4. Calibration Programming Exercises (40 points): Implement the direct parameter calibration method in order to (1) learn how to use SVD to solve systems of linear equations; (2) understand the physical constraints of the camera parameters; and (3) understand important issues related to calibration, such as calibration pattern design, point localization accuracy and robustness of the algorithms. Since calibrating a real camera involves lots of work in calibration pattern design, image processing and error controls as well as solving the equations, we will mainly use simulated data to understand the algorithms. As a by-product we will also learn how to generate 2D images from 3D models using a “virtual” pinhole camera. The calibration procedure has the following three steps:
i. Use the accurately simulated data (both 3D world coordinates and 2D image coordinates) to the algorithms, and compare the results with the “ground truth” data (which are given in step (a) and step (b)). Remember you are practicing a camera calibration, so you should pretend you know nothing about the camera parameters (i.e. you cannot use the ground truth data in your calibration process). However, in the direct calibration method, you could use the knowledge of the image center (in the homogeneous system to find extrinsic parameters) and the aspect ratio (in the Orthocenter theorem method to find image center).
ii. Show experimentally whether the unknown aspect ratio matters in estimating the image center, and how the initial estimation of image center affects the estimating of the remaining parameters. Give a solution to solve the problems if any and implement it.
iii. Accuracy Issues. Add in some random noises to the simulated data and run the calibration algorithms again. See how the “design tolerance” of the calibration target and the localization errors of 2D image points affect the calibration accuracy. For example, you can add 0.5 mm random error to 3D points and 1.0 pixel random error to 2D points. Also analyze how sensitive of the Orthocenter method is to the extrinsic parameters in imaging the three sets of the orthogonal parallel lines. (* extra points:10)
In all of the steps, you should give you results using either tables or graphs, or both of them.
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