Description
Problem 1:
In the given video, a red ball is thrown against a wall. Assuming that the trajectory of the ball follows
the equation of a parabola:
1. Detect and plot the pixel coordinates of the center point of the ball in the video. [10]
(Hint: Read the video using OpenCV’s inbuilt function. For each frame, filter the red channel)
2. Use Standard Least Squares to fit a curve to the extracted coordinates. For the estimated
parabola you must,
a. Print the equation of the curve. [5]
b. Plot the data with your best fit curve. [5]
3. Assuming that the origin of the video is at the top-left of the frame as shown below, compute
the x-coordinate of the ball’s landing spot in pixels, if the y-coordinate of the landing spot is
defined as 300 pixels greater than its first detected location. [10]
Problem 2:
Given are two csv files, pc1.csv and pc2.csv, which contain noisy LIDAR point cloud data in the form
of (x, y, z) coordinates of the ground plane.
1. Using pc1.csv:
a. Compute the covariance matrix. [15]
b. Assuming that the ground plane is flat, use the covariance matrix to compute the
magnitude and direction of the surface normal. [15]
2. In this question, you will be required to implement various estimation algorithms such as
Standard Least Squares, Total Least Squares and RANSAC.
a. Using pc1.csv and pc2, fit a surface to the data using the standard least square
method and the total least square method. Plot the results (the surface) for each
method and explain your interpretation of the results. [20]
b. Additionally, fit a surface to the data using RANSAC. You will need to write RANSAC
code from scratch. Briefly explain all the steps of your solution, and the parameters
used. Plot the output surface on the same graph as the data. Discuss which graph
fitting method would be a better choice of outlier rejection. [20]
