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Split-and-merge algorithms defined on topological maps for 3D image segmentation

Guillaume Damiand, Patrick Resch
2003 Graphical Models  
Split-and-merge algorithms define a class of image segmentation methods. Topological maps are a mathematical model that represents image subdivisions in 2D and 3D.  ...  This paper discusses a split-and-merge method for 3D image data based on the topological map model. This model allows representations of states of segmentations and of merge and split operations.  ...  Acknowledgements We wish to thank Valerie Gral and Magali Delobbe for useful comments and careful reading of this paper.  ... 
doi:10.1016/s1524-0703(03)00009-2 fatcat:rvs5eqqmejfbvl3hkzsfhscqqe

Topological Map Based Algorithms for 3D Image Segmentation [chapter]

Guillaume Damiand, Patrick Resch
2002 Lecture Notes in Computer Science  
One of the most commonly used approach to segment a 2D image is the split and merge approach. In this paper, we are defining these two operations in 3D within the topological maps framework.  ...  This mathematic model of regions segmented image representation allows us to define these algorithms in a local and generic way.  ...  It requires us to define very efficient algorithms to use them on big images. In this paper, we present the two algorithms of merge and split on the 3D topological maps.  ... 
doi:10.1007/3-540-45986-3_20 fatcat:uakmbdxsg5hojewdw7zdsmeu2u

Comparison and Convergence of Two Topological Models for 3D Image Segmentation [chapter]

Achille Braquelaire, Guillaume Damiand, Jean-Philippe Domenger, Frédéric Vidil
2003 Lecture Notes in Computer Science  
In this paper we compare two topological models of 3D segmented images representation.  ...  These models are based on a collaboration between a topological representation and a geometrical representation of the regions of the segmented image.  ...  Both models use equivalent topological representations which are 3D topological maps described by combinatorial maps.  ... 
doi:10.1007/3-540-45028-9_6 fatcat:o4h5sgvs6ba5raocdkivzijuom

Combinatorial Maps for 2D and 3D Image Segmentation [chapter]

Guillaume Damiand, Alexandre Dupas
2012 Lecture Notes in Computational Vision and Biomechanics  
We provide some experiments of 2D and 3D image segmentation using different criteria to enlighten the use of topological maps for image segmentation.  ...  Open Problems and Discussion In this chapter, we presented an efficient and generic image segmentation algorithm based on topological maps.  ... 
doi:10.1007/978-94-007-4174-4_12 fatcat:lnztpyo7bjcnvp57ihhvhzzg6m

3D Topological Map Extraction from Oriented Boundary Graph [chapter]

Fabien Baldacci, Achille Braquelaire, Guillaume Damiand
2009 Lecture Notes in Computer Science  
The extraction of a 3D topological map from an Oriented Boundary Graph can be needed to rene a 3D Split and Merge segmentation using topological information such as the Euler characteristic of regions.  ...  In this paper, we present the topological map extraction algorithm which allows to reconstruct locally a set of regions from the Oriented Boundary Graph.  ...  Introduction The Segmentation process consists in defining a partition of the image into homogeneous regions. Split and merge methods [HP74] are widely used in segmentation.  ... 
doi:10.1007/978-3-642-02124-4_29 fatcat:aa7ys37e3rgptcrzcff7dp4ekm

Region merging with topological control

Alexandre Dupas, Guillaume Damiand
2009 Discrete Applied Mathematics  
Classical and incremental algorithms to compute the Betti numbers using information represented by the topological map of an image are provided.  ...  This paper presents a region merging process controlled by topological features on regions in three-dimensional (3D) images. Betti numbers, a well-known topological invariant, are used as criteria.  ...  Acknowledgments A preliminary version of this paper was presented at the 12th International Workshop on Combinatorial Image Analysis, Buffalo, NY, USA, April 2008 [7] .  ... 
doi:10.1016/j.dam.2009.04.005 fatcat:4dzljrttjfccvepikznj5n5iei

Active Contours Under Topology Control—Genus Preserving Level Sets

Florent Ségonne
2007 International Journal of Computer Vision  
We demonstrate the strength of our method on a wide range of numerical experiments and illustrate its performance on the segmentation of cortical surfaces and blood vessels.  ...  This is typically the case in biomedical image segmentation, where the topology of the target shape is prescribed by anatomical knowledge.  ...  Algorithm 2 describes in detail the update procedure for the label map.  ... 
doi:10.1007/s11263-007-0102-8 fatcat:qvarfyp3szf5dlhj5v7oparyxm

Active Contours Under Topology Control Genus Preserving Level Sets [chapter]

Florent Ségonne, Jean-Philippe Pons, Eric Grimson, Bruce Fischl
2005 Lecture Notes in Computer Science  
We demonstrate the strength of our method on a wide range of numerical experiments and illustrate its performance on the segmentation of cortical surfaces and blood vessels.  ...  This is typically the case in biomedical image segmentation, where the topology of the target shape is prescribed by anatomical knowledge.  ...  Algorithm 2 describes in detail the update procedure for the label map.  ... 
doi:10.1007/11569541_15 fatcat:kjsb4wfb7fdgbnrd3f4ilhi5ku

Incremental Updating of 3D Topological Maps to Describe Videos [chapter]

Guillaume Damiand, Sylvain Brandel, Donatello Conte
2015 Lecture Notes in Computer Science  
A topological map is an efficient mathematical model for representing an image subdivision where all cells and adjacency relations between elements are represented.  ...  It has been proved to be a very good tool for video processing when video is seen as a 3D image.  ...  Dealing with k slices allows to make only one split and one merge instead of k splits and k merges.  ... 
doi:10.1007/978-3-319-26145-4_22 fatcat:oaflkwnmtjb6zjbqwhoupbkd5e

Machine learning of hierarchical clustering to segment 2D and 3D images [article]

Juan Nunez-Iglesias, Ryan Kennedy, Toufiq Parag, Jianbo Shi, Dmitri B. Chklovskii
2013 arXiv   pre-print
competing algorithms in EM and natural images.  ...  We advocate the use of variation of information to measure segmentation accuracy, particularly in 3D electron microscopy (EM) images of neural tissue, and using this metric demonstrate an improvement over  ...  , Steve Plaza, Phil Winston, and Nathan Clack for useful discussions.  ... 
arXiv:1303.6163v1 fatcat:2asvcm65yne2hfcp4vduvb7lpy

Representing and Segmenting 2D Images by Means of Planar Maps with Discrete Embeddings: From Model to Applications [chapter]

Achille Braquelaire
2005 Lecture Notes in Computer Science  
They encode and provide most of topological and geometrical features required by segmentation algorithms and can be efficiently updated.  ...  In this paper we give an overview of the use of planar maps with discrete embedding in the context of image segmentation and we show how to design, implement and use a general environment for 2D image  ...  of 3D discrete images with maps for 3D image segmentation [35] [36] [37] [38] [39] .  ... 
doi:10.1007/978-3-540-31988-7_10 fatcat:cumhmejerjfr7isnk4nxtftec4

Hidden Markov models for tracking neuronal structure contours in electron micrograph stacks

Min-Chi Shih, Kenneth Rose
2012 2012 9th IEEE International Symposium on Biomedical Imaging (ISBI)  
involves major topological changes including contour splits and merges.  ...  Experimental results show, both quantitatively and qualitatively, that the proposed approach can effectively and efficiently track cell contours while accounting for splitting, merging, large contour displacements  ...  Bryan Jones and Dr. James Anderson from the Univ. of Utah for providing data used in experiments.  ... 
doi:10.1109/isbi.2012.6235824 dblp:conf/isbi/ShihR12 fatcat:tntfhfnesnbm7if53g532cbzpi

Novelty detection and 3D shape retrieval using superquadrics and multi-scale sampling for autonomous mobile robots

P Drews, P Núñez, R Rocha, M Campos, J Dias
2010 2010 IEEE International Conference on Robotics and Automation  
and optimization using the split and merge paradigm.  ...  There are several applications for which it is important to both detect and communicate changes in data models.  ...  An important approach for 3D point clouds is proposed in [10] , wherein the split and merge principle is used in unstructured 3D data.  ... 
doi:10.1109/robot.2010.5509405 dblp:conf/icra/DrewsTRCD10 fatcat:irf3ei6mtref3c6m3v5e5tvnua

Discrete Region Competition for Unknown Numbers of Connected Regions

J. Cardinale, G. Paul, I. F. Sbalzarini
2012 IEEE Transactions on Image Processing  
We present a discrete, unsupervised multi-regioncompetition algorithm for image segmentation over different energy functionals.  ...  The presented framework and algorithms are implemented in the open-source Insight Toolkit (ITK) image-processing library.  ...  Helmuth for sharing his experience in many discussions and Prof. U. Greber  ... 
doi:10.1109/tip.2012.2192129 pmid:22481820 fatcat:pllbuelagbahngpt23lrczbyva

Distinguishing 3D-Topological Configurations of Two Tori

Adrian Ion, Thomas Illetschko, Yll Haxhimusa, Walter Kropatsch
2006 2006 Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing  
This paper presents 3D combinatorial maps and the primitive operations needed to simplify such representations.  ...  Minimal configurations of the three primitive topological configurations, simplex, hole, and tunnel, and two possible configurations for two tori are presented.  ...  In order to use 3D topological structures for 3D image segmentation one has to define basic operations.  ... 
doi:10.1109/synasc.2006.30 dblp:conf/synasc/IonIHK06 fatcat:e2xzdijpg5b7jarxpucuwn7liu
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