An Implementation of Combined Local-Global Optical Flow

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Abstract
Optical Flow (OF) approaches for motion estimation calculate vector fields for the apparent velocities of objects in image sequences. In 1981 Horn and Schunck (HS) introduced two basic assumptions: 'brightness value constancy' and 'smooth variation' to estimate a smooth OF field over the entire image -global approach-. In parallel, Lucas and Kanade (LK) assumed constant motion patterns for image patches, estimating piecewise-homogeneous OF fields -local approach-. Several variations of these approaches exist today. Here we present the combined local-global (CLG) approach by Bruhn et al. which encompasses properties of HS-OF and LK-OF, aiming to improve the OF accuracy for small-scale variations, while delivering the HS-OF dense and smooth fields. A multiscale implementation is provided for 2D images, together with two numerical solvers: Successive Over-Relaxation and the faster Pointwise-Coupled Gauss-Seidel by Bruhn et al.. The algorithm works on gray-scale (single channel) images, with color images being converted prior to the OF computation.

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