This article introduces a novel representation for three-dimensional (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 matching and reconstruction, allowing the acquisition of true 3D affine and Euclidean models from multiple unregistered images, as well as their recognition in photographs taken from arbitrary viewpoints. The proposed approach does not require a separate segmentation stage, and it is applicable to highly cluttered scenes. Modeling and recognition results are presented.