Lecture 11Lecture 11

Adding Edge Element to Constraint

Coarse-to-Fine Approach

Optical Flow

2

Edge Constraint for Noise RemovalEdge Constraint for Noise Removal

ijijijijijjim n

ijij vIIhIIIFE

11 211

211

1

1

1

1

2

Vertical Edge ElementON/OFF

Horizontal Edge ElementON/OFF

Tends to create problems at edgesIf edge element “ON”, turn off smoothness

""322 esShapeOfEdgvh ijij

3

Edge Constraint for Noise RemovalEdge Constraint for Noise Removal

Cost3 = 0

Cost3 = 1

Cost3 = 0.1

4

Edge Shape PrecedencesEdge Shape Precedences

Vij

HijDij

Dij Hij Vij

5

AlgorithmAlgorithm

1. Start Temperature T is high2. Initialize D(i,j) = Random 0..103. For each pixel (i,j)

if Dij = 0, Vij = 0, Hij = 0; E0= ... ; P0 = e - E0 /Tif Dij = 0, Vij = 0, Hij = 1; E1 = ... ; P1 = e - E1 /T

.

.if Dij = 10, Vij = 1, Hij = 1; E44 = ... ; P44 = e – E44 /TFor each Pi = Pi/Z Pi/sum(Pi)

Sample for state K from pdf Pi Dij = 1, Vij = 0, Hij = 0

4. Reduce T5. Repeat step 3-4 while E is not stable

6

Coarse-to-FineCoarse-to-Fine

Coarse

FineDm = 20

Dm1/2 = 10

Dm1/4 = 5Solve First

Left Right D

Dhalf

D1/4

101

41

2

7

Coarse-to-Fine - PyramidCoarse-to-Fine - Pyramid

8

Stereo – Parallel AxisStereo – Parallel Axis

Matching Points will be in the same row

Same image Plane

One Point RijX

9

Stereo – Parallel AxisStereo – 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 FlowMotion – Optical Flow

Movement of Image Points

Optical Flow is written as (u,v)tt xxx

dt

dxu 1

tt yyydt

dyv 1

Frame 1 Frame 2

11

Motion Correspondence ProblemMotion Correspondence Problem

1. Start Temperature T is high2. 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 /Tif u = -5, v = -4; E1 = ... ; P1 = e - E1 /T

.

.if u = 5, v = 5; E121 = ... ; P121 = e – E121 /TFor each Pi = Pi/Z Pi/sum(Pi)

Sample for (u,v) from pdf Pi4. Reduce T5. Repeat step 3-4 while E is not stable

12

Stereo Matching : DisparityStereo Matching : Disparity

2),()1,(12

),(),1(1

1

1

1

1

21),(

2),( yxyxyxyx

m nvyuxyx uuuuIIE

2),()1,(12

),(),1(1 yxyxyxyx vvvv

Can add 1-1 match constraint

13

Barber Pole IllusionBarber Pole Illusion

Aperture Problem – Perceive that motion is perpendicular to edge