Introduction. Scene Statistics and 3D Surface Perception. The Theory of Swirling Fields: Segmenting a Scene into Surfaces. Mechanisms for Propagating Surface Information in 3D Reconstruction. 3D Surface Representation Using Ricci Flow. Cue Interpretation and Propagation: Flat versus Nonflat Visual Surfaces. Symmetry, Shape, Surfaces, and Objects. Noncommutative Field Theory in the Primary Visual Cortex. Contour-, Surface-, and Object-Related Coding in the Visual Cortex. From Surfaces to Objects: A Neuroanalytic Approach. 3D and Spatiotemporal Interpolation in Object and Surface Formation. The Perceptual Representation of 3D Shape. References. Index.