Curve Fitting and Homography

File structure

.
├── Code
|  ├── CurveFitting.py
|  ├── Homography.py
├── Data
|  ├── Video1.mp4
|  ├── Video2.mp4
├── Results
|  ├── Video1
|  |  ├── .png files
|  ├── Video2
|  |  ├── .png files

Problem 1

A ball is thrown against a white background and a camera sensor is used to track its trajectory. We have a near perfect sensor tracking the ball in video1 and the second sensor is faulty and tracks the ball as shown in video2. Clearly, there is no noise added to the first video whereas there is significant noise in video 2. Assuming that the trajectory of the ball follows the equation of a parabola

• Use Standard Least Squares, TLS and RANSAC methods to fit curves to the given videos in each case. You have to plot the data and your best fit curve for each case.
• Briefly explain all the steps of your solution and discuss which would be a better choice of outlier rejection technique for each case.

Running the code

• Change the directory to the root folder
• Run the following command:

python3 CurveFitting.py --BasePath='./' --VideoFilePath='./Data/Ball_travel_10fps.mp4' --SaveFolderName='graphs/video1' 

Parameters

• BasePath - This is the base folder path
• VideoFilePath - By default, the path is set as ./Data/Ball_travel_2_updated.mp4
• SaveFolderName - the path to folder where all the plots will be saved. The folder must be inside the BasePath

Results

Video1

Data points

Least Square Method

Total Least Square Method

RANSAC

Video2

Data points

Least Square Method

Total Least Square Method

RANSAC

Problem 2

Mathematically compute Homograpjhy matrix for given points.

Running the code

• Change the directory to the root folder
• Run the following command:

python3 Homography.py