4.4. Homework

Downsampling is the process of reducing the size of an image. For example, Downsampling by a factor of 2 would reduce a 10 by 10 image to a 5 by 5 image. One way to do this is to divide the image into 2 x 2 blocks and calculate the average of each block as in Fig. 4.11.

Fig. 4.9 Downsampling a 4 by 4 array by a factor of 2 by averaging 2 by 2 blocks.

1. Write code which downsamples the falling cat image by a factor of 2.

2. Write a function downsample(x, k) which downsamples the array x by a factor k. Test your function against the falling cat image for various values of k.

Upsampling is the reverse process. For example, upsampling by a factor of 2 would increase a 10 by 10 image to a 20 by 20 image. This can be achieved by repeating each element in 2 by 2 blocks as in Fig. 4.12.

Fig. 4.10 Upsampling a 4 by 4 array by a factor of 2 by repeating each element in 2 by 2 blocks.

3. Write a function upsample(x, k) which upsamples the array x by a factor k. Test your function against the falling cat image for various values of k.