Behavior of edges in scale space

Abstract

An analysis is presented of the behavior of edges in scale space for deriving rules useful in reasoning. This analysis of liner edges at different scales in images includes the mutual influence of edges and identifies at what scale neighboring edges start influencing the response of a Laplacian or Gaussian operator. Dislocation of edges, false edges, and merging of edges in the scale space are examined to formulate rules for reasoning in the scale space. The theorems, corollaries, and assertions presented can be used to recover edges, and related features, in complex images. The results reported include one lemma, three theorems, a number of corollaries and six assertions. The rigorous mathematical proofs for the theorems and corollaries are presented. These theorems and corollaries are further applied to more general situations, and the results are summarized in six assertions. A qualitative description as well as some experimental results are presented for each assertion.