Geodesic Saliency of Watershed Contours and Hierarchical Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Attribute openings, thinnings, and granulometries
Computer Vision and Image Understanding
Efficiency of a Good But Not Linear Set Union Algorithm
Journal of the ACM (JACM)
Connected filtering and segmentation using component trees
Computer Vision and Image Understanding
Shape Connectivity: Multiscale Analysis and Application to Generalized Granulometries
Journal of Mathematical Imaging and Vision
Tree Representation for Image Matching and Object Recognition
DCGI '99 Proceedings of the 8th International Conference on Discrete Geometry for Computer Imagery
Efficient Algorithms to Implement the Confinement Tree
DGCI '00 Proceedings of the 9th International Conference on Discrete Geometry for Computer Imagery
Mask-Based Second-Generation Connectivity and Attribute Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
New Extinction Values from Efficient Construction and Analysis of Extended Attribute Component Tree
SIBGRAPI '08 Proceedings of the 2008 XXI Brazilian Symposium on Computer Graphics and Image Processing
Antiextensive connected operators for image and sequence processing
IEEE Transactions on Image Processing
Grayscale level connectivity: theory and applications
IEEE Transactions on Image Processing
Building the Component Tree in Quasi-Linear Time
IEEE Transactions on Image Processing
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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.