# Another Example

## Stereo pair of the calibration apparatus

They are available in PGM format HERE for the first image (158k) and THERE for the second image (147k).

The reference points corresponding to the corners of the checker pattern are automatically extracted using our local software. They are available HERE for the first image and THERE for the second image. In total, there are
128 points, and they are *numbered*.

Their corresponding coordinates in 3D space, measured in a
reference frame attached to this apparatus, are available here
HERE. They are also *numbered*.

The camera perspective projection matrix can then be estimated
for each camera by minimizing the distances between image
points and the re-projections of their corresponding 3D
points. The resulting files are available
HERE for the first image and
THERE for the second image.

## Stereo pair of Hervé's head

The two images of Hervé's head are available in PGM format HERE for the first image (193k) and THERE for the second image (212k).

Points in each image are extracted using Harris corner detector, and are available HERE for the first image and THERE for the second image.
Matches have been established automatically by software `image-matching`, and are available HERE for the first image and THERE for the second image, and the
estimated fundamental matrix is available HERE.

The epipolar lines shown (corresponding to match 11, 30, 39 and 131)
are however those corresponding to the epipolar geometry
estimated using the classical calibration technique, in order to
show the discrepancy.

## Disparity map obtained with the calibration of the classical technique

The average distance between points and epipolar lines given by
the epipolar geometry estimated using the
classical calibration technique is 1.9 pixels, which is
quite high. As a matter of fact, our correlation-based stereo
system does not work correctly, as shown below. The darker a
point is, the closer it is to the cameras. Complete white points
are those not correlated. We can find that only a small part of
the face has been correlated.

## Comparison of average distance with different fundamental
matrices

Now, we combine both the set of matches on the two-plane model and that
found on the head, and compute another fundamental matrix which is
available HERE. The average distance for the whole
set of matches is 0.72 pixels. If we only consider the set of matches
on the head, the average distance is 0.97 pixels, which should be
compared with 1.9 pixels when the epipolar geometry estimated by the
classical method is used.
Here is a complete comparison of the results:

## Calibration result

Fundamental matrix estimated with the classical technique.

Fundamental matrix estimated from the pair of head images.

Fundamental matrix estimated by combining both sets of matches.

*Projective* camera projection matrix for the first camera and for the second camera.

*Euclidean* camera projection matrix for the first camera and for the second camera.

## 3D reconstruction of the two-plane model

It is available HERE.
orthographic projection on one of the two-plane mode

orthographic projection on a plane orthogonal to both planes

## 3D reconstruction of Hervé's head

Two views (with/without shading) of the reconstructed Hervé's head

## VRML model of the 3D reconstruction of Hervé's head

If you have a VRML
viewer, click HERE to view the 3D
reconstruction of Hervé's head. When *vrweb* is used, set
*Display* option to **Texturing** and turn
*off* **Lighting Calculations**. You can download the texture image for this model.

Zhengyou Zhang
Last modified: Fri Nov 22 10:24:46 MET