Summary
Creating marbled paper art involves layering paint in ways that change the appearance of previous layers. The authors study a digital version of this process and develop a method to work backward from a final marbled image to figure out the exact painting steps that created it. They use a mathematical way to reverse the paint spreading and keep track of the painting actions efficiently with special programming techniques. Their method can reproduce marbling images accurately and allows editing of the painting actions, though some image changes based on content are not always reversible. This work offers a way to digitally capture and edit the creative process behind marbling art.
digital marblingpaint depositioninverse problemarea-preserving transportadjoint methodPyTorchimage reconstructiongesture programcapsule primitiveprogram replay
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.