1. Nick Hirsch: Progress Report

2. Track features from frame to frame using KLT Calculate their optical flow. Determine Focus of Expansion The center that all other points seem to expand from when moving forward. Determine which points aren’t expanding outward from the Focus of Expansion. Track Features (KLT) Calculate Optical Flow Compare to FoE Direction Field Update FoE

3. As you can see, the pixels belonging to stationary objects move along the lines emanating from the FoE.

4. Green Arrows = Moving Red Arrows = Stationary

5.  Jan Prokaj handed his code over to me.  Attempted to reproduce Jan’s results. ◦ His algorithm relies on the video being jitter free. ◦ His estimate of the Focus of Expansion was highly inaccurate.

6. Blue Square – Current estimate of Focus of Expansion Yellow Square – Smoothed estimate of Focus of Expansion

7.  We can assume most objects in the given video are stationary and their pixels expand outwards from the FoE.  To find the true FoE(yellow) given the optical flow vectors(black), start with a hypothesized FoE(green), generate some neighbor FoEs, calculate their energy, and update the hypothesis FoE.

8.  We assume all pixels should be traveling radially outward from the Focus of Expansion.  To calculate an updated FoE, we want to minimize the SSD of the direction that feature F i should be traveling.

9.  w i – The magnitude of the feature point I ◦ I use this weight because features with larger magnitudes are often more accurate.  Theta FoE,i – The direction of the FoE field at i  Theta i – The direction of the feature point

10.  Another way to find the FoE is to try to solve for the intersecting point of all the optical flow vectors.  To do this, I convert the optical flow vectors into homogenous lines, creating an Nx3 matrix, then I perform the Singular Value Decomposition on it. The resulting right vector of the Nx3 matrix gives me the point where the lines all intersect.

13.  To further improve my estimation of the FoE, I’m going to use RANSAC to weed out the outliers amongst the optical flow vectors.  Next, I’d like to determine a good method for clustering vectors classified as moving.