Warped-Area Reparameterization of Differential Path Integrals

Supplemental Materials

In this supplemental material, we show animated versions of a few inverse-rendering optimizations.

• In the following, we show the settings used for each inverse-rendering result.
• All warped-area algorithms use 8 auxiliary samples (per primary sample).

Scene	# Param.	# Iter.
Star emitter	3	300
Cornell-box bunny	3	200
Cornell-box caustics	12	400
Dodoco	20,000	1,200
King	20,000	1,000
Bunny in glass	20,000	1,700
Lamp	20,000	900

• This example contains a Lucy model illuminated by a complicated, star-shaped emitter.
• We search for translation along the y- and z-axis and the rotation angle of the emitter (about its normal at the center) by looking at the Lucy and the shadow.
• All comparisons are equal-sample, with spp=64.

• This scene involves a diffuse bunny lit by an area light within the Cornell box. Additionally, the light source points toward the ceiling, causing the scene to be dominated by indirect illumination.
• We search for the rotation angles about the x- and y-axis as well as translation distance along the x-axis by looking at the shadow.
• To ensure fairness, we use equal-time to compare Ours (Bidir., spp=8) and Ours (Unidir., spp=25), and equal-sample to compare Ours (Unidir.) and Bangaru et al.'s [2020] method.

• This example involves a translucent bunny inside a Cornell box lit by an area light.
• We use a control cage with 16 vertices to deform the bunny in a non-rigid fashion, and search for the positions of 4 cage vertices by looking at the caustics pattern on the floor.
• Comparison between Ours (Bidir., spp=128) and Ours (Unidir., spp=290) are equal-time.

• This example involves a dodoco inside a Cornell box lit by an area light. Additionally, the light source points toward the ceiling, causing the scene to be dominated by indirect illumination.
• We optimize for the shape of this object. The mesh error plotted below is used only for evaluation (and not for optimization). We use multiple stages of optimization with different spp and learning rates.
• To ensure fairness, we use equal-time to compare Ours (Bidir.) and Ours (Unidir.), and equal-sample to compare Ours (Unidir.) and Bangaru et al.'s [2020] method.

• This example involves a king lit by an area light.
• We optimize for the shape of this object. The mesh error plotted below is used only for evaluation (and not for optimization). We use multiple stages of optimization with different spp and learning rates.
• We use equal-sample to compare Ours (Unidir., new) , Ours (Unidir., old) and Bangaru et al.'s [2020] method.

• This example involves a bunny inside a glass cube.
• We optimize for the shape of this object. The mesh error plotted below is used only for evaluation (and not for optimization). We use multiple stages of optimization with different spp and learning rates.
• We use equal-time to compare Ours (Bidir.), PSDR (AQ guiding) and PSDR (Grid guiding).

• This example involves a monkey lit by a lamp, with area light insight a light bulb.
• We optimize for the shape of this object. The mesh error plotted below is used only for evaluation (and not for optimization). We use multiple stages of optimization with different spp and learning rates.
• We use equal-time to compare Ours (Bidir.) and PSDR (AQ guiding).