Distance between vector-valued fuzzy sets based on intersection decomposition with applications in object detection

Abstract

We present a novel approach to measuring distance between multi-channel images, suitably represented by vector-valued fuzzy sets. We first apply the intersection decomposition transformation, based on fuzzy set operations, to vector-valued fuzzy representations to enable preservation of joint multi-channel properties represented in each pixel of the original image. Distance between two vector-valued fuzzy sets is then expressed as a (weighted) sum of distances between scalar-valued fuzzy components of the transformation. Applications to object detection and classification on multi-channel images and heterogeneous object representations are discussed and evaluated subject to several important performance metrics. It is confirmed that the proposed approach outperforms several alternative single- and multi-channel distance measures between information-rich image/object representations.