A short quiz on convolution and friends

Adrian F. Clark

1. What is the effect of convolving an image with the mask $$\pmatrix{0 & 1 & 0\cr 0 & 0 & 0\cr 0 & 0 & 0\cr}$$

   • the image is blurred

   • the image is shifted down one pixel

   • the image is shifted up one pixel
   • the image is unchanged

   At each pixel, the new value becomes the value in the line above, which has the effect of moving the image down by one pixel.

2. What is matched filtering?

   • finding matches by convolution

   • designing a mask that matches a desired image feature

   • using correlation as the 'statistic' at each pixel
   • finding the morphological skeleton

   Matched filtering is designing a convolution mask that will produce a strong response at specific image features.

3. What is a morphological opening?

   • a shrink followed by an expand

   • subtracting the result of expand from the original image
   • an expand followed by a shrink
   • subtracting the result of shrink from the original image

   An opening is a shrink followed by an expand, at least as defined in the lecture notes -- some authors would call this an expand! I'm afraid you'll just have to remember this!

4. What is the effect of convolution with a 3 x 3 mask with each coefficient set to 1/9?

   • it has no effect
   • it will enhance edges

   • it will blur edges

   • it will detect isolated points

   Averaging over a region will tend to blur an image.

5. What is the effect of convolving an image with the mask $$\pmatrix{0 & 1 & 0\cr 1 & -4 & 1\cr 0 & 1 & 0\cr}$$

   • light spots will be enhanced

   • dark spots will be enhanced

   • +-shaped features will be enhanced
   • X-shaped features will be enhanced

   This produces a large output when the value below the middle of the mask is much lower than the pixels on its four sides --- and this will tend to enhance dark spots in an image.

6. How does the time taken to perform a convolution vary with the dimension of a (square) mask?

   • it is proportional to the logarithm of the dimension of the mask
   • it is proportional to the dimension of the mask

   • it is proportional to the square of the dimension of the mask

   • it is not affected by the dimension of the mask

   The execution time is proportional to the number of pixels in a mask, so for a mask of dimension 3 there will be $3 \times 3 = 9$ operations per pixel, and so on. Hence, the time taken is proportional to the square of the dimension of the mask.

7. Why is it often better to use the median then the mean when performing a convolution?

   • it blurs the image less

   • it is more accurate
   • it is faster to calculate
   • it is easier to write the software

   When one value lies well away from the others, the median is less affected then the mean, so it tends to blur the image less.

8. What is a morphological grey-level expand?

   • taking the mode when performing a convolution
   • taking the standard deviation when performing a convolution

   • taking the maximum when performing a convolution

   • taking the minimum when performing a convolution

   A morophological shrink involves taking the maximum when performing a convolution. It has the effect of increasing the size of light-coloured regions on a dark background.

9. For convolution of a single-channel 2D image with a 2D mask, how many nested loops are there in its implementation in software?

   • 3
   • 2
   • 1

   • 4

   In order, there are normally loops over the rows and columns of the image. Within those, there are loops over the rows and columns of the mask.

10. What is the effect of convolution with the following mask? $$\frac19 \pmatrix{1 & 1 & 1\cr 1 & 1 & 1\cr 1 & 1 & 1\cr}$$

    • it has no effect

    • it will blur edges

    • it will enhance edges
    • it will detect isolated points

    Averaging over a region will tend to blur an image.