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## Optical Flow

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**Optical Flow**Donovan Parks**What is optical flow?**• a method for estimating the motion of objects within an image sequence • answers the question “how are my pixels (objects) moving?”**Where is optical flow used?**• widely used in computer vision: • motion detection • camera jitter correction • video compression • video segmentation • basis on many special effects used in the movie industry**Why is calculating optical flow difficult?The Aperture**Problem • often insufficient information in a local area to fully determine motion**Motion constraint equation**• Ix, Iy, and It are just intensity derivatives • easily calculated for images • H&S suggest: • vx, vy are the pixel velocities we want to find Problem One equation with two unknowns!**What constraint do Horn and Schunck suggest?**• Global smoothness constraint on velocity field • Why? • Neighbouring pixels from a rigid object must have similar velocities • Therefore, the velocity field in the image should vary smoothly in most places**Horn-Schunck cont…**• λ controls the influence of the smoothness constraint • Iterative solution exists to find the minimum • all the ugly details are in the paper!**Example: Sparse Optical Flow**Example by David M. Stavens (http://ai.stanford.edu/~dstavens/)**Discussion: A word of caution**• Brightness constancy assumption requires: • constant illumination conditions • objects to be at least locally rigid • Higher level processing often needed to “weed out” usable information from an optical flow algorithm**Conclusion**• Major contribution of H&S: first to propose formal method for calculating optical flow • Critical point in calculating optical flow is finding another “good” equation to go along with the motion constraint equation**Questions?**Thank you!