Vision pyramids that do not grow too high

Pyramid segmentation algorithms revisited

“…This height increasing degrades the efficiency of irregular pyramids. Recent work has resolved this problem by new selection mechanisms which guarantee logarithmic heights [53]. Next subsections deal with different reduction schemes used to build the irregular pyramid.…”

“…Thus, the number of vertices between consecutive graph levels is reduced to half or less and a reduction factor of at least 2 can be guaranteed. The MIES algorithm consists of three steps [52,53]:…”

“…The MIES algorithm can be used either in a dual graph framework or for connected component analysis [57]. However, its main disadvantage is that it is only applicable where there are no constraints on direction of contraction [11,53]. As it is shown in Fig.…”

“…Only these pre-selected edges are considered as candidates for contraction and the goal is to build contraction kernels with a high reduction factor. In order to perform the contractions in parallel, a vertex disjoint union of contraction kernels is needed [53]. The MIDES algorithm defines such a union in terms of independent directed edges.…”

“…Two directed edges are independent if they do not belong to the same neighbourhood. The neighbourhood of a directed edge e, N e , is defined by all directed edges with the same source s e , targeting the source s e or emanating from t e [53]. Then, the contraction kernels can be found as in MIS, but dealing with edges instead of vertices.…”