Algorithm 1.

Incompressible Deformation Estimation Algorithm (IDEA)

1:	Initialize ρ0, M. Set yk(0) = yk, w(yk, 0) = 0, and w(xn, 0) = 0 for all k and n.
2:	for m = 0 to M − 1 do
3:	Set sm = mδ, ρm = ρ0(M − m− 1)/(M − 1);
4:	Down sample the data points x(tm) if needed;
5:	Compute rn(sm) using Eqn. (21) for all sample points;
6:	Solve Eqn. (11) to compute the interpolating coefficients with samples {xn(sm), en, rn(sm)} and ρ = ρm;
7:	Compute the velocities v(yk(sm), sm) and v(xn(sm), sm) using Eqn. (16);
8:	Set w(xn, sm+1) = w(xn, sm) + δv(xn(sm), sm), w(yk, sm+1) = w(yk, sm) + δv(yk(sm), sm), xn(sm+1) = xn(sm)+w(xn, sm+1), and yk(sm+1) = yk(sm) + w(yk, sm+1);
9:	end for
10:	Set u(xn) = w(xn, sM) and u(yk) = w(yk, sM).