Reconstructing Geometry from Its Latent Structures

Reconstructing Geometry from Its Latent Structures Geoffrey Oxholm Ko Nishino, Ph.D. Our world is full of objects with complex shapes and structures. Through extensive experience, humans quickly develop an intuition about how objects are shaped, and what their material properties are simply by analyzing their appearance. We engage this intuitive understanding of geometry in nearly everything we do. It is not surprising then, that a careful treatment of geometry stands to give machines a powerful advantage in the many tasks of visual perception. To that end, this thesis focuses on geometry recovery in a wide range of real-world problems. First, we describe a new approach to image registration. We observe that the structure of the imaged subject becomes embedded in the image intensities. By minimizing the change in shape of these intensity structures we ensure a physically realizable deformation. We then describe a method for reassembling fragmented, thin-shelled objects from range-images of their fragments using only the geometric and photometric structure embedded in the boundary of each fragment. Third, we describe a method for recovering and representing the shape of a geometric texture (such as bark, or sandpaper) by studying the characteristic properties of texture—self similarity and scale variability. Finally, we describe two methods for recovering the 3D geometry and reflectance properties of an object from images taken under natural illumination. We note that the structure of the surrounding environment, modulated by the reflectance, becomes embedded in the appearance of the object giving strong clues about the object’s shape.