Markov Random Field Function minimized by Stochastic Gradient Descent

• Main Authors: Roman Rivera, Luis Rogelio, Pedraza Ortega, Jesus Carlos, Aceves Fernandez, Marco Antonio, Ramos Arreguin, Juan Manuel, Hurtado, Efren Gorrostieta, Vargas Soto, Jose Emilio
• Format: Conference Proceeding
• Language: English
• Subjects: Adaptive optics; Cameras; Convergence; Markov Random Field; Markov random fields; Optical flow; Optimization; Stochastic Gradient Descent
• ISSN: 2642-3766
• DOI: 10.1109/ICEEE.2019.8884498

A Markov Random Field Function (MRF) is used to evaluate optical flow from two consecutive images in time, it requires to be minimized or maximized an error output in order to accept or reject a optical flow value for one pixel intensity in the first image with respect a pixel intensity in the second one. In the present paper, Stochastic Gradient Descent is proposed as an optimization method to minimized the error in the Markov Random Field Function, Gradients are computed in horizontal and vertical axis to get a direction which is used to compute the following value to be evaluated by the function until convergence is reach respect a stop condition. Experiments used a pair of images taken using only one camera from the same scene, one image taken after the other with overlapping and non overlapping image sections. A pixel is selected from the first image, then evaluating the correspondence in the second image with the MRF Function, if it returns an aceptable minimum error value, and optical flow value is obtained. The method proposed in the present paper is used to compute this minimum error value using Stochastic Gradient Descent (SGD) as a minimization method, experiments will probe SGD can be used for this goal and the proposed method will be discussed describing how it works locating the optical flow in a localized area in the pixel neighborhood of the first image.