Oriented Boundary Graph: A Framework to Design and Implement 3D Segmentation Algorithms Fabien Baldacci Achille Braquelaire Jean-Philippe Domenger Universit´ e Bordeaux 1, CNRS, LaBRI, 351, cours de la Lib´ eration 33405 Talence cedex, France {baldacci,achille,domenger}@labri.fr Abstract In this paper we show the interest of a topologi- cal model to represent 3D segmented image which is a good compromise between the complete but time con- suming representations and the partial but not expres- sive enough ones. We show that this model, called Oriented Boundary Graph, provides an effective frame- work for both volumic image analysis and segmenta- tion. The Oriented Boundary Graph provides an effi- cient implementation of a set of primitives suitable for the design complex segmentation algorithms and to im- plement the computation of the segmented image char- acteristics needed by such algorithms. We first present the framework and give the time complexity of its main primitives. Then, we give some examples of the use of this framework in order to efficiently design non-trivial image analysis operations and image segmentation al- gorithms. Those examples are applied on 3D CT-scan data. 1. Introduction Designing generic and efficient segmentation algo- rithms remains a difficult task. By essence, the seg- mentation process is intrinsic to the area of interest and the nature of the class of images to be analyzed. This leads to a vast number of dedicated algorithms, each one being specific to a specific purpose. To solve this problem, a lot of research has been done in the field of image structuring. Indeed, structuring an image allows an efficient retrieval of geometrical features (such as lengths or curvatures) and/or topological features (such as neighborhood or Betti numbers) [5]. These features are both used as criteria to drive the segmentation pro- cess and to analyze its results. Furthermore, a topolog- ical structuring encodes neighboring information such as the adjacency relation between regions and provides a convenient layout for designing split and merge algo- rithms. Existing models [7, 4] are either highly time and space consuming and for now cannot be efficiently used for real 3D segmentation problems, or does not pro- vide enough features to allow to design complex seg- mentation algorithm. To overcome this problem, we developed a new structuring model called the Oriented Boundary Graph [1]. Whereas this model does not ex- plicit the whole topology of a segmented image such as a topological map based representation does, it is designed to reduce both time and memory complexity while providing primitives and features for efficient im- plementations of split and merge algorithms. In order to fulfill these requirements, a kernel of primitives has been implemented with an API dedicated to image seg- mentation. Using this set of primitives that provides an efficient extraction of main topological and geometrical features, a large collection of segmentation algorithms can be designed and optimized for specific image pro- cessing applications. In this article we present some representative prim- itives composing our framework and detail the time complexity obtained by using the Oriented Boundary Graph model for each of them . We give several exam- ples of use of this framework in order to: • implement existing methods such as graph-based image segmentation operations [2], • redefine some operations such as morphological filters for them to be more effective, • design non-trivial segmentation algorithms. In Section 2 we present the OBG model and the re- lated framework, and in Section 3 we give some exam- ples of how to of use this framework. Examples are applied on 3D images obtained by CT-scan. 2010 International Conference on Pattern Recognition 1051-4651/10 $26.00 © 2010 IEEE DOI 10.1109/ICPR.2010.279 1120 2010 International Conference on Pattern Recognition 1051-4651/10 $26.00 © 2010 IEEE DOI 10.1109/ICPR.2010.279 1120 2010 International Conference on Pattern Recognition 1051-4651/10 $26.00 © 2010 IEEE DOI 10.1109/ICPR.2010.279 1116 2010 International Conference on Pattern Recognition 1051-4651/10 $26.00 © 2010 IEEE DOI 10.1109/ICPR.2010.279 1116 2010 International Conference on Pattern Recognition 1051-4651/10 $26.00 © 2010 IEEE DOI 10.1109/ICPR.2010.279 1116