Horn and Schunck proposed a method for computing optical flow from image sequences. Optical flow is the apparent velocity of brightness patterns in an image and cannot be computed locally due to the lack of sufficient constraints. The method assumes that the apparent velocity of brightness varies smoothly almost everywhere in the image. An iterative algorithm is used to compute the optical flow, which is robust to coarse spatial and temporal quantization and insensitive to brightness quantization and additive noise. The algorithm uses a smoothness constraint to ensure that the flow velocity varies smoothly, minimizing the square of the gradient magnitude of the flow velocity. The method also accounts for the Laplacian of the flow velocities, which is approximated using local averages. The algorithm is tested on synthetic image sequences and is shown to handle cases where the smoothness assumption is violated at singular points or along lines. The method is also applied to real-world scenarios, including rigid body motions and rotating objects. The results show that the algorithm can accurately estimate optical flow even in the presence of noise and quantization errors. The method is robust and efficient, making it suitable for a wide range of applications in computer vision and image processing.Horn and Schunck proposed a method for computing optical flow from image sequences. Optical flow is the apparent velocity of brightness patterns in an image and cannot be computed locally due to the lack of sufficient constraints. The method assumes that the apparent velocity of brightness varies smoothly almost everywhere in the image. An iterative algorithm is used to compute the optical flow, which is robust to coarse spatial and temporal quantization and insensitive to brightness quantization and additive noise. The algorithm uses a smoothness constraint to ensure that the flow velocity varies smoothly, minimizing the square of the gradient magnitude of the flow velocity. The method also accounts for the Laplacian of the flow velocities, which is approximated using local averages. The algorithm is tested on synthetic image sequences and is shown to handle cases where the smoothness assumption is violated at singular points or along lines. The method is also applied to real-world scenarios, including rigid body motions and rotating objects. The results show that the algorithm can accurately estimate optical flow even in the presence of noise and quantization errors. The method is robust and efficient, making it suitable for a wide range of applications in computer vision and image processing.