Extending maps from dense subspaces .

Dense Depth Maps from Epipolar Images

Recovering three-dimensional information from two-dimensional images is the fundamental goal of stereo techniques. The problem of recovering depth (three-dimensional information) from a set of images is essentially the correspondence problem: Given a point in one image, find the corresponding point in each of the other images. Finding potential correspondences usually involves matching some ima...

Extending Functions in the Model Subspaces of H^2(R) to C

Extending Rational Maps

We investigate when a rational endomorphism of the Riemann sphere C extends to a mapping of the upper half-space H3 which is rational with respect to some measurable conformal structure. Such an extension has the property that it and all its iterates have uniformly bounded distortion. Such maps are called uniformly quasiregular. We show that, in the space of rational mappings of degree d, such ...

Extending Generalized Whitney Maps

For metrizable continua, there exists the well-known notion of a Whitney map. If X is a nonempty, compact, and metric space, then any Whitney map for any closed subset of 2X can be extended to a Whitney map for 2X [3, 16.10 Theorem]. The main purpose of this paper is to prove some generalizations of this theorem.

Real Linear Maps Preserving Some Complex Subspaces

We find configurations of subspaces of a complex vector space such that any real linear map with sufficiently high rank that maps the subspaces into complex subspaces of the same dimension must be complex linear or antilinear.