This chapter proposes a representation of rigid threedimensional (3D) objects in terms of local affine-invariant descriptors of their images and the spatial relationships between the corresponding surface patches. Geometric constraints associated with different views of the same patches under affine projection are combined with a normalized representation of their appearance to guide the matching process involved in object modeling and recognition tasks. The proposed approach is applied in two domains: (1) Photographs — models of rigid objects are constructed from small sets of images and recognized in highly cluttered shots taken from arbitrary viewpoints. (2) Video — dynamic scenes containing multiple moving objects are segmented into rigid components, and the resulting 3D models are directly matched to each other, giving a novel approach to video indexing and retrieval.