1. EE 7730 Parametric Motion Estimation

2. Bahadir K. Gunturk2 Parametric (Global) Motion Affine Flow

3. Bahadir K. Gunturk3 Parametric (Global) Motion Perspective flow

4. Bahadir K. Gunturk4

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9. EE 7730 RANSAC: RANdom SAmple Consensus

10. Bahadir K. Gunturk10 Outliers Consider the least squares fit for optical flow: If some of the values are wrong, it will degrade the estimation.

11. Bahadir K. Gunturk11 Outliers It is best not to include outliers in the estimation. Outliers Best fit is degraded due to the outliers Line Fitting Problem: Given (x1,y1), …, (xN,yN); find the line y=ax+b

12. Bahadir K. Gunturk12 Robust Estimation Two step process:  Classify data points as outliers or inliers  Use inliers only to fit a model

13. Bahadir K. Gunturk13 RANSAC Repeat for k times:  Randomly choose n points (the smallest number of points required) from the data.  Estimate the parameters using these points.  For each data point other than these n points: Check if the data point is within a threshold, t, distance of current model; if it is, the data point is consistent with current model. The total number of data points that are consistent is model’s support. If the support is larger than a predetermined number, d, then there is a good fit. Re-estimate the parameters using these inliers. Choose the best fit with the smallest fitting error.

14. Bahadir K. Gunturk14 RANSAC Two samples and their supports for line-fitting

15. Bahadir K. Gunturk15 Example Find the perspective parameters from Hartley & Zisserman

16. Bahadir K. Gunturk16 Example Apply corner detectors to both images from Hartley & Zisserman

17. Bahadir K. Gunturk17 Example Find the best match within a search window. from Hartley & Zisserman

18. Bahadir K. Gunturk18 Example Initial match results 188 matched features in left image pointing to locations of corresponding right image features from Hartley & Zisserman

19. Bahadir K. Gunturk19 Example Inliers and outliers after RANSAC 89 outliers 99 inliers from Hartley & Zisserman

20. Bahadir K. Gunturk20 Panoramic Image Reconstruction Application: Mosaic construction Find features Match features Fit parametric model