[Solved] CV1 Assignment 4

Task 1: SIFT (pen & paper)

Explain why0, with , 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 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 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.

1

Task 3: SIFT (pen & paper)

Consider Figure 2, which shows a normalized orientation histogram for a SIFT keypoint after weighting^[1].

Orientation (degrees)

Figure 2: A normalized orientation histogram of a SIFT keypoint.

• What is the dominant local direction of the keypoint?
• 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.