Abstract: Images contain much more information than seen at first glance. Whether they are apparent to the naked eyes or not, they encode the intrinsic structures,
i.e., the inherent variabilities, of the physical world. These latent structures, if extracted properly, provide rich information that leads to novel approaches to long-standing problems and enables new applications of visual processing. In this talk, I will demonstrate this in two different domains: 3D geometry and appearance. I will first discuss the modeling and use of geometric scale-variability, the size variation of local geometric structures comprising objects and scenes. I will show that, by exploiting this hidden dimension of 3D geometric data, novel applications such as reconstructing objects from a mixed pile of range images can be made possible. Next, I will discuss exploiting the variability of reflectance underlying real-world appearance by introducing a novel reflectance model that enables compact yet faithful characterizations of real-world materials and the space they span. I will show that this enables a sound probabilistic approach to radiometric scene decomposition, e.g., joint estimation of illumination and reflectance from an image, that remains challenging for arbitrary real-world objects and scenes.