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 problem is approached via a reconstruction framework. A new mathematical framework, using relative affine structure, on the lines of Luong and Vieville, has been proposed. Using this mathematical framework, translationally repeated objects have been projectively reconstructed, from a single image, with four image point correspondences of the distinguished points on the object and its translate. This has been used to obtain a reconstruction of a pair 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 reconstructed quadrics. Experimental results on synthetic and real images, establish the discriminatory power and stability of the proposed invariant-based recognition strategy. As a specific example, we have applied this technique for discriminating images of monuments which are characterized by translationally repeated domes modeled as quadrics.