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Enhancing Optical Flow with Edge Elements: A Coarse-to-Fine Constraint Approach

This lecture explores the integration of edge elements into the optical flow computation, focusing on a coarse-to-fine approach for effective noise removal and enhancing edge detection. It discusses the challenges at edges, the impact of activating or deactivating edge elements on the smoothness constraint, and presents an algorithm for processing pixel states through iterations of simulated annealing. Techniques such as stereo matching and motion correspondence are examined to solve disparity and improve optical flow accuracy, while addressing issues like the Barber Pole illusion and the aperture problem.

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Enhancing Optical Flow with Edge Elements: A Coarse-to-Fine Constraint Approach

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

  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

  3. Edge Constraint for Noise Removal Cost3 = 0 Cost3 = 1 Cost3 = 0.1

  4. Edge Shape Precedences Vij Dij Hij Hij Vij Dij

  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

  6. Coarse-to-Fine 101 Right Left D Fine Dm = 20 Dhalf Dm1/2 = 10 41 D1/4 Dm1/4 = 5 Solve First Coarse 2

  7. Coarse-to-Fine - Pyramid

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

  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

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

  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

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

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

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