Nonsingular α-rigid maps

On the Spectrum of Α-rigid Maps

It is shown that there exists an α-rigid transformation with α less or equal to 1 2 whose spectrum has Lebesgue component. This answers the question raised by Klemes and Reinhold in [30]. Moreover, we introduce a new criterium to identify a large class of α-rigid transformations with singular spectrum.

Nonsingular Bilinear Maps, Spaces of Matrices, Immersions and Embeddings

In every differential topology textbook one finds Whitney’s immersion and embedding theorems. But, the real story of immersions started with the results of Hirsch ([15]) and Smale ([30]). We do not intend to follow closely all these developments. Rather, we restrict ourselves mainly to the problem of the existence of immersions of real projective spaces into Euclidean spaces and the problems re...

Nonsingular Curves

The primary goal of this note is to prove that every abstract nonsingular curve can be realized as an open subset of a (unique) nonsingular projective curve. Note that this encapsulates two facts in one: that every nonsingular abstract curve is quasiprojective, and that it can be “compactified” into a projective curve without introducing singularities. We start from the definitions and state th...

α-Limit Points of Graph Maps

Rigid and non-rigid face motion tracking by aligning texture maps and stereo 3D models

Accurate rigid and non-rigid tracking of faces is a challenging task in computer vision. Recently, appearance-based 3D face tracking methods have been proposed. These methods can successfully tackle the image variability and drift problems. However, they may fail to provide accurate out-of-plane face motions since they are not very sensitive to out-of-plane motion variations. In this paper, we ...