This paper presents a new approach to computing dense depth and motion estimates from multiple images. Rather than computing a single depth or motion map from such a collection, we associate motion or depth estimates with each image in the collection (or at least some subset of the images). This has the advantage that the depth or motion of regions occluded in one image will still be represente...

The paper is concerned with the multivariate global optimization with box constraints. A new underestimator is investigated for twice continuously differentiable function on a box which is an extension of the approach developed in [5] for univariate global optimization. AMS Subject Classification: 65K05, 90C30, 90C34

Piecewise linear convex and concave support functions combined with Pijavskii’s method are proposed to be used for solving global optimization problems. Rules for constructing support functions are introduced.

Optimization methods for a given class are easily modified to utilize additional information and work faster on a more·restricted class. In particular algorithms that use only the Lipschitz constant (e.g. Mladineo, Piyavskii, Shubert and Wood) can be modified to use second derivative bounds or gradient calculations. The algorithm of Breiman & Cutler can be modified to use Lipschitz bounds. Test...