A system and method for recognizing instances of classes in a 2D image using 3D class models and for recognizing instances of objects in a 2D image using 3D class models. The invention provides a system and method for constructing a database of 3D class models comprising a collection of class parts, where each class part includes part appearance and part geometry. The invention also provides a system and method for matching portions of a 2D image to a 3D class model. The method comprises identifying image features in the 2D image; computing an aligning transformation between the class model and the image; and comparing, under the aligning transformation, class parts of the class model with the image features. The comparison uses both the part appearance and the part geometry.