In this paper, some methods for representing objects usingpath-based distances are considered. The representations can be usedas anchor points when extracting medial representations of the objects.The distance transform (DT) is obtained by labeling each object elementwith the distance to the background. By local operations on the DT,different sets of anchor points can be obtained. We present two differentmethods based on local operations and prove that the representations arereversible, when this is the case. The methods are defined for weighteddistances based on neighborhood sequences, which includes for examplethe well known cityblock and chessboard distances.