Fig. 2.

Arc-weighted graph construction for the incorporation of the shape prior penalty on surface S_i between neighboring columns p and q. The intra-column arcs are shown in orange with +∞ weight. The hard shape constraint $\mid {\mathrm{\Delta }}_{pq}^i-{\overline{\mathrm{\Delta }}}_{pq}^i\mid \le L_{pq}^i$ is enforced by green arcs. Here we suppose ${\overline{\mathrm{\Delta }}}_{pq}^i=0$ and $L_{pq}^i=2$. The shape prior penalty is incorporated by arcs with dashed lines (brown, purple, yellow, and gray). Here we assume ${\overline{\mathrm{\Delta }}}_{pq}^i=0$, [f_s(0)]′ = 0 and f_s(0) = 0. Target surface S_i cuts arcs with weight [f_s(1)]″ (brown) and [f_s(0⁺)]″ = f_s(1) − f_s(0) (yellow). The total weight is equal to f_s(2).