Variational-Bayes Optical Flow

• Published in: Journal of mathematical imaging and vision 2014-11, Vol.50 (3), p.199-213
• Main Authors: Chantas, Giannis, Gkamas, Theodosios, Nikou, Christophoros
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Applied sciences; Artificial intelligence; Computer Science; Computer science; control theory; systems; Exact sciences and technology; Image Processing and Computer Vision; Linear inference, regression; Mathematical Methods in Physics; Mathematics; Pattern recognition. Digital image processing. Computational geometry; Probability and statistics; Sciences and techniques of general use; Signal,Image and Speech Processing; Statistics
• ISSN: 0924-9907; 1573-7683
• DOI: 10.1007/s10851-014-0494-3

The Horn-Schunck (HS) optical flow method is widely employed to initialize many motion estimation algorithms. In this work, a variational Bayesian approach of the HS method is presented, where the motion vectors are considered to be spatially varying Student’s t -distributed unobserved random variables, i.e., the prior is a multivariate Student’s t -distribution, while the only observations available is the temporal and spatial image difference. The proposed model takes into account the residual resulting from the linearization of the brightness constancy constraint by Taylor series approximation, which is also assumed to be a spatially varying Student’s t -distributed observation noise. To infer the model variables and parameters we recur to variational inference methodology leading to an expectation-maximization (EM) framework with update equations analogous to the Horn-Schunck approach. This is accomplished in a principled probabilistic framework where all of the model parameters are estimated automatically from the data. Experimental results show the improvement obtained by the proposed model which may substitute the standard algorithm in the initialization of more sophisticated optical flow schemes.