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[1].
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?
[1] For simplicity, we consider an 8-bin orientation histogram. In the original SIFT algorithm, 36 bins are used.
