University of Bern

TI Algorithms for generalized digital images represented by
bintrees 

LT 91-001 

YR 1991 

AU Bieri, Hanspeter 

AU Metz, Igor 

OR BERN 

AV ftp iam.unibe.ch:TechReports1991iam-91-001.ps.Z 

AB Generalized digital images, subsequently called hyperimages,
represent a variation of the conventional digital images which
implies pixels of different dimensions within the same image. 
The extent of a hyperimage is the disjoint union of all pixel
extents it contains, which are relatively open unit cubes with
respect to the euclidean topology of the underlying space.  This
approach is independent of any specific dimension of image and
space, respectively, and allows strict partitioning of images
into subimages, not just subdividing.  Since the storage required
by a $d$-dimensional hyperimage of resolution $n^d$ is $\approx
2^{d}n^{d}$ when using a binary matrix representation, a more
space efficient bintree representation is investigated.
Algorithms for the Boolean operations, the computation of
elementary topological properties and the computation of some
important measures of $d$-dimensional hyperimages (volume,
surface, Euler characteristic) are presented. Because of the
nature of bintrees, the implemeation of these algorithms, too,
can be performed independently of any specific dimension of image
and space.