TBR: Transport-Based Rendering with Deposition Strokes for Inverse Graphics

We present a stroke design in which strokes are transport-coupled: each stroke deposits material of its own area and moves every earlier mark without changing its area, so later strokes deform earlier ones. We then solve the inverse problem under this design: given a target image, we optimise an ordered program of such strokes whose replay approximates it, with digital marbling as the motivating medium. The stroke is a capsule that continuously joins circular drops to drawn deposits; its transport is exactly area-preserving, with a closed-form inverse outside the deposit, and a variant with the same inverse differs from line-source potential flow by 8% of the mean displacement. A replay adjoint regenerates intermediate states instead of storing them and uses 8.7x less memory than checkpointed automatic differentiation; a fused implementation fits a 2000-stroke program at 1024x1024 in about four minutes on one GPU. On five marbled sheets the recovered programs are level with a published stroke-based fitter as rasters, replay across a fourfold resolution range, and support edits in program order and palette space that stay valid under transport.