2. Lecture 11 Adding Edge Element to Constraint Coarse-to-Fine Approach Optical Flow

3. 2 Edge Constraint for Noise Removal Vertical Edge Element ON/OFF Horizontal Edge Element ON/OFF Tends to create problems at edges If edge element “ON”, turn off smoothness

4. 3 Edge Constraint for Noise Removal Cost 3 = 0 Cost 3 = 1 Cost 3 = 0.1

5. 4 Edge Shape Precedences Vij Hij Dij HijVij

6. 5 Algorithm 1. Start Temperature T is high 2. Initialize D(i,j) = Random 0..10 3. For each pixel (i,j) if Dij = 0, Vij = 0, Hij = 0; E0=... ; P0 = e - E0 /T if Dij = 0, Vij = 0, Hij = 1; E1 =... ; P1 = e - E1 /T. if Dij = 10, Vij = 1, Hij = 1; E44 =... ; P44 = e – E44 /T For each Pi = Pi/Z Pi/sum(Pi) Sample for state K from pdf Pi Dij = 1, Vij = 0, Hij = 0 4. Reduce T 5. Repeat step 3-4 while E is not stable

7. 6 Coarse-to-Fine Coarse Fine Dm = 20 Dm 1/2 = 10 Dm 1/4 = 5 Solve First Left Right D Dhalf D1/4 10  1 4141 2

8. 7 Coarse-to-Fine - Pyramid

9. 8 Stereo – Parallel Axis Matching Points will be in the same row Same image Plane One Point

10. 9 Stereo – Parallel Axis Epipolar – Line formed by intersection of epipolar plane with image plane Epipolar Plane – Planes defined by 2 camera center and viewed 3-D point

11. 10 Motion – Optical Flow Movement of Image Points Optical Flow is written as (u,v) Frame 1 Frame 2

12. 11 Motion Correspondence Problem 1. Start Temperature T is high 2. u = Random (-5,-4,….,0,…., 4, 5); v = Random (-5,-4,….,0,…., 4, 5) 3. For every (edge) pixel if u = -5, v = -5; E0=... ; P0 = e - E0 /T if u = -5, v = -4; E1 =... ; P1 = e - E1 /T. if u = 5, v = 5; E121 =... ; P121 = e – E121 /T For each Pi = Pi/Z Pi/sum(Pi) Sample for (u,v) from pdf Pi 4. Reduce T 5. Repeat step 3-4 while E is not stable

13. 12 Stereo Matching : Disparity Can add 1-1 match constraint

14. 13 Barber Pole Illusion Aperture Problem – Perceive that motion is perpendicular to edge