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 Supervised Thesis  
 Karolina Golec, Début le 1/10/2014. Generic topological and physical model for soft tissue simulation.
Supervisors: Guillaume Damiand, Stéphane Nicole (LBMC) et Florence Zara (LIRIS).Within the framework of simulators for training of medical procedures, the main issue concerns the interactive simulation of behavior of organs taking into account interaction between them and/or with external surgical tools. The goal of this thesis concerns thus the implementation of a new biomedical model of soft tissues suitable for interactive simulations and allowing simulations of organ movements. LBMC, LIRIS and Physic laboratory of ENS grouped their skills to create a new physical model based on the topological massspring system (MSS) and masstensor model (MT) of LIRIS by integrating the new behavior laws developed by LBMC and Physic laboratory of ENS.
 Abdoulaye Abou Diakité, du 1/10/2012 au 10/12/2015. Applying combinatorial maps to geometrical and semantics modeling of buildings.
Supervisors: Guillaume Damiand et Dirk Van Maercke (CSTB).The building is a complex system composed by several
components. Practically, CAD computer softwares described a
building by a set of geometrical shapes. However, there is
only few simulating tools that use directly such a
description of the building object. In most cases, the
simulations represent a building by a graph or an
equivalent network, i.e. a topological structure made of
vertices and connections between them, representing
identifiable portions of the building: premises, walls,
junctions, arrays, structures carrier, doublings,
... Identify these entities, build the equivalent graph,
extract dimensional characteristics, ... represent as many
difficult problems given the wide variety of data handled.
Combinatorial maps provide a simple and effective formalism
to describe a complex geometry from its topological
structure. Such a structure code firstly the connecting
links between vertices, curves, surfaces and volumes, then
embed it into a geometric support. The creation,
modification or deformation of the representation involves
a small number of clearly defined operations, which
facilitates transcription of the mathematical formalism
into computer software. This work should be part of all
strategic software tools developed at CSTB (EVEBIM, ICARE,
PHANIE, ACOUBAT, ...)
The goal of this thesis is to conceive and develop the
numerical tools allowing: (a) the semiautomatic
construction of a combinatorial map representing themodel
of a building in its immediate surroundings, with the
possibility of identifying entire rooms structural elements
and components, from CAD data (such as DXF, IFC or
equivalent) and GIS. (b) the semiautomatic extraction,
from the topological/geometric unified description, of
different specific representations for different simulation
domains: surface envelope of rooms, adjacency graphs and
dimensional properties, estimators depending on the nature
of the materials... (c) To simplify and/or to enhance the
representation of buildings to facilitate the
representation of elements at different levels of detail.
This thesis is in an industrial context. Thus there is a
strong constraint for software development of the proposed
methods.
The development will be done in C++ language, related to the 3D
geometric modeler Moka and the combinatorial map kernel of CGAL.
 Camille Combier, du 1/10/2009 au 28/11/2012. Similarity measure for generalized maps.
Supervisors: Guillaume Damiand et Christine Solnon (LIRIS).A generalized map is a topological model that represents implicitly a set of cells (vertices, edges, faces, volumes, ...) as well as all the incidence and adjacency relations through darts and involutions. Generalized maps are mainly used to model images and 3D objects. There are few tools to analyze and compare generalized maps. Our goal is to define a set of tools for comparing generalized maps. We first define a similarity measure based on the size of the common part between two generalized maps called greatest common submap. We define two types of submaps, partial and induced. Induced submap must preserved all involutions while partial submap allows to remove also some involutions. Partial submaps allow to not preserved all the involutions in analogy to the partial subgraph for which the edges can not all be present. Then we define a set of modification operations of darts and sewings and use them to define the generalized map edit distance. This edit distance is equal to the minimum cost generated by all sequences of operations transforming a generalized map into another one. This distance allows the use of labels, with the substitution operation. Labels are placed on the darts and allow to add information to generalized maps. We then show that for certain costs our edit distance can be directly computed from the largest common submap. The computation of the edit distance is an NPhard problem. We propose a greedy algorithm to compute in polynomial time an approximation of our edit distance. We propose a set of heuristics based on descriptors of the neighborhood darts of the generalized map to guide the greedy algorithm, and we evaluate these heuristics on randomly generated test sets, for which we know a bound of the distance. We propose some possible use of our similarity measures in the field of image and meshes analysis. We compare our edit distance of generalized maps with the edit distance of graphs, often used in structural pattern recognition. We also define a set of heuristics taking into account the labels generalized maps modeling images and meshes. We emphasize the qualitative aspect of our matching, allowing to match areas of the image and mesh points.
 Stéphane Gosselin, du 1/10/2008 au 24/10/2011. Frequent pattern discovery in combinatorial maps databases.
Supervisors: Guillaume Damiand et Christine Solnon (LIRIS).A combinatorial map is a topological model that represents
the subdivisions of an nD space into cells and their
adjacency relations in n dimensions. This data structure
is increasingly used in image processing, but it still
lacks tools for analysis. Our goal is to define new tools
for combinatorial nD maps. We are particularly interested
in the extraction of submaps in a database of maps.
We define two combinatorial map signatures: the first one
has a quadratic space complexity and may be used to decide
of isomorphism with a new map in linear time whereas the
second one has a linear space complexity and may be used
to decide of isomorphism in quadratic time. They can be
used for connected maps, non connected maps, labbeled maps
or non labelled maps. These signatures can be used to
efficiently search for a map in a database. Moreover, the
search time does not depend on the number of maps in the
database.
We introduce the problem of finding frequent submaps in a
database of combinatorial nD maps. We describe two
algorithms for solving this problem. The first algorithm
extracts the submaps with a breadthfirst search approach
and the second one uses a depthfirst search approach. We
compare these two algorithms on synthetic database of
maps.
Finally, we propose to use the frequent patterns in an
image classification application. Each image is described
by a map that is transformed into a vector representing
the number of occurrences of frequent patterns. From
these vectors, we use standard techniques of
classification defined on vector spaces. We propose
experiments in supervised and unsupervised classification
on two image databases.
 Romain Goffe, du 1/12/2007 au 14/09/2011. Topdown irregular pyramids for large histological images segmentation.
Supervisors: Luc Brun (GREYC) et Guillaume Damiand.Some data acquisition devices produce images of several
gigabytes. Analyzing such large images raises two main
issues. First, the data volume to process forbids a
global image analysis, hence a hard partitioning
problem. Second, a multiresolution approach is required
to extract global features at low resolution. For
instance, regarding histological images, recent
improvments in scanners' accuracy allow nowadays to
examine cellular structures on the whole slide. However,
produced images are up to 18\,GB. Besides, considering a
tissue as a particular layout of cells is a global
information that is only available at low
resolution. Thus, these images combine multiscale and
multiresolution information.
In this work, we define a topological and hierarchical model
which is suitable for the segmentation of large images. Our work
is based on the models of topological map and
combinatorial pyramid. We introduce the tiled map
model in order to encode the topology of large partitions and a
hierarchical extension, the tiled topdown pyramid, to
represent the duality between multiscale and multiresolution
information. Finally, we propose an application of our model for
the segmentation of large images in histology.
 Alexandre Dupas, du 1/10/2006 au 25/11/2009. Operations and Algorithms for Topological Segmentation of 3D Images.
Supervisors: Guillaume Damiand et Pascal Lienhardt (XLIMSIC).A 3D topological map is a model used in image processing
which represents the partition of a 3D image into
regions. In this work, we introduce some tools that allow
to modify a partition presented by a topological map, and
we use these tools to propose segmentation algorithms
implementing topological criteria. In a first part, we
propose three operations. The region merging is defined
with a local approach suited for interactive use, and a
global approach suited for automatic processing like image
segmentation. The region splitting is introduced with a
burst into voxel approach, and the split with a
guide. Last, a deformation of the partition based on the
definition of MLSimple points: voxels that can be flipped
of region without changing the topology of the
partition. With these operations, we implement in a second
part image segmentation processes using topological
maps. First we adapt to our model an existing algorithm
using a criterion based on the notion of contrast. Then,
we propose methods to compute topological invariants of
regions: the Betti numbers. Using these methods we
implement a topological criterion that controls the number
of tunnels and cavities of the regions. Last, we give an
overview of the possibilities of our tools by creating a
toolchain to segment brain tumors in medical images.
 Sébastien Horna, du 1/10/2005 au 27/11/2008. Geometrical and topological reconstruction of 3D architectural complexes from 2D vectoriel plans.
Supervisors: Yves Bertrand (XLIMSIC), Guillaume Damiand, et Daniel Meneveaux (XLIMSIC).Virtual architectural (indoor) scenes are often modelled
in 3D for various types of simulation systems. For instance, some
authors propose methods dedicated to lighting, heat transfer, acoustic
or radio wave propagation simulations. These methods rely in most
cases on a volumetric representation of the environment, with
adjacency and incidence relationships. Unfortunately, many buildings
data are only given by 2D plans and the 3D needs varies from one
application to another. To solve these problems, we propose a formal
representation of consistency constraints dedicated to building
interiors and associated with a topological model . We show that such
a representation can be used for: (i) reconstructing a 3D model from
2D architectural plans ; (ii) detecting automatically geometrical,
topological and semantical inconsistencies ; (iii) designing automatic
and semiautomatic operations to correct and enrich a 2D plan. All our
constraints are homogeneously defined in 2D and 3D, implemented with
generalized maps and used in modeling operations. We explain how this
model can be successfully used with various raytracing methods.
 Carine GrassetSimon, du 1/10/2003 au 6/12/2006. Definition and study of nD generalized pyramids:
application in multilevel segmentation of 3D images.
Supervisors: Guillaume Damiand et Pascal Lienhardt (XLIMSIC).In this work, we are interested in the hierarchical
geometrical modeling with a topological basis. We propose
the definition of a generic model in any dimension, and we
show a possible application in multilevel segmentation of
3D images.
In the first part of this work, we define and study the
nD generalized pyramids. This is a generic hierarchical
topological model which represents all the cells of a
subdivision as well as the adjacency and incidence
relations existing between these cells. We propose and
compare three possible representations of these pyramids.
In order to retrieve the information which corresponds to
a cell, we define the notion of generalized orbit. This
notion extends the notion of receptive field. We also
define a local modification operation of a pyramid level
allowing to preserve the model coherence by propagating
the modifications at the upper levels.
In the second part of this work, we show how to use this
model in the case of a multilevel segmentation of 3D
images. We define the properties which have to be
respected by the pyramid, and we give the algorithms that
allow to construct such a pyramid. Then, we show how to
use the generalized orbits in order to retrieve the
voxels or the intervoxel elements which compose a region
or its boundary. Finally we define an operation allowing
to locally modify the segmentation criterion of a region
set. This operation is based on the operation defined in
the first part in order to preserve the coherence
constraints.
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