Given that decoder side motion vector refinement/derivation is a normative aspect of a coding system, the encoder will also have to perform the same error surface technique in order to not have any drift between the encoder's reconstruction and the decoder's reconstruction. Hence, all aspects of all embodiments are applicable to both encoding and decoding systems. In template matching, the refinement movement occurs only in the reference starting from the sub-pixel accurate center that is derived based on the explicitly signaled merge index or implicitly through cost evaluations. In bilateral matching (with or without averaged template), the refinements start in the reference lists L0 and L1 starting from the respective sub-pixel accurate centers that are derived based on the explicitly signaled merge index or implicitly through cost evaluations.