A New Multiplication-Free Block Matching Criterion

In block matching, the matching criterion plays a pivotal role in both matching accuracy and computational complexity. Mean squared error (MSE) is one most widely accepted benchmark for matching accuracy. To avoid multiplication operations for simpler implementation, the sum of absolute difference (SAD) is normally taken as a substitute to approximate MSE. In this paper, we first examine statistically the quantitative deviation of SAD from MSE in terms of maximum and average deviations. To minimize the average deviation, a new measure, namely, weighted sum of absolute difference (WSAD), is proposed in a two-element case first, for which an optimal weight is obtained theoretically. The weight is approximately adapted to 1/2 so that the weighting operation can be simplified to a shift operation, and the resulting multiplication-free WSAD also shows better matching accuracy with a smaller deviation from MSE than SAD. The two-element WSAD is further extended to a multi-element case in a multilevel pyramid structure. The proposed WSAD is experimentally validated by applying it in block motion estimation for video coding, showing better rate-distortion performance than SAD.