approximates this procedure. Splatting algorithms interpret volume data as a set of particles that are absorbing and emitting light. Line integrals are precomputed across each particle separately, resulting in fotprint functions. Each footprint spreads its contribution in the image plane. These contributions are composited back to front into the final image.

Overview

We introduce a new footprint function for volume splatting algorithms integrating an elliptical Gaussian reconstruction kernel and a low-pass filter. Our derivation proceeds along similar lines as Heckbert's elliptical weighted average (EWA) texture filter, therefore we call our algorithm EWA volume splatting. EWA volume rendering is attractive because it prevents aliasing artifacts in the output image while avoiding excessive blurring. Moreover, it works with arbitrary elliptical Gaussian reconstruction kernels and efficiently supports perspective projection. Our method is based on a novel framework to compute the footprint function, which relies on the transformation of the volume data to so-called ray space. This transformation is equivalent to perspective projection. By using its local affine approximation at each voxel, we derive an analytic expression for the EWA footprint in screen space. The rasterization of the footprint is performed using forward differencing requiring only one 1D footprint table for all reconstruction kernels and any viewing direction.

Results

We compare EWA volume splatting to the method proposed by Swan et al. Using a volume with a different resolution in the x- and y-direction, we illustrate the ability of EWA volume splatting to handle elliptical kernels. On the other hand, Swan's method leads to overly blurred images.

a) 1024 x 512 x 3 volume texture.

EWA Volume Splatting [736 KB TIFF]	Swan et al. [736 KB TIFF]

b) 1024 x 256 x 3 volume texture.

EWA Volume Splatting [736 KB TIFF]	Swan et al. [736 KB TIFF]

Next, we compare EWA volume versus EWA surface splatting. The projection of surface kernels leads to high quality anisotropic filtering with surface splatting, whereas EWA volume splatting renders slightly blurrier textures.

EWA Volume Splatting [150 KB TIFF]	EWA Surface Splatting [150 KB TIFF]

Here are some more datasets rendered using EWA volume splatting. Isosurfaces are rendered using flattened volume kernels.

UNC CT scan of a human head [142 KB TIFF]	UNC CT scan of an engine [58 KB TIFF]	Visible Woman foot and textured plane [90 KB TIFF]

Animations

Comparison between EWA volume splatting and Swan et al.

a) 1024 x 512 x 3 volume texture.

Left: EWA volume splatting. Right: Swan's method. [2.75 MB MPEG]	Left: EWA volume splatting. Right: Swan's method. [2.77 MB MPEG]

b) 1024 x 256 x 3 volume texture.

Left: EWA volume splatting. Right: Swan's method. [2.76 MB MPEG]	Left: EWA volume splatting. Right: Swan's method. [2.76 MB MPEG]