Optimal Transport Sand Workshop: Sinkhorn Algorithm, Wasserstein Distance and Displacement Interpolation of Sand Piles (3D)

Setting up the workshop...

Presets

Live readouts

Graphs

Sinkhorn convergence: marginal error against iteration (green = tolerance)

Mass projected on the x axis: source, target, transport pile and plain average at time t

Epsilon sweep: transport cost against epsilon, with the extrapolated W2 squared

Numerical checks

running...

How to use

Pick a preset. The big tray shows the sand pile at time t: press play or drag the time slider and the pile flows from the source shape (left mini tray) to the target (right mini tray). Glowing grains travel along the transport map; the cyan lines are the arrows. The middle mini tray is the plain average of the two piles: it fades one pile out and another in instead of moving sand, which is why transport is the better way to morph shapes. Epsilon blurs the plan: small values give sharp maps but need many more Sinkhorn iterations (watch the convergence graph and the console screen). Try Few iterations to see an unfinished plan and Blurry to see a smeared one, then run the epsilon sweep to see the cost approach the true Wasserstein distance as epsilon shrinks. Click a camera button or start the guided tour.

The science