COMP90086 Computer Vision - Assignment 3: Fundamental Matrix Calculation
COMP90086 Computer Vision, 2022 Semester 2
Assignment 3: Fundamental Matrix Calculation
Introduction
In this project you will implement the calculation of a Fundamental matrix using your own algorithms. You can use the keypoint detection and matching approach used in the week 8 Workshop, as well as code for drawing lines on images, but the implementation of the Fundamental Matrix calculation must be your own work.
Coding tasks
Your tasks are:
1. Find keypoints and correspondences between two images
2. To implement the 8 point algorithm you will need to:
a. Shift and scale the pixel coordinates
b. Compute the design matrix from sets of (at least) 8 points
c. Perform an SVD of the design matrix to find its null space (you can use a library function for the SVD)
d. Compose the draft fundamental matrix F
e. Perform an SVD of the draft fundamental matrix, set the smallest singular value to zero and reassemble so that F now has determinant = 0
f. Calculate which correspondences are inliers and which are outliers using this F. You will need to allow for some error because the keypoint coordinates won’t lie exactly on the epipolar line so you will need to allow for 1-2 pixels error for a correct correspondence. Also remember to take into account any scaling you applied at step a.
g. Wrap steps b-f in a RANSAC loop that runs enough times that you have a probability > 99% of finding 8 inliers and computing a good quality F.
h. Re-estimate F using all the inliers.
i. Compute F in terms of the original pixel coordinates (ie undo the effects of step a).
3. Randomly
to your best F estimate and display these on the images, together with their epipolar lines.
sample ten keypoint pairs from correspondences you have detected as inliers
If you make this a separate cell in your jupyter notebook, you can run the cell more than once to see different random samplings.
Report
Your report should describe why you need each of these steps and any design choices you have made along with numerical quantities, e.g. choice of error tolerance at step f, or the calculation needed to determine the number of RANSAC iterations at step g.
You should also discuss whether there are images that work better than others in the dataset and why.
Dataset
The dataset is the kusvod2 dataset. Image files are of the form <something>A.png and <something>B.png for each image pair.
Using Library Code
You may use library code for everything except the implementation of the 8 point algorithm which you must implement yourself. This means that you can use library implementations of keypoint detection and correspondence (e.g. SIFT or FAST and BRIEF) as well as implementations of SVD or other linear algebra operations.
Submission
You should make two submissions on the LMS: your code and a short written report explaining your method and results. Your report should be no more than 1500. Submission will be made via the Canvas LMS. Please submit your code and written report separately under the Assignment 3: Code and the Assignment 3: Report links on Canvas.
· ● Your code submission should include the Jupyter Notebook (please use the provided template) with your code and any additional files we will need to run your code. You do not need to include the provided images in your submission.
· ● Your written report should be a .pdf with your answers to each of the questions. The report should address the questions posed in this assignment and include any images, diagrams, or tables required by the question.
Evaluation
Your submission will be marked on the correctness of your code/method, including the quality and efficiency of your code. You should use built-in Python functions where appropriate and use descriptive variable names. Your written report should clearly explain your approach and any experimentation used to produce your results, and include all of the specific outputs required by the question (e.g., images, diagrams, tables, or responses to sub-questions).
Late submission
The submission mechanism will stay open for one week after the submission deadline. Late submissions will be penalised at 10% of the total possible mark per 24-hour period after the original deadline. Submissions will be closed 7 days (168 hours) after the published assignment deadline, and no further submissions will be accepted after this point.
