Parametric scene reduction algorithm from geometric relations

Straight lines, rectangles and other simple geometric features are common in man-made environments. Moreover, these geometric features often share particular relationships, for instance parallelism or orthogonality. Such a scene is very constrained, and its 3D description in terms of points is over-determined if the relations are taken into account. Sometimes a constraint solver can maintain the relations, but when estimated positions of the features are unavailable a priori, the knowledge from geometric relations is left unexploited. A better approach would consist in finding a parametric representation that directly merges the relations within a reduced set of parameters, which enforces the relational constraints once and for all. A problem with this idea is that both features and relationships are heterogeneous, so general methods are difficult to design. We propose here a method based on geometric reduction rules for automatically remodeling a scene into such a representation. The method is general for points, linear and planar elements together and can handle at the same time parallelism, orthogonality, collinearity and coplanarity. The number of reduced parameters is equal to the number of degrees of freedom of the system. The approach has been tested with segments, rectangles and points in various scenes, to evaluate the generality and performance of the method.