Description
1 Harris Corner Detection (10 points)
1. Load and Convert Image to Grayscale:
path = ‘/content/drive/Mydrive/Assignment_x/images/’
image = cv2.imread(path + ‘img1.png’)
Read the image ./images/mcgill_arts_building.jpg and convert it to grayscale using an
appropriate image processing library.
2. Compute Image Derivatives:
Calculate the image derivatives and in both the x and y directions using Sobel
filters or another derivative method.
Compute the products of the derivatives: , , and .
3. Apply Gaussian Filtering:
Smooth the derivative products , , and using Gaussian filtering to reduce
noise.
4. Compute the Corner Response:
For each pixel, calculate the corner response function using the formula:
where is the second moment matrix formed from the smoothed derivative products, and
.
5. Non-Maximum Suppression:
Perform non-maximum suppression on the corner response map to identify potential corner
points by keeping only the local maxima.
6. Detect and Mark Corners:
Apply a threshold to the corner response map, and mark the local maxima that exceed the
threshold as detected corners.
Overlay the detected corners on the original image for visualization, similar to the
example shown in the demo.
7. Experiment with Thresholds:
Experiment with different threshold values to control the sensitivity of corner
detection.
Summarize your findings on the effect of varying thresholds in a markdown cell.
2 SIFT Features (20 points)
2.1 SIFT Keypoint Matching Between Two Images
1. Compute SIFT Keypoints and Descriptors:
Detect SIFT keypoints and compute descriptors for the images ./images/graf1.png and
./images/graf2.png .
2. Match Keypoints:
Use a brute-force matching method to find correspondences between the keypoints of both
images.
3. Sort Matches by Distance:
Sort the matched keypoints in ascending order based on their matching distance.
4. Display the Top Ten Matches:
Visualize the top ten matched keypoints, overlaying them on both images.
5. Plot the Matching Distances for the Top 100 Matches:
Create a plot with keypoint indices on the x-axis and their corresponding matching
distances on the y-axis to visualize the distribution of matching distances.
2.2 Scale Invariance
1. Compute SIFT Keypoints for the Original Image:
Detect the SIFT keypoints and compute their descriptors for ./images/graf1.png .
2. Scale the Original Image:
Create 4 scaled versions of ./images/graf1.png using scaling factors of 0.25, 0.6, 3,
and 5.
Display each of the scaled images.
3. Compute SIFT Keypoints for the Scaled Images:
For each scaled image, compute the SIFT keypoints and their descriptors.
4. Match Keypoints:
Perform brute-force matching between the keypoints of the original image
( ./images/graf1.png ) and each of the scaled images.
5. Sort Matches by Distance:
For each pair of images (original vs. scaled), sort the matches according to the
matching distance.
6. Display the Top Ten Matches:
Visualize the top ten matches between the original and each scaled image.
7. Plot the Matching Distances:
For each pair, plot the matching distance for the top 100 keypoints, using the keypoint
index on the x-axis and matching distance on the y-axis.
8. Discuss Trends:
Analyze the results and discuss how increasing the scale affects the matching distances.
2.3 Rotation Invariance
1. Rotate Image:
Rotate ./images/graf1.png by the following angles: 30°, 75°, 90°, and 180°.
Display the four rotated images.
2. Compute SIFT Keypoints for Rotated Images:
For each of the four rotated images, compute SIFT keypoints and descriptors.
3. Match Keypoints:
Use a brute-force matching method to match the keypoints of the original image
( ./images/graf1.png ) to each of the rotated images.
4. Sort Matches by Distance:
Sort the matched keypoints for each image pair based on the matching distance in
ascending order.
5. Display the Top Ten Matches:
Visualize the top ten matched keypoints for each image pair (original vs. rotated).
6. Plot the Matching Distances for the Top 100 Matches:
Create a plot showing the matching distance for the top 100 keypoints, with keypoint
indices on the x-axis and corresponding matching distances on the y-axis.
7. Discuss Trends:
Analyze how increasing the angle of rotation affects the matching distances. Explain the
trends observed in the plot.
2.4 Repeat 2.1-2.3 using the image pair you obtained from
assignment 1.
Image Stitching (20 points)
You are given three different views of the same scene located in the folder ./images/Q3 .
Follow these steps to stitch the images together:
1. Keypoint Detection and Matching:
a. Compute SIFT keypoints and descriptors for images 1 and 2.
b. Match the keypoints between images 1 and 2. Display the 20 best matching pairs.
2. Homography Estimation and Transformation:
a. Use the RANSAC method to compute the homography matrix that aligns keypoints from image
1 to image 2.
b. Apply the computed homography to transform image 1. Image 2 should remain unchanged.
3. Image Stitching:
a. Stitch the transformed image 1 with the original image 2. For better visualization,
average the pixel intensity in the overlap region so that you can see patterns from both
images. Name this result image_12 . Display image_12 .
4. Repeat the Process for Image 3:
a. Compute SIFT keypoints and descriptors for image_12 and image 3.
b. Match the keypoints between image_12 and image 3. Display the 20 best matching pairs.
c. Compute the homography using RANSAC to align keypoints from image_12 to image 3. Apply
this homography to transform image 3. Image image_12 should remain unchanged.
5. Final Stitching:
a. Stitch the transformed image 3 with image_12 . Also average the pixel intensity in the
overlap region. Display the final stitched image.
