λ-connectedness: method and application

Introduces a systematic approach, which we call a λ-connectedness method, that can be applied to several real image processing problems, such as segmentation/classification, searching and data reconstruction. In this paper, we integrate previous research work into a network/graph-based system to build a unified framework for these processes. This technique is based on a graph G=(V,E) and an associated “potential function” ρ on the vertices of the graph. A measure C_ρ(x,y) is defined for the λ-connectedness on vertices x,y∈G with respect to ρ. For a certain λ∈[0,1], x and y are said to be λ-connected if C_ρ(x,y)⩾λ. If every pair of vertices are λ-connected, then ρ is called λ-connected on G. λ-connectedness is a measure of continuity in discrete spaces or systems. In this paper, we introduce λ-connected segmentation and λ-connected fitting. The λ-connected method can be viewed as a fuzzy system method, and it has a close relationship to rough sets. This method also has potential uses in network economics and resource management