The entire process of feature extraction can be divided into $4$ parts:

i$.$ Constructing a Scale Space: To make sure that features are scale$-$independent

ii$.$ Keypoint Localisation: Identifying the suitable features or keypoints

iii. Orientation Assignment: Ensure the keypoints are rotation invariant

iv$.$ Keypoint Descriptor: Assign a unique fingerprint to each keypoint

Finally, we can use these keypoints for feature matching!

Consider the sample image shown below:

Obtain a histogram given that we have these magnitude and orientation values for the pixels. $(25$pts$)$