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