On the connectedness of planar self-affine sets

On the Connectedness of Self-affine Tiles

Let T be a self-affine tile in 2n defined by an integral expanding matrix A and a digit set D. The paper gives a necessary and sufficient condition for the connectedness of T. The condition can be checked algebraically via the characteristic polynomial of A. Through the use of this, it is shown that in 2#, for any integral expanding matrix A, there exists a digit set D such that the correspondi...

Affine Matching of Planar Sets

To recognize an object in an image, we must determine the best-fit transformation which maps an object model into the image data. In this paper, we propose a new alignment approach to recovering those parameters, based on centroid alignment of corresponding feature groups built in the model and data. To derive such groups of features, we exploit a clustering technique that minimizes intraclass ...

Overlapping Self-affine Sets

We study families of possibly overlapping self-affine sets. Our main example is a family that can be considered the self-affine version of Bernoulli convolutions and was studied, in the non-overlapping case, by F. Przytycki and M. Urbański [23]. We extend their results to the overlapping region and also consider some extensions and generalizations.

Zeros of {-1, 0, 1} Power Series and Connectedness Loci for Self-Affine Sets

On affine registration of planar point sets using complex numbers

1077-3142/$ see front matter Published by Elsevier doi:10.1016/j.cviu.2010.07.007 ⇑ Corresponding author. E-mail addresses: [email protected] (J. Ho), mhyang We propose a novel algorithm for affine registration of 2D point sets. The main idea is to treat the 2D points as complex numbers and from each point set, a polynomial with complex coefficients can be computed whose roots are the points in ...