Efficient computation of new extinction values from extended component tree

A gray-scale image can be interpreted as a topographical surface, and represented by a component tree, based on the inclusion relation of connected components obtained by threshold decomposition. Relations between plateaus, valleys or mountains of this relief are useful in computer vision systems. An important definition to characterize the topographical surface is the dynamics, introduced by Grimaud (1992), associated with each regional minimum. This concept has been extended, by Vachier and Meyer (1995), by the definition of extinction values associated with each extremum of the image. This paper proposes three new extinction values - two based on the topology of the component tree: (i) number of descendants and (ii) sub-tree height; and one geometric: (iii) level component bounding box (subdivided into extinctions of height, width or diagonal). This paper describes an efficient computation of these extinction values based on the incremental determination of attributes from the component tree construction in quasi-linear time, compares the computation time of the method and illustrates the usefulness of these new extinction values from real examples.

[1]  Fernand Meyer.  The Dynamics of Minima and Contours , 1996, ISMM.

[2]  Michael H. F. Wilkinson,et al.  Mask-Based Second-Generation Connectivity and Attribute Filters , 2007, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[3]  Michel Couprie,et al.  Building the Component Tree in Quasi-Linear Time , 2006, IEEE Transactions on Image Processing.

[4]  Michael W. Berry,et al.  Using dendronal signatures for feature extraction and retrieval , 2000, Int. J. Imaging Syst. Technol..

[5]  J. Roerdink,et al.  Mathematical Morphology and its Applications to Image and Signal Processing , 1998 .

[6]  Corinne Vachier.  Extraction de caractéristiques, segmentation d'image et morphologie mathématique , 1995 .

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

[8]  Michael H. F. Wilkinson,et al.  Interactive Shape Preserving Filtering and Visualization of Volumetric Data , 2002 .

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

[10]  Gilles Bertrand,et al.  On the dynamics , 2007, Image Vis. Comput..

[11]  Edward R. Dougherty,et al.  Mathematical Morphology in Image Processing , 1992 .

[12]  Alexandre Gonçalves Silva,et al.  New Extinction Values from Efficient Construction and Analysis of Extended Attribute Component Tree , 2008, SIBGRAPI.

[13]  Emmanuel Bertin,et al.  Effective Component Tree Computation with Application to Pattern Recognition in Astronomical Imaging , 2007, 2007 IEEE International Conference on Image Processing.

[14]  Michel Grimaud,et al.  New measure of contrast: the dynamics , 1992, Optics & Photonics.

[15]  Petros Maragos,et al.  Shape Connectivity: Multiscale Analysis and Application to Generalized Granulometries , 2004, Journal of Mathematical Imaging and Vision.

[16]  Laurent Najman,et al.  Geodesic Saliency of Watershed Contours and Hierarchical Segmentation , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[17]  Corinne Vachier,et al.  Valuation of image extrema using alternating filters by reconstruction , 1995, Optics + Photonics.

[18]  Pierre Soille,et al.  Mathematical Morphology and Its Applications to Image Processing , 1994, Computational Imaging and Vision.

[19]  Luís Garrido Ostermann.  Hierarchical region based processing of images and video sequences: application to filtering, segmentation and information retrieval , 2002 .

[20]  Ulisses Braga-Neto,et al.  Grayscale level connectivity: theory and applications , 2004, IEEE Transactions on Image Processing.

[21]  Ronald Jones,et al.  Attribute Openings, Thinnings, and Granulometries , 1996, Comput. Vis. Image Underst..

[22]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[23]  Jacques Demongeot,et al.  Efficient Algorithms to Implement the Confinement Tree , 2000, DGCI.

[24]  Robert E. Tarjan,et al.  Efficiency of a Good But Not Linear Set Union Algorithm , 1972, JACM.

[25]  José Crespo,et al.  The flat zone approach: A general low-level region merging segmentation method , 1997, Signal Process..

[26]  Michael H. F. Wilkinson,et al.  Fast Morphological Attribute Operations Using Tarjan's Union-Find Algorithm , 2000, ISMM.

[27]  Philippe Salembier,et al.  Binary partition tree as an efficient representation for filtering, segmentation and information retrieval , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[28]  Jacques Demongeot,et al.  Tree Representation for Image Matching and Object Recognition , 1999, DGCI.

[29]  H. Gao,et al.  Disjoint set data structure for morphological area operators , 2003, Fourth International Conference on Information, Communications and Signal Processing, 2003 and the Fourth Pacific Rim Conference on Multimedia. Proceedings of the 2003 Joint.

[30]  Edward R. Dougherty,et al.  Hands-on Morphological Image Processing , 2003 .