๐ค AI Summary
ๆฌๆ้่ฟไผๅ่ถๅๆๅ
ฅ็จๅบๅนถไฝฟ็จ้ๆพไผด้ๆนๆณ๏ผ่งฃๅณไบไป็ฎๆ ๅพๅๆขๅคๆฐๅญๅคง็็ณ็บน็็ๆ็จๅบ็้ฎ้ขใ
๐ Abstract
Pigment deposition in paper marbling displaces the pattern already present, coupling the appearance of each gesture to later actions. We recover executable programs for a deposition-based digital marbling model: given a target image, we optimise an ordered program of capsule insertions whose replay approximates it. The capsule primitive continuously joins circular drops to elongated deposits. Its transport is exactly area-preserving and has a closed-form inverse on the exterior of the deposited region. A replay adjoint reconstructs intermediate states, retaining coordinates lost inside deposits and periodic position checkpoints. At 2000 gestures and 1024^2 pixels, the PyTorch replay implementation uses 8.7x less memory than the tested checkpointed-autograd configuration at comparable step time; the fused implementation fits a program in about four minutes on one workstation GPU. We evaluate image reconstruction on five marbled sheets, compare against transport-disabled fitting, one-pass geometric compensation and a published stroke-based fitter at matched stroke count, and measure sensitivity to an alternative ordered-drop transport. Recovered programs replay across a 4x range of linear resolution. Edits specified in program order or in palette space -- inserting a gesture, recolouring a stage, translating a stage -- replay correctly under the same model; edits specified by image content, such as moving a motif, do not. On synthetic targets with known generating programs, the recovered programs match the images but not the generating gestures under a positional matching statistic. The output is an editable program in the specified digital medium.