Embedding fuzzy logic in content based image retrieval

This paper focuses on the possible embedding of the uncertainty regarding the colors of an image into histogram-type descriptors. The uncertainty naturally arises from both the quantization of the color components and the human perception of colors. Fuzzy histograms measure the typicality of each color within the image. We define various fuzzy color histograms following a taxonomy that classifies fuzzy techniques as crude fuzzy, fuzzy paradigm based, fuzzy aggregational and fuzzy inferential. For these fuzzy sets we must develop appropriate similarity measures and distances. We propose a class of such distances, derived from the fuzzy set equality and which we particularize according to various T-norms (fuzzy logical “or” operators). We also prove that the L1 metric naturally arises as a distance for fuzzy sets, considering the fuzzy set symmetric difference