Reconstruction-based recognition of scenes with translationally repeated quadrics

This paper addresses the problem of invariant-based recognition of quadric configurations from a single image. These configurations consist of a pair of rigidly connected translationally repeated quadric surfaces. This proble m is approached via a reconstruction framework. A new mathematical framewor k, using relative affine structure, on the lines of Luong and Vieville [12] , has been proposed. Using this mathematical framework, translationally rep eated objects have been projectively reconstructed, from a single image, wi th four image point correspondences of the distinguished points on the obje ct and its translate. This has been used to obtain a reconstruction of a pa ir of translationally repeated quadrics. We have proposed joint projective invariants of a pair of proper quadrics. For the purpose of recognition of quadric configurations, we compute these invariants for the pair of reconst ructed quadrics. Experimental results on synthetic and real images, establi sh the discriminately power and stability of the proposed invariant-based r ecognition strategy. As a specific example, we have applied this technique for discriminating images of monuments which are characterized by translati onally repeated domes modeled as quadrics.