1. Apparatus for fast motion estimation for video pre-processing, comprising: at least one processor; a memory coupled to the at least one processor via a bus structure, wherein the memory comprises non-transitory computer-readable instructions, when executed by the at least one processor, are configured to (A) select a second-order distortion criterion for identifying a best reference image portion for comparison with a current image portion, said second-order distortion criterion being a Lagrange-optimized combination of a mean squared error criterion with an entropy criterion, (B) use said second-order distortion criterion to select an initial reference image portion as an initial starting point for a motion estimation search, said initial starting position being chosen based on at least one motion vector from a neighboring image portion, (C) perform a fast motion estimation search, wherein the non-transitory computer-readable instructions configured to perform a fast motion estimation search further comprise non-transitory computer-readable instructions further configured to (i) perform a diamond search starting from said initial reference image portion to identify a candidate best reference image portion, (ii) perform a nearest neighbor search starting from the candidate best reference image portion to identify either the candidate best reference image portion or a different neighboring reference image portion as a better reference image portion within a search range, (iii) re-identify the better reference image portion as the candidate best reference image portion, (iv) wherein the nearest neighbor search and the re-identification are repeated until, in performing the nearest neighbor search, either (a) the candidate best reference image portion is identified as the better reference image portion so that said second-order distortion criterion cannot be improved, or (b) any further search would exceed the adaptive search range cap, and (v) identify the candidate best reference image portion as the best reference image portion.