Single View Modeling of Free-Form Scenes

1. Introduction Problem Formulation User Constraints Objective: reconstruct a depth map from a single image, without restrictions on surface shape and reflectance User-specified constraints: normals, creases, discontinuities (b) (c) (a) Constrained Optimization A single image Humans are good at perceiving shape from a single view, but general-purpose automatic methods solutions do not presently exist. Textured 3D Model (d) (e) (f) • position and surface normal constraints • depth discontinuity constraint • crease constraint • planar region constraint • fairing curve minimizing curvature • fairing curve minimizing torsion Given a single image and user-specified constraints, the smoothest surface is computed subject to the constraints. The smoothness is only maximized in places where discontinuities and creases are not specified. Our approach leverages the human visual system to provide cues that are sufficient to obtain rich shape models semi-automatically. Single View Modeling of Free-Form Scenes Li Zhang† Guillaume Dugas-Phocion‡ Jean-Sebastien Samson‡ Steven M. Seitz† †University of Washington ‡Ecole Polytechique Seattle, WA 98195 91128 Palaiseau Cedex, France http://grail.cs.washington.edu/projects/svm Human Perception Linearly Constrained Quadratic Optimization The surface is represented as a depth map z = [zi,j]. • Constraints are expressed as a set of linear equations, Az = b; • Smoothness objective function is expressed as a quadratic form, Q(z) = zTQz. The surface z* is computed as z*=argmin{zTQz | Az = b} • Human are good at specifying surface orientation, but less good at specifying pixel depth, [Koenderink 1999]. • Humans are good at specifying depth discontinuities and surface creases. This problem is solved iteratively and quickly using a novel hierarchical transformation technique that models discontinuities.