Knowledge test and application exercises

Must the intrinsic parameters of a camera be estimated again if we move the camera?

We use a camera CCD 1/2' which sensor size equals 6.4×4.8 mm. Its resolution equals 800×600 pixels. We use a 25mm prime lens objective.

1. Calculate the size of the pixels.

2. Calculate the value of .

3. Calculate the value of (that) the calibration must provide.

We want to estimate the model R3D1P1 of a camera (12 intrinsic parameters). Can we calibrate this camera with the photogrammetric approach using three views of a 9-point target? Explain.

The calibration of a camera the resolution of which is 800× 600 pixels (sensor with square pixels) provided the following results:

What enables us to suspect that the calibration is wrong?

You must show that in the case of a model of parametric distortion type 1 (1st order radial distortion), equation (14) of the lesson linking the distorted and non-distorted coordinates enables to calculate the non-distorted coordinates (correction from the distortion) by the resolution of a third degree equation of the form:

Calculate both coefficients and .

Solution

Distortion R1:

According to equation (13) of the lesson:

(1) [zoom...]

According to (1):

(2)

Namely:

(3)

Reporting in the 1st equation (1) comes:

(4)

Namely:

(5)

Of the form:

(6)

The equation (6) enables calculating , and then the equation (3) makes it possible to calculate .