@inproceedings{ion-2005,
author={A. Ion, Y.; Haxhimusa, W. Kropatsch, L. Brun},
title={Hierarchical Image partitioning using Combinatorial Maps},
year={2005},
month={February},
address={Zell an der Pram, Austria},
booktitle={CVWW 2005},
theme = {hierarchical},
abstract ="We present a hierarchical partitioning of images
using a pairwise similarity function on a
combinatorial map based representation. We used the
idea of minimal spanning tree to find region
borders quickly and effortlessly in a bottom-up
way, based on local differences in a color
space. The result is a hierarchy of partitions with
multiple resolutions suitable for further goal
driven analysis. The algorithm can handle large
variation and gradient intensity in images. Dual
graph pyramid representations lack the explicit
encoding of edge orientation around vertices i.e
they lack an explicit encoding of the orientation
of planes, existing in combinatorial maps. Moreover
with combinatorial maps, the dual must not be
explicitly represented because one map is enough to
fully characterize the partition.",
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/cvww2005.pdf}
}
@InProceedings{CI-BRUN-2008,
author = {Brun, L. and Pruvot, J.H.},
title = {Hierarchical Matching Using Combinatorial Pyramid Framework},
booktitle = {ICISP 2008},
pages = {346-355} ,
year = 2008,
volume = 5099,
address = {Cherbourg},
theme = {hierarchical},
}
@INPROCEEDINGS{barchadier-04,
AUTHOR = {Marchadier, Jocelyn and {B}run, Luc and {{K}ropatsch}, Walter G.},
TITLE = {Rooted kernels and Labeled Combinatorial Pyramids},
BOOKTITLE = {Computer Vision - CVWW'04, Proceedings of the Computer Vision Winter Workshop},
EDITOR = {{Leonardis}, Ale{v s} and {Solina}, Franc (eds.)},
PUBLISHER = {IEEE Slovenia Section},
ADDRESS = {Ljubljana},
YEAR = {2004},
theme = {hierarchical}
abstract = "An irregular pyramid consists of a stack of
successively reduced graphs. Each smaller graph is deduced
from the preceding one using contraction or removal kernels. A
contraction (resp. removal) kernel defines a forest of the
initial (resp. dual ) graph, each tree of this forest being
reduced to a single vertex (resp. dual vertex) in the reduced
graph. A combinatorial map encodes a planar graph thanks to
two permutations encoding the edges and their orientation
around the vertices. We present in this article a new
definition of contraction and removal kernels which allows to
encode the different values attached to a given vertex, dual
vertex or edge along the pyramid.",
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/cvww2004.pdf},
}
@InProceedings{CI-Pruvot-2007,
author = {Pruvot, Jean Hugues and Luc Brun},
title = {Scale Set representation for image segmentation},
booktitle = {Graph based Representation in Pattern Recognition'2007},
pages = {126-137},
year = 2007,
editor = {Francisco Escolano and Mario Vento},
number = 4538,
address = {Alicante},
month = {June},
organization = {IAPR TC15},
publisher = {LNCS},
abstract= "Segmentation algorithms based on an energy minimisation framework
often depend on a scale parameter which balances a fit to data and a
regularising term. Irregular pyramids are defined as a stack of
graphs successively reduced. Within this framework, the scale is
often defined implicitly as the height in the pyramid. However,
each level of an irregular pyramid can not usually be readily
associated to the global optimum of an energy or a global criterion
on the base level graph. This last drawback is addressed by the
scale set framework designed by Guigues. The methods designed by
this author allow to build a hierarchy and to design cuts within
this hierarchy which globally minimise an energy. This paper
studies the influence of the construction scheme of the initial
hierarchy on the resulting optimal cuts. We propose one sequential
and one parallel method with two variations within both. Our
sequential methods provide partitions near the global optima while
parallel methods require less execution times than the sequential
method of Guigues even on sequential machines.",
url="article(ps):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/gbr2007.ps, slides(pdf):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/slides_gbr2007.pdf, video:=http://videolectures.net/gbr07_pruvot_hcs/",
theme = {hierarchical},
}
@InProceedings{CN-Brun-2006,
author = {Luc Brun},
title = {Segmentation, Graphes et structures hi{'e}rarchiques},
booktitle = {ORASIS 2007},
year = 2007
address = {Obernai, France},
month = {June},
theme = {hierarchical},
url = {slide(pdf):=http://wwww.greyc.ensicaen.fr/~luc/ARTICLES/orasis2007.pdf}
}
@article{brun-06-1,
author = {Luc Brun and Walter Kropatsch},
title = {Contains and Inside relationships within combinatorial Pyramids},
journal = {Pattern Recognition},
year = 2006,
volume = 39,
number = 4,
pages = {515-526},
month = {April},
abstract= "Irregular pyramids are made of a stack of successively
reduced graphs embedded in the plane. Such pyramids are used within
the segmentation framework to encode a hierarchy of partitions. The
different graph models used within the irregular pyramid framework
encode different types of relationships between regions. This paper
compares different graph models used within the irregular pyramid
framework according to a set of relationships between regions. We
also define a new algorithm based on a pyramid of combinatorial maps
which allows to determine if one region contains the other using
only local calculus.",
theme = {hierarchical}
}
@InProceedings{brun-05,
author = {Luc Brun and Myriam Mokhtari and Fernand Meyer},
title = {Hierarchical watersheds within the Combinatorial Pyramid framework},
booktitle = {Proc. of DGCI 2005},
year = 2005,
organization = {IAPR-TC18},
publisher = {LNCS},
theme = {hierarchical},
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/dgci2005.ps, slides:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/slides_dgci2005.pdf},
abstract= "Watershed is the latest tool used in mathematical
morphology. The algorithms which implement the
watershed transform generally produce an over
segmentation which includes the right image's
boundaries. Based on this last assumption, the
segmentation problem turns out to be equivalent to
a proper valuation of the saliency of each
contour. Using such a measure, hierarchical
watershed algorithms use the edge's saliency
conjointly with statistical tests to decimate the
initial partition. On the other hand, Irregular
Pyramids encode a stack of successively reduced
partitions. Combinatorial Pyramids consitute the
latest model of this family. Within this framework,
each partition is encoded by a combinatorial map
which encodes all topological relationships between
regions such as multiple boundaries and inclusion
relationships. Moreover, the combinatorial pyramid
framework provides a direct access to the embedding
of the image's boundaries. We present in this paper
a hierarchical watershed algorithm based on
combinatorial pyramids. Our method overcomes the
problems connected to the presence of noise both
within the basins and along the watershed
contours."
}
@InProceedings{brun-05-2,
author = {Luc Brun and Walter Kropatsch},
title = {Inside and Outside within Combinatorial Pyramids},
booktitle = {5th IAPR-TC15 Workshop on Graph-based Representations in Pattern Recognition},
year = 2005,
editor = {Luc Brun and Mario Vento},
series = {Lecture Notes in Computer Science},
address = {Poitiers (France)},
month = {April},
organization = {IAPR-TC15},
publisher = {Springer, Berlin Heidelberg, New York},
theme= {hierarchical},
note = {ISBN: 3-540-25270-3},
url= {springerLink:=http://www.springerlink.com/index/V6UYD78EF8CLHQQ2}
abstract= "Irregular pyramids are made of a stack of
successively reduced graphs embedded in the
plane. Such pyramids are often used within the
segmentation and the connected component analysis
frameworks to detect meaningful objects together
with their spatial and topological
relationships. The graphs reduced in the pyramid
may be region adjacency graphs, dual graphs or
combinatorial maps. Using any of these graphs each
vertex of a reduced graph encodes a region of the
image. Using simple graphs one edge between two
vertices encodes the existence of a common boundary
between two regions. Using dual graphs and
combinatorial maps, each connected boundary segment
between two regions is associated to one
edge. Moreover, special edges called loops may be
used to differentiate a special type of adjacency
where one region surrounds the other. We show in
this article that the loop information does not
allow to distinguish inside and outside of the loop
by local computations. We provide a method based on
the combinatorial pyramid framework which uses the
orientation explicitly encoded by combinatorial
maps to determine inside and outside with local
calculus."
}
@InProceedings{brun-04,
author = {Luc Brun and Philippe Vautrot and Fernand Meyer},
title = {Hierarchical Watersheds with Inter-pixel Boundaries},
booktitle = { Image Analysis and Recognition: International Conference ICIAR 2004, Part I},
year = 2004,
pages= {840-847},
address = {Proto (Portugal)},
publisher = {Springer Verlag Heidelberg (LNCS)},
theme = {hierarchical},
abstract = "Watersheds are the latest segmentation tool developed in
mathematical morphology. These algorithms produce a segmentation of
an image into a set of basins separated by watershed pixels. The
over segmentation produced by these algorithms is reduced by
removing all contours with a low saliency. This contour's saliency
is generally defined from the minimal height of the watershed pixels
along the contour. However, such a definition does not allow to
define a contour's saliency in case of thick watersheds. Moreover,
the set of basins which corresponds to the intuitive notion of
regions does not define an image partition. In this paper we propose
a method which allows to aggregate the watershed pixels to the
basins while preserving the notion of contour and the associated
saliency. The model used to encode the image partition is then
decimated according to the contour saliency to obtain a hierarchy of
partitions.",
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/iciar2004.ps}
}
@Article{brun-02-6,
author = {Luc Brun and Walter Kropatsch},
title = {Receptive Fields within the Combinatorial Pyramid Framework},
journal = {Graphical Models},
year = 2003,
pages= {23-42},
volume= 65,
abstract = "A hierarchical structure is a stack of successively
reduced image representations. Each basic element of a hierarchical
structure is the father of a set of elements in the level below. The
transitive closure of this father-child relationship associates to
each element of the hierarchy a set of basic elements in the base
level image representation. Such a set, called a receptive field,
defines the embedding of one element on the original
image. Combinatorial pyramids are defined as a stack of successively
reduced combinatorial maps, each combinatorial map being defined by
two permutations acting on a set of half edges named darts. The
basic element of a combinatorial pyramid is thus the dart. This
paper defines the receptive field of each dart within a
combinatorial pyramid and study the main properties of these sets.",
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/recep_field.pdf},
theme = {hierarchical}
}
@Article{brun-02-7,
author = {Luc {B}run and Walter {K}ropatsch},
title = {Contraction Kernels and Combinatorial Maps},
journal = {Pattern Recognition Letters},
volume = {24},
number = 8,
pages= {1051-1057},
year = 2003,
month = {April},
abstract= "Graph pyramids are made of a stack of successively
reduced graphs embedded in the plane. Such pyramids overcome the
main limitations of their regular ancestors. The graphs used in the
pyramid may be region adjacency graphs, dual graphs or combinatorial
maps. Compared to usual graph data structures, combinatorial maps
offer an explicit encoding of the orientation of edges around
vertices. Each combinatorial map in the pyramid is generated from
the one below by a set of edges to be contracted. This contraction
process is controlled by kernels that can be combined in many
ways. This paper shows that kernels producing a slow reduction rate
can be combined to speed up reduction. Conversely, kernels decompose
into smaller kernels that generate a more gradual reduction. We also
propose one sequential and one parallel algorithm to compute the
contracted combinatorial maps.",
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/cont_kernel_combi_maps.pdf},
theme = {hierarchical}
}
@InProceedings{brun-03,
author = {Luc Brun and Walter Kropatsch},
title = {Implicit encoding of combinatorial Pyramids},
booktitle = {Proceedings of the Computer Vision Winter Workshop},
pages = {49-54},
year = 2003,
editor = {Ondrej Drbohlav},
address = {Valtice, Czech Reublic},
month = {February},
url = { article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/cvww2003.pdf},
abstract = " An irregular pyramid consists of a stack of
successively reduced graphs. Each smaller graph is deduced from the
preceding one by the contraction or the removal of a set of
edges. Using a fixed decimation ratio we need approximately
O(log(image size)) graphs to encode the whole
pyramid. A combinatorial map encodes a planar graph thanks to two
permutations encoding the edges and their orientation around the
vertices. We present in this article an encoding of a combinatorial
pyramid which allows to fold the whole pyramid in the base level
layer and provides at the same time a measure of the importance of
every pixel. Any reduced combinatorial maps of the pyramid maybe
directly retrieved from this encoding if needed.",
theme = {hierarchical}
}
@InProceedings{brun-03-2,
author = {Luc Brun and Walter Kropatsch},
title = {Construction of Combinatorial Pyramids},
booktitle = {Graph based Representations in Pattern Recognition},
pages = {1-12},
year = 2003,
editor = {Edwin Hancock and Mario Vento},
volume = 2726,
series = {LNCS},
address = {York, UK},
month = {June},
organization = {IAPR-TC15},
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/gbr2003.pdf,slides:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/slides_gbr2003.pdf},
abstract = "Irregular pyramids are made of a stack of successively
reduced graphs embedded in the plane. Each vertex of a reduced graph
corresponds to a connected set of vertices in the level below. One
connected set of vertices reduced into a single vertex at the above
level is called the reduction window of this vertex. In the same
way, a connected set of vertices in the base level graph reduced to
a single vertex at a given level is called the receptive field of
this vertex. The graphs used in the pyramid may be region adjacency
graphs, dual graphs or combinatorial maps. This last type of
pyramids are called Combinatorial Pyramids. Compared to usual graph
data structures, combinatorial maps encode one graph and its dual
within a same formalism and offer an explicit encoding of the
orientation of edges around vertices. This paper describes the
construction scheme of a Combinatorial Pyramid. We also provide a
constructive definition of the notions of reduction windows and
receptive fields within the Combinatorial Pyramid framework.",
theme = {hierarchical}
}
@InProceedings{brun-03-1,
author = {Luc Brun and Walter Kropatsch},
title = {Combinatorial Pyramids},
booktitle = {IEEE International conference on Image Processing (ICIP)},
pages = {33-37},
year = 2003,
editor = {Suvisoft},
volume = {II},
address = {Barcelona},
month = {September},
organization = {IEEE},
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/icip2003.pdf, slides:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/slides_icip2003.pdf},
abstract = "An irregular pyramid consists of a stack of successively
reduced graphs. Each smaller graph is deduced from the preceding one
by the contraction or the removal of a set of edges. Using a fixed
decimation ratio we need approximately O(log(image size)) graphs to
encode the whole pyramid. A combinatorial map encodes a planar graph
thanks to two permutations encoding the edges and their orientation
around the vertices. We present in this article an encoding of a
combinatorial pyramid which allows to fold the whole pyramid in the
base level layer and provides at the same time a measure of the
relevance of every pixel. This encoding is used to retreive any
reduced combinatorial map of the pyramid from its base and to
compute the borders of the partition encoded by the combinatorial
maps.",
theme = {hierarchical}
}
@TechReport{brun-02-4,
author = "Luc {B}run and Walter Kropatsch",
institution ="PRIP, TU Wien",
number = "PRIP-TR-yy",
title = "Labeled Pyramids with Combinatorial Maps",
year = 2002,
theme = {hierarchical},
price = "20,-",
url = {article:=ftp://www.prip.tuwien.ac.at/pub/publications/trs/tr57.ps.gz},
abstract = " Combinatorial Pyramids are defined as a stack of
successively reduced combinatorial maps. The Pyramid
construction plan defined in TR-63~cite{brun-00-1}
allows to describe a pyramid by two functions $level$ and
$state$ defined respectively on the set of darts of the
initial combinatorial map and the set of levels of the
pyramid. These two functions encode respectively the
maximum level on which a dart survives and the type of
each reduction operation. Based on these functions any
combinatorial map of the pyramid may be build from the
base by a one pass algorithm scanning all the darts of
the initial combinatorial map~cite{brun-00-1}. In this
technical report we show that algorithms with a same
sequential and parallel complexity may be designed in
order to build all the reduced combinatorial maps of the
Pyramid."
}
@PhdThesis{brun-02-9,
author = {Luc Brun},
title = {Traitement d'images couleur et pyramides combinatoires},
school = {Universit{'e} de Reims},
year = 2002,
theme = {topologie,hierarchical,couleur,quantification,inversion},
type = {Habilitation {`a} diriger des recherches},
abstract = "We describe in this thesis three key steps of image
processing algorithms. We first study the reflexion models which
describe the image formation process. These models are used to
obtain a segmentation of the image into materials and to reconstruct
the surface of some of the regions previously segmented. The
materials studded for the reconstruction stage are metallic ones.
We also study quantization and inverse colormap operations. These
operations are used to display an image onto low cost
terminals. Such processes may also be applied into the image
compression or image segmentation framework. We finally describe a
new hierarchical model based on a topological representation of an
image partition. The model named Combinatorial Pyramid is the only
hierarchical model currently developed which allows to encode all
the topological information.",
url= {pdf:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/hdr.pdf,ps.gz:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/hdr.ps.gz}
}
@INPROCEEDINGS{brun-02-2,
AUTHOR = {Luc Brun and Walter Kropatsch},
TITLE = {Receptive Fields within the Combinatorial Pyramid Framework},
BOOKTITLE = {Discrete Geometry for Computer Imagery},
PAGES = {92-101},
YEAR = 2002,
EDITOR = {Achille Braquelaire and Lachaud, Jacques-Olivier and Anne Vialard},
VOLUME = 2301,
SERIES = {LNCS},
ADDRESS = {Bordeaux},
theme = {hierarchical},
MONTH = {April},
PUBLISHER = {Springer-Verlag},
NOTE = {ISBN 3-540-43380-5, ISSN 0302-9743},
ABSTRACT = {A hierarchical structure is a stack of successively
reduced image representations. Each basic element of a
hierarchical structure is the father of a set of
elements in the level below. The transitive closure of
this father-child relationship associates to each
element of the hierarchy a set of basic elements in
the base level image representation. Such a set,
called a receptive field, defines the embedding of one
element of the hierarchy on the original image. Using
the father-child relationship, global properties of a
receptive field may be computed in $O(log(m))$
parallel processing steps where $m$ is the diameter of
the receptive field. Combinatorial pyramids are
defined as a stack of successively reduced
combinatorial maps, each combinatorial map being
defined by two permutations acting on a set of half
edges named darts. The basic element of a
combinatorial pyramid is thus the dart. This paper
defines the receptive field of each dart within a
combinatorial pyramid and studies the main properties
of these sets.},
url = {article:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/dgci2002.pdf},
}
@InProceedings{brun-02-3,
author = {Luc Brun and Walter Kropatsch},
title = {Defining regions within the Combinatorial Pyramid framework},
booktitle = {Proceedings of the Computer Vision Winter Workshop},
pages = {198-207},
year = 2002,
theme = {hierarchical},
abstract = "Irregular Pyramids are defined as a stack of
successively reduced graphs. Each vertex of a reduced graph is
associated to a set of vertices in the base level graph named its
receptive field. If the initial graph is deduced from a planar
sampling grid its reduced versions are planar and each receptive
field is a region of the initial grid. Combinatorial Pyramids are
defined as a stack of successively reduced combinatorial
maps. Combinatorial maps are based on half edges named darts and the
receptive field of a dart is a sequence of darts in the base level
combinatorial map. We present in this paper preliminary results
showing how to define regions from the receptive fields of the
darts.",
url = {article(pdf):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/cvww2002.pdf},
editor = {Horst Wildenauer and Walter Kropatsch},
address = {Bad Ausse Austria},
month = {February}
}
@INCOLLECTION{brun-02-1,
AUTHOR = {Luc {B}run and Walter {K}ropatsch},
TITLE = {Introduction to Combinatorial Pyramids},
BOOKTITLE = {Digital and Image Geometry},
PAGES = {108-127},
PUBLISHER = {Springer Verlag},
YEAR = 2001,
EDITOR = {G. Bertrand, A. Imiya, R. Klette},
VOLUME = 2243,
SERIES = {LNCS},
abstract= "A pyramid is a stack of image representations with
decreasing resolution. Many image processing algorithms
run on this hierarchical structure in O(log(n))
parallel processing steps where n is the diameter of
the input image. Graph pyramids are made of a stack of
successively reduced graphs embedded in the plane. Such
pyramids overcome the main limitations of their regular
ancestors. The graphs used in the pyramid may be region
adjacency graphs or dual graphs. This paper reviews the
different hierarchical data structures and introduces a
new representation named combinatorial pyramid.",
url = {slides (ppt):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/dgi.ppt, article (pdf):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/dgi.pdf},
theme = {hierarchical}
}
@InProceedings{brun-01,
author = {Luc {B}run and Walter {K}ropatsch},
title = {Contraction Kernels and Combinatorial Maps},
booktitle = {$3^{rd}$ IAPR-TC15 Workshop on Graph-based Representations in Pattern Recognition},
pages = {12-21},
year = 2001,
editor = {{J}olion, Jean Michel and Walter Kropatsch and Mario Vento},
address = {Ischia Italy},
month = {May},
organization = {IAPR-TC15},
publisher = {CUEN},
theme = {hierarchical},
url = {slides:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/slides_gbr2001_1.ppt},
abstract = "Graph pyramids are made of a stack of successively
reduced graphs embedded in the plane. Such pyramids
overcome the main limitations of their regular
ancestors. The graphs used in the pyramid may be
region adjacency graphs, dual graphs or
combinatorial maps. Compared to the usual graph data
structures, combinatorial maps offer an explicit
encoding of the orientation of edges around
vertices. Each combinatorial map in the pyramid is
generated from the one below by a set of edges to be
contracted. This contraction process is controlled
by kernels that can be combined in many ways. We
show in this paper, that kernels producing a slow
reduction rate can be combined to speed up
reduction. Or, conversely, kernels decompose into
smaller kernels that generate a more gradual
reduction. We also propose one sequential and one
parallel algorithm to compute the contracted
combinatorial maps defined by kernels."
}
@TechReport{brun-00-1,
author = {L. {B}run and Walter {K}ropatsch},
title = {The Construction of Pyramids with Combinatorial Maps},
institution = {Institute of Computer Aided Design},
year = 2000,
number = 63,
url = {article:=ftp://www.prip.tuwien.ac.at/pub/publications/trs/tr63.ps.gz},
address = {Vienna University of Technology, lstr. 3/1832,A-1040 Vienna AUSTRIA},
month = {June},
url = {http://www.prip.tuwien.ac.at/},
abstract = " This paper presents a new formalism for irregular
pyramids based on combinatorial maps. This
technical report continues the work begun with the
TR-54 and TR-57 reports (see ~cite{brun-99-1}
and~cite{brun-99-3}).We provide in this technical
report algorithms allowing efficient parallel or
sequential implementation of combinatorial
pyramids",
theme={hierarchical}
}
@inproceedings{brun-00,
AUTHOR = {L. {B}run and {{K}ropatsch},Walter },
TITLE = {Irregular Pyramids with Combinatorial Maps},
BOOKTITLE = {Advances in Pattern Recognition, Joint IAPR
International Workshops SSPR'2000 and SPR'2000},
EDITOR = {{Amin}, Adnan and
{Ferri}, Francesc J. and
{Pudil}, Pavel and
{I~{n}esta}, Francesc J.},
PUBLISHER = {Springer, Berlin Heidelberg, New York},
SERIES = {Lecture Notes in Computer Science},
VOLUME = {Vol.~1451},
ADDRESS = {Alicante, Spain},
YEAR = {2000},
MONTH = {August},
PAGES = {256-265},
abstract = "This paper presents a new formalism for
irregular pyramids based on combinatorial
maps. Such pyramid consists of a stack of
successively reduced graph. Each smaller graph
is deduced from the preceding one by a set of
edges which have to be contracted or
removed. In order to perform parallel
contractions or removals, the set of edges to
be contracted or removed has to verify some
properties. Such a set of edges is called a
Decimation Parameter. A combinatorial map
encodes a planar graph thanks to two
permutations encoding the edges and their
orientation around the vertices. Combining the
useful properties of both combinatorial maps
and irregular pyramids offers a potential
alternative for representing structures at
multiple levels of abstraction.",
theme={hierarchical}
}
@TechReport{brun-99-1,
author = {Luc {B}run and Walter Kropatsch},
title = {Dual Contractions of Combinatorial Maps},
institution = {Institute of Computer Aided Design},
year = 1999,
number = 54,
url = {article:=ftp://www.prip.tuwien.ac.at/pub/publications/trs/tr54.ps.gz},
theme = {hierarchical},
address = {Vienna University of Technology, lstr. 3/1832,A-1040 Vienna AUSTRIA},
month = {January},
url = { http://www.prip.tuwien.ac.at/},
abstract = " This paper presents a new formalism for irregular
pyramids based on combinatorial maps. The
combinatorial map formalism allows us to encode a
planar graph thanks to two permutations encoding the
edges and the vertices of the graph.The combinatorial
map formalism encode explicitly the orientation of the
planar graph. This last property is useful to describe
the partitions of an image which may be considered as
a subset of the oriented plane $IR^2$. This new
constraint allows us to design interesting properties
for irregular pyramids. Finally the combinatorial
formalism allows us to encode efficiently the graph
transformations used in irregular pyramids."
}
@TechReport{brun-99-3,
author = "Luc {B}run and Walter Kropatsch",
institution ="PRIP, TU Wien",
number = "PRIP-TR-057",
title = "Pyramids with Combinatorial Maps",
year = 1999,
price = "20,-",
theme = {hierarchical},
url = {article:=ftp://www.prip.tuwien.ac.at/pub/publications/trs/tr57.ps.gz},
abstract = "This paper presents a new formalism for irregular pyramids
based on combinatorial maps. This technical report continue the work
began with the TR-54 report. Definition and
properties of Contraction kernels are generalized and completed. The
definition and properties of Equivalent contraction kernels are also
given. ",
}
@inproceedings{brun-99-2,
AUTHOR = {L. {B}run and {K}ropatsch, Walter},
TITLE = {Dual Contraction of Combinatorial Maps},
BOOKTITLE = {$2^{nd}$ IAPR-TC-15 Workshop on Graph-based Representations},
EDITOR = {{Kropatsch},Walter and
{{J}olion}, J.-M.},
PUBLISHER = {{"O}sterreichische Computer Gesellschaft},
VOLUME = {126},
ADDRESS = {Haindorf, Austria},
YEAR = {1999},
MONTH = {May},
PAGES = {145-154},
theme = {hierarchical},
url = {slides:=http://www.greyc.ensicaen.fr/~luc/ARTICLES/slides_cvww1999.ps},
abstract = "This paper presents a new formalism for
irregular graph pyramids based on
combinatorial maps. Such pyramids consist of
a stack of successively reduced graphs. Each
smaller graph is derived from the larger one
in the stack by a graph transformation called
dual graph contraction. The basic operations
of this transformation are contraction and
removal of edges. In this paper these two
basic operations are translated into the
formalism of combinatorial maps and should
enable the construction of combinatorial
pyramids. A combinatorial map encodes a
planar graph by two permutations encoding the
edges and their orientation around the
vertices. Combining the useful properties of
irregular pyramids offers a potential
alternative for representing structures at
multiple levels of abstraction."
}
@InProceedings{kropatsch-00,
author = {Walter G. {K}ropatsch and Luc {B}run},
title = {Hierarchies of Combinatorial Maps},
booktitle = {CPRW'00 Proceedings},
year = 2000,
editor = {Thom{'a}s Svoboda},
address = {Persl{'a}k},
month = {February},
organization = {Czech Pattern Recognition Society} ,
abstract = "Hierarchies of graphs can be generated by
dual graph contraction. The goal is to reduce
the data structure by a constant reduction
factor while preserving certain image
properties like connectivity. Since these
graphs are typically samplings of the plane
they are by definition plane. The particular
embedding can be represented in different
ways, e.g. a pair of dual graphs relating
points and faces through boundary
segments. Combinatorial maps determine the
embedding by explicitely recording the
orientation of edges around vertices. We
summarize the formal framework which has been
set up to perform dual graph contraction with
combinatorial maps. Contraction is controlled
by kernels that can be combined in many
ways. We have shown that kernels producing a
slow reduction rate can be combined to speed
up reduction. Or, conversely, kernels
decompose into smaller kernels that generate a
more gradual reduction.",
theme = {hierarchical},
url = {article(ps):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/cprw00.ps}
}
@InProceedings{CI-BRUN-2009,
author = {Romain Goffe and Guillaume Damiand and Luc Brun},
title = {A top down construction scheme for irregular pyramids},
booktitle = {V.I.S.A.P.P.'2009},
year = 2009,
series = {LNCS},
month = {February},
publisher = {Springer},
theme = {hierarchical},
note = {To be published}
}
@InProceedings{CI-Goffe-2009,
author = {Romain {Goffe} and Guillaume {Damiand} and Luc {Brun}},
title = {Extraction of tiled top-down irregular pyramids from large images.},
booktitle = {13th International Workshop on Combinatorial Image
Analysis (IWCIA'09)},
series = {Research Publishing Services},
publisher = {RPS, Singapore},
pages = {123-137},
month = {November},
year = {2009},
editor = {Petra {Wiederhold} and Reneta P. {Barneva}},
theme="hierarchical",
keywords = {Irregular pyramid; Topological model; Tiled data
structure; Combinatorial map;},
url = {paper(pdf):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/GoffeAl09b.pdf, slides(pdf):=http://www.greyc.ensicaen.fr/~luc/ARTICLES/slidesIWCIARomain.pdf},
abstract = {Processing large images is a common issue in the
computer vision framework with applications such as
satellite or microscopic images. The major problem
comes from the size of those images that prevents
them from being loaded globally into
memory. Moreover, such images contain different
information at different levels of resolution. For
example, global features, such as the delimitation
of a tissue, appear at low resolution whereas finer
details, such as cells, can only be distinguished at
full resolution. Thus, the objective of this paper
is the definition of a suitable hierarchical data
structure that would provide full access to all the
properties of the image by representing topological
information. The idea consists in transposing the
notion of tile for top-down topological pyramids to
control accurately the amount of memory required by
the construction of our model. As a result, this
paper defines the topological model of tiled
top-down pyramid and proposes a construction scheme
that would not depend on the system memory
limitations. }
}
@InProceedings{yll-05,
author = {Yll Haxhimusa and Adrian Ion and Kropatsch, Walter G. and Luc Brun},
title = {Hierarchical Image Partitioning using Combinatorial Maps},
booktitle = {Joint Hungarian-Austrian Conference on Image Processing and Pattern Recognition},
pages = {179--186},
year = 2005,
editor = {D. Chetverikov and L. Czuni and M. Vincze},
address = {Hungary},
month = {May},
theme = {hierarchical}
}
@PhdThesis{TH-PRUVOT-2008,
author = {Jean Hugues Pruvot},
title = {Segmentation et appariement hiérarchiques basés sur les pyramides combinatoires },
school = {Université de Caen Basse Normandie - ED SIMEM },
year = 2008,
address= {France},
theme = {hierarchical},
url = {Phd:=http://wwww.greyc.ensicaen.fr/~luc/ARTICLES/pruvotPhd.pdf}
}
