  Direct volume rendering is often used to compare different 3D scalar fields.
The choice of the transfer function which maps scalar values to color and
opacity plays a critical role in this task. We present a technique for the
automatic optimization of a transfer function so that rendered images of a
second field match as good as possible images of a field that has been rendered
with some other transfer function. This enables users to see whether
differences in the visualizations can be solely attributed to the choice of
transfer function or remain after optimization. We propose and compare two
different approaches to solve this problem, a voxel-based solution solving a
least squares problem, and an image-based solution using differentiable volume
rendering for optimization. We further propose a residual-based visualization
to emphasize the differences in information content.
