1. Binocular Stereo Vision
Stereo viewing geometry and the stereo correspondence problem

2. Constraints on stereo correspondence
Uniqueness
each feature in the left image matches with only one feature in the right (and vice versa…)
Similarity
matching features appear “similar” in the two images
Continuity
nearby image features have similar simple version: matching features have similar disparities
Epipolar constraint
vertical positions, but…

3. Marr-Poggio cooperative stereo algorithm
 matches corresponding black & white dots in the left & right images
 stereo disparities computed by a parallel network of simple computing elements
 iterative: state of network changes with each iteration, to resolve matching ambiguity
disparity map emerges over time

4. Input x 1 1 y
left
right
(epipolar constraint)

5. 3D cooperative network: initial state
C(x,y,d) = 1 if L(x,y) = R(x+d,y)
C(x,y,d) = 0 otherwise
(similarity constraint)
3D cooperative network: initial state x
C(x,y,d) +3 +2 +1 -1 -2 -3 y d +3 +2 +1 -1 -2 -3 1 1 1 1 1
left
right

6. Updating the network
For each iteration, the state of every element in the 3D network is updated:
(1) S(x,y,d) = Ct(x,y,d) + E – ε I
(2) Ct+1(x,y,d) = 1 if S(x,y,d) ≥ 
= 0 if S(x,y,d) < 
“inhibition” evidence for other disparities at location (x,y)
support for disparity d at location (x,y)
“excitation” neighborhood support for disparity d at location (x,y)
current state of network (0 or 1)
threshold
new, updated state at time t+1

7. 3D cooperative network x y d C(x,y,d) = 0 or 1 left right 1 1 1 1 1 +3+2 +1 -1 -2 -3 y d +3 +2 +1 -1 -2 -3 1 1 1
C(x,y,d) = 0 or 1 1 1
left
right

8. Enforcing the continuity constraintx 1
disparity = +2 y
E = sum of 1’s in a neighborhood around (x,y)
E = 10
S(x,y,d) = Ct(x,y,d) + E – ε I

9. 3D cooperative network C(x,y,d) x y d 1 1 1 +3 +2 +1 -1 -2 -3 +3 +2 +1-1 -2 -3 y d +3 +2 +1 -1 -2 -3 1 1 1

10. Enforcing the uniqueness constraintx +3 +2 +1 -1 -2 -3 1
I = total number of alternative disparities d
I = 3
S(x,y,d) = Ct(x,y,d) + E – ε I

11. x x 1 1 y y x
right
left 1
initial state:
C0(x,y,d)
d = -1 y
E =

12. row 3: Y = 3 I = left right x d initial state: C0(x,y,d) 1 1
left
right x +2 +1 -1 -2 1
Y = 3 d
initial state:
C0(x,y,d)
I =
S(x,y,d) = Ct(x,y,d) + E – ε I
Ct+1(x,y,d) =
(ε = 2)
( = 3)