We present a new method for the detection and estimation of multiple directional illuminants, using a single image of any object with known geometry and Lambertian reflectance. We use the resulting highly accurate estimates to modify virtually the illumination and geometry of a real scene and produce correctly illuminated Augmented Reality images. Our method obviates the need to modify the imaged scene by inserting calibration objects of any particular geometry, relying instead on partial knowledge of the geometry of the scene. Thus, the recovered multiple illuminants can be used both for image-based rendering and for shape reconstruction. Our method combines information both from the shading of the object and from shadows cast on the scene by the object. Initially, we use a method based on shadows and a method based on shading independently. The shadow-based method utilizes brightness variation inside the shadows cast by the object, whereas the shading-based method utilizes brightness variation on the directly illuminated portions of the object. We demonstrate how the two sources of information complement each other in a number of occasions. We then describe an approach that integrates the two methods, with results superior to those obtained if the two methods are used separately. The resulting illumination information can be used (i) to render synthetic objects in a real photograph with correct illumination effects, and (ii) to virtually relight the scene.