Gradient-Based Optical Flow Method with Global Smoothness Constraint

This article presents a MATLAB implementation of gradient-based optical flow method, specifically focusing on its realization under global smoothness constraints. We begin by detailing the significance and advantages of global smoothness constraints, explaining how they integrate into the gradient-based optical flow framework through regularization terms in the energy minimization function. The implementation utilizes spatial and temporal gradient computations from image sequences, coupled with a smoothness penalty term that enforces coherence across neighboring pixels.

Next, we provide a step-by-step walkthrough of the algorithm's code structure, highlighting key MATLAB functions including: gradient calculation using finite differences, matrix formulation of the optical flow equations, and iterative solvers for the linear system. The implementation handles the smoothness constraint through a Laplacian-based regularization term that minimizes flow field variations.

We further discuss the algorithm's strengths in handling noise and producing coherent flow fields, while addressing limitations such as computational complexity and potential oversmoothing of motion boundaries. Potential improvements include adaptive smoothness weighting, multi-scale implementations, and integration with robust estimation techniques.

Finally, we summarize the core methodology and outline applications in computer vision domains like motion analysis, video stabilization, and object tracking, suggesting directions for future optimization and real-world deployment.