Assignment 3

Topic: Camera Calibration

Due on or before: 03 October, 2021

Maximum Marks: 5

This assignment has two parts: using a calibrated stereo camera system, and calibrating cameras.

Using a Calibrated Stereo System

Here is a stereo image pair [please click on the above images to save/download the full-sized 384x288 images]. Let use refer to the two cameras as the `Left Camera' and the `Right Camera', respectively. Tsai's method was used for the calibration: The calibration information is as follows (all parameters are according to the Tsai camera model):
The physical sensor size is 8.8mm by 6.6mm (width by height), and the image size is 384 by 288. Here, assume that the radial distortion is negligible, and that there is no skew factor.

For the Left Camera:
u_0 = 186.11619191 pixels
v_0 = 164.15264850 pixels
sx = 1.0166343583
f = 16.551086572 mm
Tx = -621.06754176 mm
Ty = -58.069551431 mm
Tz = 984.55520522 mm
Rx = 0.15540547317 radians
Ry = 0.27888534145 radians
Rz = 0.017528059127 radians

For the Right Camera:
u_0 = 193.89675221 pixels
v_0 = 144.43431051 pixels
sx = 1.0116374294
f = 16.842326127 mm
Tx = -659.19737229 mm
Ty = -76.572279751 mm
Tz = 1055.8014876 mm
Rx = 0.16112722935 radians
Ry = 0.36219027236 radians
Rz = 0.026911763000 radians

The first part of the assignment is as follows:

Calibrating Cameras

Here are two images of a calibration object taken as a part of a calibration set for one camera. (What is the significance of the 16mm in the names of the images? The lens is marked 16mm. The actual focal length one gets after calibration may not exactly be 16mm. Why? The calibration gives is the parameters of the corresponding pin-hole model, to which the thin lens model is a rough approximation.) [please click on the above images to save/download the full-sized 384x288 images]. (Why two images for one calibration set? We need a set of points in 3-D general position, not all coplanar - to get a full set of calibration points.) The world coordinate system is such that the first image corresponds to Z_w = 0mm, and the second image corresponds to Z_w = 200mm. (i.e., we use the same calibration box at two depth positions to generate a set of 3-D world points.) The calibration object has 25 squares, each with 4 corners. This gives a total of 100 points for Z_w = 0mm, and 100 more for Z_w = 200mm. Each square has side 40mm, and two squares are horizontally and vertically separated by 20mm. Assume the upper left corner of the upper left square to have world coordinates X_w = 500mm, Y_w = 0mm (and Z_w = 0mm or 200mm, depending on whether it has been taken from the first position, or the second one). Thus, the raw material for calibration will be a set of 200 5-tuples:
[X_w, Y_w, Z_w, x y]
where [x, y] are the image coordinates of the corresponding point, which you can pick off the image - either manually, or semi-manually, by using the output of a corner detector, or a junction detector, or a combination of line detectors - any way is fine.
In the second part of this assignment,
Demo Schedule:

(To be announced)

Sumantra Dutta Roy  Department of Electrical Engineering, IIT Delhi, Hauz Khas,
New Delhi - 110 016, INDIA.