1983 - Surface Constraints From Linear Extents

This pa.per demonstrates how image features of linear extent (lengths and spacings) image-independent constraints on un erlying surface cf encrate nearly orientations. General constraints are derived from the shape-from-texture paradigm; then. certain special cases are shown to be especially useful. Under orthography, the assumption that two extents are equal is shown to be identical to the assumption that an ima angle (i.e. orthogra hit e extent is a s e angle is a right skewed symmetry . are assumed equa 1 nder and para Ii erspective, orm of slope or if image extents into slope. In the * eneral cl, extent again de enerates constraints are usua y fi perspective case, t i! e shape complex fourth-order equationas, but they often simplify--even to graphic constructions m the image space itself. assumed e If image est ents are colinear and order, wit ual, the constraint equations reduce to second ‘fi several graphic analogs. If extents are adjacent as well, the e uations are first order and the derived construction 4 the “‘acli-knife particularly straightforward an d method”) is general. This method works not only on measures of extent per texel, but also on reciprocal measures: texels per extent. Several examples and discussion indicate that the methods are robust, derivin search, where ot B surface informat ion cheaply, without er methods must fail.*