An E cient Two-pass MAP-MRF Algorithm for Motion Estimation Based on Mean Field Theory

This paper presents a two-pass algorithm for estimating motion vectors from image sequences. In the proposed algorithm, the motion estimation is formulated as a problem of obtaining the Maximum A Posteriori in the Markov Random Field (MAP-MRF). An optimization method based on the Mean Field Theory (MFT) is opted to conduct the MAP search. The estimation of motion vectors is modeled by only two MRF's, namely, the motion vector eld and unpredictable eld. Instead of utilizing the line eld, a truncation function is introduced to take care of the discontinuity between the motion vectors on neighboring sites. In this algorithm, a \double threshold" preprocessing pass is rst employed to partition the sites into three regions, whereby the ensuing MFT-based pass for each MRF is conducted on one or two of the three regions. With this algorithm, no signiicant diierence exists between the block-based and pixel-based MAP searches any more. Consequently, a good compromise between precision and eeciency can be struck with ease. In order to render our algorithm more resilient against noises, the Mean Absolute Diierence (MAD) instead of Mean Square Error (MSE) is selected as the measure of diierence which is more reliable according to the knowledge of robust statistics. This is supported by our experimental results from both synthetic and real-world image sequences. The proposed two-pass algorithm is much faster than any other MAP-MRF motion estimation methods reported in the literature so far.