This paper presents a path-based distance where local displacement costs vary both according to the displacement vector and with the travelled distance. The corresponding distance transform algorithm is similar in its form to classical propagation-based algorithms, but the more variable distance incre- ments are either stored in look-up-tables or computed on-the-fly. These distances and distance trans- form extend neighborhood-sequence distances, chamfer distances and generalized distances based on Minkowski sums. We introduce algorithms to compute a translated version of a neighborhood sequence distance map both for periodic and aperiodic sequences and a method to derive the centered distance map. A decomposition of the grid neighbors, in ℤ² and ℤ³, allows to significantly decrease the number of displacement vectors needed for the distance transform. Overall, the distance transform can be com- puted with minimal delay, without the need to wait for the whole input image before beginning to provide the result image.