HornSchunck

HornSchunck is a mathematical model used to estimate the optical flow in a sequence of images. Optical flow refers to the pattern of apparent motion of objects, surfaces, and edges in a visual scene caused by the relative motion between an observer and the scene. The HornSchunck method is a foundational technique in computer vision for computing this motion.

The core idea behind HornSchunck is to enforce two main constraints. The first is the brightness constancy assumption, which states that the intensity of a pixel remains constant over time, even as it moves. Mathematically, this is expressed as the total derivative of image intensity with respect to time being zero. The second constraint is a smoothness assumption, which posits that the optical flow vector should vary smoothly across the image. This means that neighboring pixels are assumed to have similar motion.

To solve for the optical flow, HornSchunck uses an iterative approach that minimizes an error function. This function balances the error from the brightness constancy constraint with a term that penalizes large gradients in the flow field, thus enforcing smoothness. The algorithm starts with an initial guess for the flow and iteratively refines it until convergence.

While influential, the HornSchunck method has limitations. It tends to blur motion at object boundaries where brightness constancy might not hold perfectly, and it can struggle with large displacements or significant illumination changes. Despite these drawbacks, it laid the groundwork for many subsequent optical flow algorithms.