Variational motion estimation in digital images with fluid and rotational motion

Abstract

Motion estimation is a fundamental problem in computer vision and image processing. newlineIt refers to the process of calculating the motion vectors that describe the displacement newlineof pixels or features between consecutive frames in a video sequence. It involves deter- newlinemining how each pixel s position changes from one frame to the next due to pixel motion. newlineUnderstanding motion is essential for various applications like analyzing dynamic scenes, newlinetracking objects, stabilizing videos, compressing video data efficiently, robot navigation newlineand so on. newlineOver the years, optical flow has emerged as a natural candidate for motion estimation newlinedue to its ability to capture motion patterns at pixel-levels. The pioneering contribution newlineof Horn and Schunck opened up new directions for estimating rigid body motions within newlinea variational framework. newlineHowever, the Horn and Schunck (HS) model has limitations when it comes to rota- newlinetional and fluid motion estimation, where the intensity patterns themselves can change newlinesignificantly due to deformation, turbulence or complex interactions. Due to these newlinechanges, the brightness constancy assumption of traditional optical flow methods is vi- newlineolated and pixel correspondence is lost. Consequently, the performance of the optical newlineflow algorithms, including the Horn-Schunck method, deteriorates when applied to these newlinescenarios. newlineThe current research works aims to address these fundamental issues associated with newlinemotion estimation in digital images with fluid and rotational motion. We first consider a newlinesingle-phase linear refinement model for accurate estimation of rotational motion. This newlineis a standard Horn and Schunck optical flow model with an additional constraint term newlinepenalizing the curl of the flow. While the linear refinement model shows good results newlineon rotational sequences, however, it does not capture the flow edges accurately due to newlinethe isotropic smoothness assumption. In view of this, we study the nonlinear refinement newlinemodel by replacing the quadratic smoothness term with the total-variation smoothness newlinet