Preprint: Combinatorial homology and image analysis

Preprint: Combinatorial homology and image analysis

[Marco Grandis]

The following preprint is available, at my home page and by ftp:


Combinatorial homology and image analysis
M. Grandis

ABSTRACT. This is the sequel of a paper, cited as Part I ("An intrinsic
homotopy theory for simplicial complexes, with applications to image
analysis"), introducing intrinsic homotopies and homotopy groups for
simplicial complexes. We study here the relations of this intrinsic
homotopy theory with the well-known intrinsic homology theory of simplicial
complexes.
     Also here, the applications are aimed at image analysis. A metric
space  X  has a structure  t_e(X)  of simplicial complex at each resolution
e > 0;  the corresponding *metric combinatorial homology groups*  H_n(
t_e(X)) can be directly computed, in cases of interest for applications,
via the Mayer-Vietoris exact sequence and a study of deformation retracts
given in Part I.


http://www.dima.unige.it/STAFF/GRANDIS/

"ftp://pitagora.dima.unige.it/WWW/FTP/GRANDIS/Cmb2.May99.ps


With best regards

Marco Grandis

Dipartimento di Matematica
Universita' di Genova
via Dodecaneso 35
16146 GENOVA, Italy

e-mail: grandis@dima.unige.it
tel: +39.010.353 6805
fax: +39.010.353 6752