Image labeling and grouping by minimizing linear functionals over cones

We consider energy minimization problems related to image labeling, partitioning, and grouping, which typically show up at mid-level stages of computer vision systems. A common feature of these problems is their intrinsic combinatorial complexity from an optimization pointof-view. Rather than trying to compute the global minimum - a goal we consider as elusive in these cases - we wish to design optimization approaches which exhibit two relevant properties: First, in each application a solution with guaranteed degree of suboptimality can be computed. Secondly, the computations are based on clearly defined algorithms which do not comprise any (hidden) tuning parameters. In this paper, we focus on the second property and introduce a novel and general optimization technique to the field of computer vision which amounts to compute a sub optimal solution by just solving a convex optimization problem. As representative examples, we consider two binary quadratic energy functionals related to image labeling and perceptual grouping. Both problems can be considered as instances of a general quadratic functional in binary variables, which is embedded into a higher-dimensional space such that sub optimal solutions can be computed as minima of linear functionals over cones in that space (semidefinite programs). Extensive numerical results reveal that, on the average, sub optimal solutions can be computed which yield a gap below 5% with respect to the global optimum in case where this is known

Object-Centered Surface Reconstruction: Combining Multi-Image Stereo and Shading

Our goal is to reconstruct both the shape and reflectance properties of surfaces from multiple images. We argue that an object-centered representation is most appropriate for this purpose because it naturally accommodates multiple sources of data, multiple images (including motion sequences of a rigid object), and self-occlusions. We then present a specific objectcentered reconstruction method and its implementation. The method begins with an initial estimate of surface shape provided, for example, by triangulating the result of conventional stereo. The surface shape and reflectance properties are then iteratively adjusted to minimize an objective function that combines information from multiple input images. The objective function is a weighted sum of stereo, shading, and smoothness components, where the weight varies over the surface. For example, the stereo component is weighted more strongly where the surface projects onto highly textured areas in the images, and less strongly othe..

Modeling the Digital Earth in VRML

This paper describes the representation and navigation of large, multi-resolution, georeferenced datasets in VRML97. This requires resolving nontrivial issues such as how to represent deep level of detail hierarchies efficiently in VRML, how to model terrain using geographic coordinate systems instead of only VRML's Cartesian representation, how to model georeferenced coordinates to sub-meter accuracy with only single-precision floating point support, how to enable the integration of multiple terrain datasets for a region, as well as cultural features such as buildings and roads, how to navigate efficiently around a large, global terrain dataset, and finally, how to encode metadata describing the terrain. We present solutions to all of these problems. Consequently, we are able to visualize geographic data in the order of terabytes or more, from the globe down to millimeter resolution, and in real-time, using standard VRML97