Learning OpenCV, 2nd Edition

6. A log-polar transform takes shapes of different rotations and sizes into a space where these correspond

to shifts in the 𝜃-axis and log!(𝑟) axis. The Fourier transform is translation invariant. How can we use

these facts to force shapes of different sizes and rotations to automatically give equivalent

representations in the log-polar domain?

7. Draw separate pictures of large, small, large rotated, and small rotated squares. Take the log-polar

transform of these each separately. Code up a two-dimensional shifter that takes the center point in the

resulting log-polar domain and shifts the shapes to be as identical as possible.

8. Take the Fourier transform of a small Gaussian distribution and the Fourier transform of an image.

Multiply them and take the inverse Fourier transform of the results. What have you achieved? As the

filters get bigger, you will find that working in the Fourier space is much faster than in the normal

space.

9. Load an interesting image, convert it to grayscale, and then take an integral image of it. Now find

vertical and horizontal edges in the image by using the properties of an integral image.

Use long skinny rectangles; subtract and add them in place.

10. A good computer vision programming interview question is to code up an integral image. Let’s do

that:

• Write a routine that takes an image and returns an integral image.

• Write a routine ...