In this paper, we propose a novel method for the construction of a distance function and demonstrate its application in image segmentation. In algorithms for image segmentation, distance functions represent a criterion that divides pixels into groups of segments. We introduce two extended aggregation functions, extended powers product, and extended weighted arithmetic mean of powers. Their relevant properties are examined, as well as certain resulting properties of distance functions, which are constructed by an application of mentioned aggregation functions. In addition, one pixel descriptor, which is motivated by Local Bi- nary Pattern family of descriptors (LBPs), is introduced and discussed. In the experimental section, we present an application of the introduced extended aggregation functions and descriptor, by a construction of a new distance function,used in Fuzzy c-Means Clustering Algorithm (FCM) for image segmentation.