This is essentialy a Bayesian implementation of the classical Horn-Schunck optical flow algorithm. The optical flow inference is formulated as an inverse problem which is solved via Gibbs sampling. It is based primarily on [1] however there are some slight changes to improve efficiency. In particular the optical flow is split into the vertical (u) and horizontal (v) component and each is sampled from its conditional pdf separately. Furthermore a more efficient method is used for sampling from a high-dimensional Gaussian distribution [2].

[1] Sun, J., Quevedo, F. J. and Bollt, E. (2018) ‘Bayesian Optical Flow with Uncertainty Quantification’, Inverse Problems. Available at: https://arxiv.org/abs/1611.01230.

[2] F. Orieux, O. Féron, and J. Giovannelli, “Sampling high-dimensional Gaussian distributions for general linear inverse problems,” IEEE Signal Process. Lett., vol. 19, no. 5, p. 251, 2012