Line processes [Marroquin:84a] are binary variables arranged in a two-dimensional array. An active line process () between two neighboring pixels indicates that there is a physical discontinuity between them. Activation is, therefore, based on a measure of the difference in pixel properties but must also take into account the presence of other LPs. The idea is that continuous nonintersecting chains of LPs are preferred to discontinuous and intersecting ones, as it is shown in Figure 6.23.
Figure: The Multiscale Interaction Favors the Formation of Continuous Chains of Line Processes. The figure on the left sketches the multiscale interaction of LPs that, together with the local interaction at the same scale, favors the formation of continuous chains of Line Processes (LP caused by ``noise'' are filtered out at the coarse scales, the LPs caused by real discontinuities remain and act on the finer scales, see Figure 6.24). On the right, we show a favored (top) and a penalized (bottom) configuration. On the left, we see coarsest scale with increasing resolution in two lower outlines of hand.
We propose to combine the surface reconstruction and discontinuity detection phases in time and scale space. To do this, we introduce line processes at different scales, ``connect'' them to neighboring depth processes (henceforth DPs) at the same scale and to neighboring LPs on the finer and coarser scale. The reconstruction assigns equal priority to the two process types.
This scheme not only greatly improves convergence speed (the typical multigrid effect) but also produces a more consistent reconstruction of the piecewise smooth surface at the different scales.