Topological interpolation in SOM by affine transformations

Som with Topological Interpolation for the Prediction of Interference Spectra

Adaptive Transformation of Cartographic Bases by Means of Multiresolution Spline Interpolation

GIS databases often need to include maps from diverse sources. These can differ one another by many characteristics: different projections or reference systems, (slightly) different scales, etc. Theoretical and/or empirical transformations are available in literature to obtain maps in a unique system with a fixed tolerance. These transformations are nevertheless insufficient to completely remov...

Quasiconformal distortion of projective transformations and discrete conformal maps

We consider the quasiconformal dilatation of projective transformations of the real projective plane. For non-affine transformations, the contour lines of dilatation form a hyperbolic pencil of circles, and these are the only circles that are mapped to circles. We apply this result to analyze the dilatation of the circumcircle preserving piecewise projective interpolation between discretely con...

Affine congruence by dissection of intervals

Tarski’s circle squaring problem (see [8]) has motivated the following question: Can a circular disc be dissected into finitely many topological discs such that images of these pieces under suitable Euclidean motions form a dissection of a square? Dubins, Hirsch, and Karush give a negative answer in [1]. However, one can get positive results if the group of Euclidean motions is replaced by suit...

Piecewise affine registration of biological images for volume reconstruction

This manuscript tackles the reconstruction of 3-D volumes via mono-modal registration of series of 2-D biological images (histological sections, autoradiographs, cryosections, etc.). The process of acquiring these images typically induces composite transformations that we model as a number of rigid or affine local transformations embedded in an elastic one. We propose a registration approach cl...