  We present a differentiable volume rendering solution that provides
differentiability of all continuous parameters of the volume rendering process.
This differentiable renderer is used to steer the parameters towards a setting
with an optimal solution of a problem-specific objective function. We have
tailored the approach to volume rendering by enforcing a constant memory
footprint via analytic inversion of the blending functions. This makes it
independent of the number of sampling steps through the volume and facilitates
the consideration of small-scale changes. The approach forms the basis for
automatic optimizations regarding external parameters of the rendering process
and the volumetric density field itself. We demonstrate its use for automatic
viewpoint selection using differentiable entropy as objective, and for
optimizing a transfer function from rendered images of a given volume.
Optimization of per-voxel densities is addressed in two different ways: First,
we mimic inverse tomography and optimize a 3D density field from images using
an absorption model. This simplification enables comparisons with algebraic
reconstruction techniques and state-of-the-art differentiable path tracers.
Second, we introduce a novel approach for tomographic reconstruction from
images using an emission-absorption model with post-shading via an arbitrary
transfer function.
