时空MRF描述的连续视频帧运动速度场和概率模型的贝叶斯同时推断
Simultaneous Bayesian inference of motion velocity fields and probabilistic models in successive video-frames described by spatio-temporal MRFs
摘要：
我们数值研究的平均场贝叶斯方法的马尔可夫链蒙特卡罗方法的协助下，估计运动速度场和概率模型，同时在连续的数字图像所描述的时空马尔可夫随机场。初步建设我们的程序，我们发现，平均场变量在迭代发散，由于不适当的正规化项的归一化因子出现在后验。为了避免这个困难，我们通过引入比例因子来重新调整正则化项，并通过最小化均方误差来优化它。我们确认，最佳比例因子稳定的平均场迭代过程中的运动速度估计。接下来，我们尝试通过使用基于相对于超参数的边际似然（II型似然）的梯度下降的玻尔兹曼机类型学习算法来估计包括正则化项的超参数的最优值，所述正则化项从宏观上定义我们的概率模型。在我们的框架中，可以同时估计概率模型（超参数）和运动速度场。我们发现我们的运动估计比Zhang和Hanouer（1995）的结果要好得多，在Zhang和Hanouer（1995）中，超参数被设置为一些ad-hoc值，而没有任何理论依据。
英文摘要：
We numerically investigate a mean-field Bayesian approach with the assistance of the Markov chain Monte Carlo method to estimate motion velocity fields and probabilistic models simultaneously in consecutive digital images described by spatio-temporal Markov random fields. Preliminary to construction of our procedure, we find that mean-field variables in the iteration diverge due to improper normalization factor of regularization terms appearing in the posterior. To avoid this difficulty, we rescale the regularization term by introducing a scaling factor and optimizing it by means of minimization of the mean-square error. We confirm that the optimal scaling factor stabilizes the mean-field iterative process of the motion velocity estimation. We next attempt to estimate the optimal values of hyper-parameters including the regularization term, which define our probabilistic model macroscopically, by using the Boltzmann-machine type learning algorithm based on gradient descent of marginal likelihood (type-II likelihood) with respect to the hyper-parameters. In our framework, one can estimate both the probabilistic model (hyper-parameters) and motion velocity fields simultaneously. We find that our motion estimation is much better than the result obtained by Zhang and Hanouer (1995) in which the hyper-parameters are set to some ad-hoc values without any theoretical justification.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
