Using Local Planar Geometric Invariants to Match and Model Images of Line Segments

Image matching consists of finding features in different images that represent the same feature of the observed scene. It is a basic process in vision whenever several images are used. This paper describes a matching algorithm for lines segments in two images. The key idea of the algorithm is to assume that the apparent motion between the two images can be approximated by a planar geometric transformation (a similarity or an affine transformation) and to compute such an approximation. Under such an assumption, local planar invariants related the kind of transformation used as approximation, should have the same value in both images. Such invariants are computed for simple segment configurations in both images and matched according to their values. A global constraint is added to ensure a global coherency between all the possible matches: all the local matches must define approximately the same geometric transformation between the two images. These first matches are verified and completed using a better and more global approximation of the apparent motion by a planar homography and an estimate of the epipolar geometry. If more than two images are considered, they are initially matched pairwise; then global matches are deduced in a second step. Finally, from a set of images representing different aspects of an object, it is possible to compare them and to compute a model of each aspect using the matching algorithm. This work uses in a new way many elements already known in vision; some of the local planar invariants used here were presented as quasi-invariants by Binford and studied by Ben-Arie in his work on thepeaking effect. The algorithm itself uses other ideas coming from the geometric hashing and the Hough algorithms. Its main limitations come from the invariants used. They are really stable when they are computed for a planar object or for many man-made objects which contain many coplanar facets and elements. On the other hand, the algorithm will probably fail when used with images of very general polyhedrons. Its main advantages are that it still works even if the images are noisy and the polyhedral approximation of the contours is not exact, if the apparent motion between the images is not infinitesimal, if they are several different motions in the scene, and if the camera is uncalibrated and its motion unknown. The basic matching algorithm is presented in Section 2, the verification and completion stages in Section 3, the matching of several images is studied in Section 4 and the algorithm to model the different aspects of an object is presented in Section 5. Results obtained with the different algorithms are shown in the corresponding sections.