Moment Bounds are Differentiable: Efficiently Approximating Measures in Inverse Rendering

All rendering methods aim at striking a balance between realism and efficiency. This is particularly relevant for differentiable rendering, where the additional aspect of differentiablity w.r.t. scene parameters causes increased computational complexity while, on the other hand, in the common application of inverse rendering, the diverse effects of real image formation must be faithfully reproduced. An important effect in rendering is the attenuation of light as it travels through different media (visibility, shadows, transmittance, transparency). This can be modeled as an integral over non-negative functions and has been successfully approximated in forward rendering by so-called moments. We show that moment-based approximations are differentiable in the parameters defining the moments, and that this leads to efficient and practical methods for inverse rendering. In particular, we demonstrate the method at the examples of shadow mapping and visibility in volume rendering, leading to approximations that are similar in efficiency to existing ad-hoc techniques while being significantly more accurate.