Learning object representations from greyscale images
This thesis develops algorithms for learning the surface geometry and albedo of an object from image sets taken under varying lighting conditions and from different viewpoints. In principle, recovery of this information allows all sources of image variation--pose, lighting, viewpoint, albedo, geometric deformations, articulations--to be modeled independently and explicitly. The algorithms described rely on the assumption that the lambertian reflectance model is adequate for these surfaces. To support this claim, the dimensionality of the space of appearance changes due to lighting variations is empirically investigated. It is concluded that a low-dimensional lighting model is sufficient even for surfaces with sharp specularities or cast shadows, as these can be treated as outliers. It is then shown that surface normals can be recovered up to an undetermined $3\times 3$ transformation by performing singular value decomposition on the image set. Several methods are explored for determining this matrix, including use of a prototype model, and use of the integrability constraint. This allows surface geometry, albedo, and light-source direction to be determined. Finally, an algorithm is developed for recovery of shape and albedo from a set of images taken from different viewpoints. This algorithm uses both shading information and geometric disparity to determine shape. Key use is made of a prototype shape model to give an initial estimate of the correspondence of points in the several images. This algorithm is demonstrated on synthetic images.