Description

• For each programming task, submit a .py source code file. Do not need to include any images or data files you used.
• For each pen & paper task, submit a .pdf file. Type your solution in LaTeX, Word, or another text editor of your choice and convert it to PDF – do not submit photographs or scans of handwritten solutions!
• In all files, include at the top names of all students in the group
• Choose exactly one person in your group that submits your solution via Moodle, it will count for the entire group.
Task 1: SIFT (pen & paper)
Explain why 0, with α,β being the eigenvalues of the Hessian matrix at a keypoint.
Using this result, prove that when r > 0, the function has a minimum at r = 1.
Task 2: ORB Feature Detectors (programming)
ORB is a fast and efficient alternative to SIFT. Download and read the image Elbphilharmonie.jpg on Moodle.

Figure 1: Hamburg Elbphilharmonie. Image source: Wikipedia
• Convert the image to grayscale image im.
• Using skimage.transform.AffineTransform, obtain a transformed image im2 with the following parameters: shrink the dimensions by half, 20 degree counter-clockwise rotation, 300 pixels to the right and 300 pixels to the bottom translation.
• Visualize the images im, im2.
• Using skimage.feature.ORB, extract 100 ORB key points and descriptors of the two images above. Visualize the matching results.
Note: Follow the example at http://scikit-image.org/docs/dev/auto_examples/ features_detection/plot_orb.html.
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Task 3: SIFT (pen & paper)
Consider Figure 2, which shows a normalized orientation histogram for a SIFT keypoint after weighting .

Orientation θ (degrees)
Figure 2: A normalized orientation histogram of a SIFT keypoint.
(a) What is the dominant local direction of the keypoint?
(b) How many new keypoints will be created, and why? What are their orientations?
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