We present a novel framework for detection and recognition of deformable objects undergoing geometric deformations. Assuming the geometric deformations belong to some finite dimensional family, it is shown that there exists a set of nonlinear operators that universally maps each of the different manifolds, where each manifold is generated by the set all of possible appearances of a single object, into a unique linear subspace. In this paper we concentrate on the case where the deformations are affine. Thus, all affine deformations of some object are mapped by the above universal manifold embedding into the same linear subspace, while any affine deformation of some other object is mapped by the above universal manifold embedding into a different subspace. It is therefore shown that the highly nonlinear problems of detection and recognition of deformable objects can be formulated in terms of evaluating distances between linear subspaces. The performance of the proposed detection and recognition solutions is evaluated in various settings.