Component-Graph Construction

Component-trees are classical tree structures for grey-level image modelling. Component-graphs are defined as a generalization of component-trees to images taking their values in any (totally or partially) ordered sets. Similar to component-trees, component-graphs are a lossless image model; then, they can allow for the development of various image processing approaches. However, component-graphs are not trees, but directed acyclic graphs. This makes their construction non-trivial, leading to nonlinear time cost and resulting in nonlinear space data structures. In this theoretical article, we discuss the notion(s) of component-graph, and we propose a strategy for their efficient building and representation, which are necessary conditions for further involving them in image processing approaches.

[1]  Hugues Talbot,et al.  Directed Connected Operators: Asymmetric Hierarchies for Image Filtering and Segmentation , 2015, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[2]  Nicolas Passat,et al.  Connected Filtering Based on Multivalued Component-Trees , 2014, IEEE Transactions on Image Processing.

[3]  Nicolas Passat,et al.  Towards Connected Filtering Based on Component-Graphs , 2013, ISMM.

[4]  Thierry Géraud,et al.  MToS: A Tree of Shapes for Multivariate Images , 2015, IEEE Transactions on Image Processing.

[5]  Hugues Talbot,et al.  Mathematical Morphology: from theory to applications , 2013 .

[6]  Nicolas Passat,et al.  An extension of component-trees to partial orders , 2009, 2009 16th IEEE International Conference on Image Processing (ICIP).

[7]  Philippe Salembier,et al.  Binary partition tree as an efficient representation for image processing, segmentation, and information retrieval , 2000, IEEE Trans. Image Process..

[8]  Hugues Talbot,et al.  Shape-Based Analysis on Component-Graphs for Multivalued Image Processing , 2019 .

[9]  Nicolas Passat,et al.  Colour Image Filtering with Component-Graphs , 2014, 2014 22nd International Conference on Pattern Recognition.

[10]  Philippe Salembier,et al.  Antiextensive connected operators for image and sequence processing , 1998, IEEE Trans. Image Process..

[11]  Nicolas Passat,et al.  Implicit Component-Graph: A Discussion , 2017, ISMM.

[12]  Nicolas Passat,et al.  Component-Trees and Multi-value Images: A Comparative Study , 2009, ISMM.

[13]  Nicolas Passat,et al.  Component-Hypertrees for Image Segmentation , 2011, ISMM.

[14]  Alfred V. Aho,et al.  The Transitive Reduction of a Directed Graph , 1972, SIAM J. Comput..

[15]  J. W. Modestino,et al.  Flat Zones Filtering, Connected Operators, and Filters by Reconstruction , 1995 .

[16]  Nicolas Passat,et al.  Component-Trees and Multivalued Images: Structural Properties , 2013, Journal of Mathematical Imaging and Vision.

[17]  Rolf Adams,et al.  Seeded Region Growing , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Pascal Monasse,et al.  Scale-Space from a Level Lines Tree , 2000, J. Vis. Commun. Image Represent..

[19]  Ronald Jones,et al.  Connected Filtering and Segmentation Using Component Trees , 1999, Comput. Vis. Image Underst..

[20]  Azriel Rosenfeld,et al.  Digital topology: Introduction and survey , 1989, Comput. Vis. Graph. Image Process..

[21]  Yongchao Xu,et al.  Connected Filtering on Tree-Based Shape-Spaces , 2016, IEEE Transactions on Pattern Analysis and Machine Intelligence.