EE 7730 Parametric Motion Estimation Bahadir K Gunturk

Parametric (Global) Motion n Affine Flow Bahadir K. Gunturk 2

Parametric (Global) Motion n Perspective flow Bahadir K. Gunturk 3

EE 7730 RANSAC: RANdom SAmple Consensus Bahadir K. Gunturk

Outliers n Consider the least squares fit for optical flow: If some of the

Outliers n It is best not to include outliers in the estimation. Line Fitting

Robust Estimation n Two step process: q q Classify data points as outliers or

RANSAC n Repeat for k times: q q q Randomly choose n points (the

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

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

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

Example n Find the best match within a search window. from Hartley & Zisserman

Example n Initial match results from Hartley & Zisserman 188 matched features in left

Example n Inliers and outliers after RANSAC from Hartley & Zisserman Bahadir K. Gunturk

Panoramic Image Reconstruction Find features Match features Fit parametric model Application: Mosaic construction Bahadir

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EE 7730 Parametric Motion Estimation Bahadir K. Gunturk

Parametric (Global) Motion n Affine Flow Bahadir K. Gunturk 2

Parametric (Global) Motion n Perspective flow Bahadir K. Gunturk 3

Bahadir K. Gunturk 4

Bahadir K. Gunturk 5

Bahadir K. Gunturk 6

Bahadir K. Gunturk 7

Bahadir K. Gunturk 8

EE 7730 RANSAC: RANdom SAmple Consensus Bahadir K. Gunturk

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

Outliers n It is best not to include outliers in the estimation. Line Fitting Problem: Given (x 1, y 1), …, (x. N, y. N); find the line y=ax+b Outliers Best fit is degraded due to the outliers Bahadir K. Gunturk 11

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

RANSAC n Repeat for k times: q q q 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: n n 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. Bahadir K. Gunturk 13

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

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

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

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

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

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

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