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.

Research highlights
► Dynamics of a regional extremum is a contrast measure.
► Extinction of an extremum as maximal size of an attribute filter for extinguish it.
► Fast and flexible algorithm for extinction by any increasing attribute.
► New geometric and topological extinctions.
► Relevant markers for image segmentation.