Hierarchical image analysis using irregular tessellations

Pyramid segmentation algorithms revisited

“…These tools permitted a hierarchical data structure to adapt itself to the image layout, since the proposed hierarchy was not restricted to a rigid sampling structure. The stochastic decimation procedure was successfully applied to multiscale smoothing of chain-coded curves [60] and segmentation of grey level images [48]. In this last case, a hierarchy of region adjacency graphs (RAG) is generated.…”

“…Thus, contrary to the original stochastic decimation idea, the resulting decimation procedure is dependent on the image data. In order to define the classes, several approaches have been experimentally proven [48]. The simplest approach is to define class membership by thresholding the grey level differences between a vertex and their neighbours.…”

“…Non-surviving vertices of V l are linked to surviving ones. Thus, each vertex v of G l+1 has associated a set of vertices of G l , the reduction window of v, which includes itself and all non-surviving vertices linked to it [48]. This is a decimation process which requires rules for:…”

“…custom-made pyramids [42] and Voronoi tesselation-based approaches [43,44]). The first irregular pyramid to be applied in image analysis was proposed by Montanvert et al [48]. They employed a stochastic decimation algorithm [27] to construct irregular tessellations and generate a hierarchical representation of the input image.…”

“…• Simple Graphs [48]: This is the simplest data structure where the pyramid is defined as a stack of successively reduced simple graphs. This type of structures have two main drawbacks for image processing tasks: (i) they do not permit to know if two adjacent receptive fields have one or more common boundaries, and (ii) they do not allow to differentiate an adjacency relationship between two receptive fields from an inclusion relationship.…”