A revision of pyramid segmentation

Dual graph contraction reduces the number of vertices and of edges of a pair of dual image graphs while, at the same time, the topological relations among the 'surviving' components are preserved. Repeated application produces a stack of successively smaller graphs: a pair of dual irregular pyramids. The process is controlled by selected decimation parameters which consist of a subset of surviving vertices and associated contraction kernels. Equivalent contraction kernels (ECKs) combine two or more contraction kernels into one single contraction kernel which generates the same result in one single dual contraction. This is the basis to the proof that any segmentation can be represented in one single level of such a pyramid. Experimental results demonstrate the applicability on synthetic and real images respectively.