Object 3D reconstruction has always been one of the main objectives of computer vision. After many decades of research, most techniques are still unsuccessful at recovering high resolution surfaces, especially for objects with limited surface texture. Moreover, most shiny materials are particularly hard to reconstruct.

Photometric Stereo (PS), which operates by capturing multiple images under changing illumination has traditionally been one of the most successful techniques at recovering a large amount of surface details, by exploiting the relationship between shading and local shape. However, using PS has been highly impractical because most approaches are only applicable in a very controlled lab setting and limited to objects experiencing diffuse reflection.

Nevertheless, recent advances in differential modelling have made complicated Photometric Stereo models possible and variational optimisations for these kinds of models show remarkable resilience to real world imperfections such as non-Gaussian noise and other outliers. Thus, a highly accurate, photometric-based reconstruction system is now possible.

The contribution of this thesis is threefold. First of all, the Photometric Stereo model is extended in order to be able to deal with arbitrary ambient lighting. This is a step towards acquisition in a non-fully controlled lab setting. Secondly, the need for a priori knowledge of the light source brightness and attenuation characteristics is relaxed as an alternating optimisation procedure is proposed which is able to estimate these parameters. This extension allows for quick acquisition with inexpensive LEDs that exhibit unpredictable illumination characteristics (flickering etc). Finally, a volumetric parameterisation is proposed which allows one to tackle the multi-view Photometric Stereo problem in a similar manner, in a simple unified differential model. This final extension allows for complete object reconstruction merging information from multiple images taken from multiple viewpoints and variable illumination.

The theoretical work in this thesis is experimentally evaluated in a number of challenging real world experiments, with data captured by custom-made hardware. In addition, the applicability of the generality of the proposed models is demonstrated by presenting a differential model for the shape of polarisation problem, which leads to a unified optimisation problem, fusing information from both methods. This allows for the acquisition of geometrical information about objects such as semi-transparent glass, hitherto hard to deal with.