1. Course 6 Stereo

2. Course 6 Stereo Depth Stereo
The distance from camera center to scene points, is an important information to understand the 3-dimentional scene from its images. 
Stereo
A vision technique to compute the depth of scene by the position difference of a scene point in the two camera’s image planes.

3. Figure 1

4. 1. Typical stereo imaging system
Two identical cameras.
Left camera and right camera are separated by distance b, the “baseline”.
Two image planes and image coordinates are parallel, cameras’ optical axis are parallel.
Epipolar plane: the plane passing through the camera centers and the scene point is called epipolar plane.
Epipolar lines: the intersections of the epipolar plane and image planes are called epipolar lines

6. Def. feature correspondences:
the two features in different images that are the projections from the same feature in the scene. Usually, point feature is used, which is called point correspondence, or conjugate point pairs.
Def. Disparity:
the distance between the points of a pair of point correspondence when the two image are supperimposed.

7. From Figure 1,
left camera:
right camera:
we can solve for Z:

8. Similarly, we can obtain:
If we use
to denote 3D point , and
to denote image point of left camera.

9. Then,
2. Stereo matching:
For each point in the left image, find the corresponding point in the right image.
The two points of a correspondence of two images lie on the same epipolar plane. Thus, if stereo system is typically arranged, the two points should lie on the same rows of left and right image planes.

10. Reference of matching criteria.
epipolar constraint.
disparity constraint (disparity cannot be too large)
  edge orientation
edge strength.
Algorithm (coarse to fine matching)
a)  Filter images with wider Gaussian filter .
b) Compute edge points of each image.
c) Find point correspondences at coarse image level.
d) Refine the disparity estimates by matching at
finer scales.

11. 3. Stereo of arbitrary camera arrangement:
Image points still lie on eppipolar plane and
each epipolar lines.
epipolar lines are not image rows.

13. 4. Structured Lighting
Another method using triangular relation to find the depth of 3D scene.

14. 3D point
Focal length
Camera
Light projector
Projection angle
and are into paper

15. From the figure, the normal of projecting plane is
the baseline:
Since scene point
lies in projecting plane, we have

16. As central projection, scene point can be expressed by image point.
where t is parameter.
Substitute the expressions of , and into the triple-product, we can solve for parameter t

17. Thus, we finally got