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Fast and accurate block-based motion estimation (BME) is desired in many video coding systems. By conducting block matching in lower dimensional projection space, followed by candidate exclusion through thresholding, projection-based BME (PBME) methods can run several times faster than the exhaustive full search method, with little loss in accuracy. In PBME methods, the appropriate choice of threshold is critical, as the threshold controls the important trade-offs between complexity and accuracy. In the literature, PBME methods rely on fixed thresholds that were chosen on an ad hoc basis. This paper provides an in-depth analysis of errors due to thresholding in PBME, based on the sum absolute difference (SAD) as the matching criterion. A new PBME method is proposed that can adaptively select thresholds according to a target probability of error. Simulation results show that this adaptive method can offer highly scalable complexity/accuracy tradeoffs desired in many fast BME algorithms.