In the domain of computer vision, optical flow stands as a cornerstone for unraveling dynamic visual scenes. However, the challenge of accurately estimating optical flow under conditions of large nonlinear motion patterns remains an open question. The image flow constraint is vulnerable to substantial displacements, and rapid spatial transformations. Inaccurate approximations inherent in numerical differentiation techniques can further amplify such intricacies. In response, this research proposes an innovative algorithm for optical flow computation, utilizing the higher precision of second-order Taylor series approximation within the differential estimation framework. By embracing this mathematical underpinning, the research seeks to extract more information about the behavior of the function under complex real-world scenarios and estimate the motion of areas with a lack of texture. An impressive showcase of the algorithm's capabilities emerges through its performance on renowned optical flow benchmarks such as KITTI (2015) and Middlebury. The average endpoint error (AEE), which computes the Euclidian distance between the calculated flow field and the ground truth flow field, stands notably diminished, validating the effectiveness of the algorithm in handling complex motion patterns.

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