Invariants are properties of geometric configurations that remain unchanged under an appropriate class of transformations. The key objective is to identify and implement numerical quantities which are measurable on images and are invariant under deformations induced by specific projection-related transformations. Successful extraction of these invariants drastically lowers recognition times because the determination of positional information can be completely decoupled from determining object type. Moreover, their use might render calibrations obsolete to some point, depending on whether camera parameters can be absorbed into the transformation already imposed by the group deformations under projection.
Numerical quantities which are measurable on images and are invariant under deformations induced by specific projection related transformations are being identified and implemented. Such invariants are of special interest because they allow efficient matching of spatial structures when comparing images taken from different viewpoints.
For the recognition of planar shapes from single orthographic and perspective views, several invariant based methods for recognition are available and have been compared. Recognition remains possible under a wide range of conditions, due to the complementary scope of the different methods. Some unanticipated theoretical results were obtained as well, such as invariants for articulated objects and scenes with additional constraints or symmetries.
Important progress has been made on the extraction of invariants for nonplanar structures. Not only have invariants been found for single views of 3-dimensional structures such as polyhedra and symmetric objects. Moreover, crucial progress has been made in understanding the information that can be extracted from both orthographic and perspective stereo views.
Quite some emphasis has been put on issues of robustness. Detailed analysis on the accuracy and noise sensitivity of the cross ratio was carried out and methods were developed for improved extraction of contour coordinate derivatives.
With respect to curved surfaces, apart from results on the qualitative distinction between physical versus occluding contours, substantial progress was made in deepening the understanding of surface dual height functions, and aspect graphs and the relevance thereof for vision. As a new tool, a real time interactive geometry viewer for algebraic surfaces was developed.
Psychophysical results have shown that affine structure can to a large extent be retrieved from minimal information (4 points), but that qualitative aspects such as collinearity and parallelism have an important influence. These nonaccidental properties therefore seem good candidates to be included more firmly into the recognition strategies, since their basis is to be found in invariance theory as well.
APPROACH AND METHODS
The emphasis in the project is on cases that go beyond the intuitive type of invariance, like straightness of a line. Therefore, the consortium envisages developing a theoretical framework which encompasses the different aspects of invariants, and which will provide the vision community with tools which make possible a systematic search for, and a thorough investigation of, new classes of invariants. Current emphasis is shifting towards detecting situations that allow the extraction of invariants for non-planar structures, both from simple and multiple views. Secondly, these scientific advances will be incorporated in the development of new and robust practical vision competences.
Moreover in view of the intricate and complex nature of the issues at hand, the consortium intends to tackle the problems on as broad a front as possible. For this reason the partners have made sure that they are in a position to assign interdisciplinary teams, consisting of engineers, phycisists, mathematicians and psychologists, to the different tasks, because they are convinced that an approach which integrates these different sources of expertise stands a better chance of making real progress.
Several longstanding problems in the application of machine vision may well benefit from the results. The expected impact is to broaden the scope of object recognition to the efficient handling of general viewpoints and large databases, to eliminate the need for painstaking calibration procedures if recognition rather than precise Euclidean reconstruction matters and to make motion and stereo correspondence searches faster and more reliable. The potential use lies mainly in assembly, inspection, surveillance, security, agriculture and medical imaging.
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