Feature detection, Harris corners

Question 1

Formula for Harris cornerness score

Answer 1

a = eigenvalue 1
b = eigenvalue 2
R=ab + k(a + b)^2
k is a constant [0.04 0.06]
ab ~ det(M)
a+b ~ tr(M)
R ~ det(M) + k(tr(M)^2)

Question 2

Invariance

Answer 2

If we shift an image geometrically, rotate it, or change the brightness/intensity, the features should stay in the same spot

Question 3

Equivariance

Answer 3

If we have two transformed versions of the same image, features should be detected in the corresponding location

Question 4

Automatic scale selection method

Answer 4

Perform the feature detection metric at varying window sizes, pick the one that detects the most corners

Question 5

Gaussian pyramid

Answer 5

Instead of computing the corners at different window sizes, we can compute the corners at a fixed window size with varying sized images

Question 6

What kernel can we use instead of doing Harris corner detection

Answer 6

Laplacian of Gaussian kernel (LoG)

Question 7

How can we pick the size of the LoG kernel

Answer 7

Make another Gaussian pyramid, dilute the results by picking the local maximum in the image plane AND image scale plane

Question 8

What kernel can we use instead of the Laplacian of Gaussian kernel

Answer 8

Difference of Gaussians kernel (DoG)

Question 9

What criteria do we have for feature description

Answer 9

Invariance - descriptor shouldn’t change if image is translated
Discriminability - Descriptor should be highly unique

Question 10

How do we find the dominant orientation of a feature

Answer 10

Direction of smoothed gradient

Question 11

MOPS (Multiscale Oriented Patches Descriptor)

Answer 11

1. Take 40x40 window around feature
2. Scale to 1/5 size
3. Rotate to horizontal
4. Sample 8x8 window centered at feature
5. Normalize intensity

Question 12

SIFT (Shift Invariant Feature Transform)

Answer 12

1. Take 16x16 window around feature
2. Compute edge orientation (angle against gradient) of each pixel
3. Throw out weak edges (thresholding)
4. Plot edges on histogram

Question 13

Given a feature in I1, how do we match in with features in I2

Answer 13

Using some distance function, we find the ratio distance function defined by
|| f1 - f2 ||
—————-
||f1 - f2’ ||
where f1 is the feature from I1, f2 and f2’ are the best and second best matched from I2, this will still give a high value for ambiguous matches