Geometric grouping of repeated elements within images

The objective of this work is the automatic detection and grouping of image d elements which repeat on a plane in a scene (for example tiled floorings) . It is shown that structures that repeat on a scene plane are related by p articular parametrized transformations in perspective images. These image t ransformations provide powerful grouping constraints, and can be used at th e heart of hypothesize and verify grouping algorithms. The parametrized tra nsformations are global across the image plane and may be computed without knowledge of the pose of the plane or camera calibration. Parametrized transformations are given for several classes of repeating ope ration in the world as well as groupers based on these. These groupers are demonstrated on a number of real images, where both the elements and the gr ouping are determined automatically. It is shown that the repeating element can be learnt from the image, and he nce provides an image descriptor. Also, information on the plane pose, such as its vanishing line, can be recovered from the grouping.