Compute LoG Pyramid, show your code

Learning Goal: I’m working on a mathlab exercise and need an explanation and answer to help me learn.

Description:

This assignment consists of LoG Key Points where he objective of this homework is to reinforce the scale space response extrema concept in key points detection, and ask you to compute a LoG pyramid for scale space extrema detection, and compare that with the DoG pyramid based SIFT detection.

Exercises explained on detail under the word document down below.

The LoG pyramid is computed for

You may choose to do SIFT like spatial-scale neighborhood extrema detection, or you may use the ALP like polynomial fitting and direct extrema detection method. The ALP like method is illustrated in the figure below:

The LoG response is given as =a3 + b2 + c +d, the fitting can be done with polyfit(x, y, 3), and you can also compute its gradient. An extrema is detected by checking its gradient value.

Q1 [20 pts] Compute LoG Pyramid, show your code

Q2 [30 pts] Compute LoG response extrema,

Q3 [50 pts] Give the image level LoG key points detection and visualize and compare with SIFT detection.