Projective Invariants for Planar Contour Recognition

In this paper, we have proposed a new paradigm for the feature grouping problem, with sp ecial emphasis on the problem of particle tracking. First and foremost , we sugg est a mathematical enco ding of the pr oblem , which takes into account metric cons traints specific to the pr obl em , perceptual pr operties of t he image and physics pr operties of the ph enomena. Second, we prop os a new st ate-ment of th e parti cle tracking problem as a glob al, optimization problem. Endly, in order to solve this com bin atoria l optim ization problem, we devise original neural netw orks, nam ed pulsed neural netw orks. The advantages of these new neural networks are:-They need no coefficient. Accordingly it has a completely black-box behaviour from a user points of view.-Wh en th e network has converged (Vi, ~ = 0), all constraints are necessarily satisfied. The it er ations number necessary to converge is mu ch smaller than mo st of ot her methods. References 1. R.J. Adrian. Particl e-imaging techniques for experimental fluid mechanics. Abstract. Implementation results for projective invariant descriptions of planar curves are presented. The paper outlines methods for the generation of projectively invariant representations of curve segments between bitangent points as well as-and this for the first time-segments between inflections. Their usefulness for recognition is illustrated. The semi-local nature of the invariant descriptions allows recognition of objects irrespective of overlap and other image degradations. 1 Projective, semi-differential invariants For recognition of plane contours from arbitrary perspective views, projectively invariant descriptions can be used. Trying to minimize the efforts of calculating robust estimates for derivatives (as with differential invariants [5]) and reducing the dependence on finding points for a basis [6], semi-differential invariant descriptions were proposed [1, 3, 4]. These invariants need fewer points than required for a basis and lower ord er derivatives than needed for the differential invariants. The use of these semi-differential invariants for the recognition of planar, overlapping objects is demonstrated. In the sequel, contour point coordinates (z, y)T will be written x. Subscripts are used to denote fixed reference points, whereas superscripts will be used for the specification of the order of differentiation in the case of derivatives. Vertical bars indicate determinants. Two new semi-local schemes for the generation of projectively invariant curve descriptions are discussed, one for segments between bitangent point pairs, …