This thesis addresses the problem of visual recognition under two sources of variability: geometric and photometric. The geometric deals with the relation between 3D objects and their views under parallel, perspective, and central projection. The photometric deals with the relation between 3D matte objects and their images under changing illumination conditions. Taken together, an alignment-based method is presented for recognizing objects viewed from arbitrary viewing positions and illuminated by arbitrary settings of light sources. In the first part of the thesis we show that a relative non-metric structure invariant that holds under both parallel and central projection models can be defined relative to four points in space and, moreover, can be uniquely recovered from two views regardless of whether one or the other was created by means of parallel or central projection. As a result, we propose a method that is useful for purposes of recognition (via alignment) and structure from motion, and that has the following properties: (1) the transition between projection models is natural and transparent, (2) camera calibration is not required, and (3) structure is defined relative to the object and does not involve the center of projection.... Object recognition, Correspondence, Motion analysis, Structure from motion, Stereopsis, Projectile geometry.