Incremental Modiication of Segmented Images

A model of representation of regions of segmented images has been recently introduced 3]. This model provides an eecient implementation of region segmentation laying on discrete maps. In this paper, we present the two basic primitives used to modify the discrete map data structure: the insertion of a new segment and the suppression of an existing segment. These both primitives are the basic ones used to design split and merge algorithms. The region segmentation processings subdivide an image into connected set of pixels, called the regions of an image. The basic common idea of region segmentation methods is to modify the partition until all the regions of the image satisfy a given homogeneity criterion. Among region segmentation methods, three main diierent approaches may be distinguished: (i) The top-down approach 21,19,8] starts with large regions and divide the image into smaller and smaller regions. (ii) The bottom-up approach 5,14] starts with small regions and merges them until the homogeneity criterion is satissed. (iii) The mixed approach 6,22,9], introduced by Pavlidis and Horowitz 15,16], modiies the partition by splitting or merging regions until they satisfy some homogeneity criterion. Horowitz and Pavlidis have introduced a distinction between the merging step and the grouping step, the merging step beeing restricted by the representation data structure (quadtree). The most common structures used by top-down approaches are pyramids 6,25] and quadtree 24,12,23]. Although the quadtree is simple and eecient for top-down processing, its main drawback to implement merge processings is the time overhead needed to compute complex boundaries or to compute the set of neighbor regions of a given region. This drawback may be reduced using roped quadtrees 17], which allows an eecient computation of the adjacent blocks of a given block. Nevertheless the problem of boundary computation remains. The bottom-up methods begins with atomic regions of one or two pixels which grow untill a partition of the image is performed (see for example 27]). This initial partition may be represented by an array of labels 13,20]. Starting from this partition some adjacent regions with close features can be merged. The usual data structure used to eeectively perform the