A short quiz on convolution and friends

Adrian F. Clark

1. What is a morphological grey-level shrink?

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

   • taking the minimum when performing a convolution

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

2. 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 will enhance edges

   • it will blur edges

   • it has no effect
   • it will detect isolated points

   Averaging over a region will tend to blur an image.

3. What is the effect of convolving an image with a +-shaped mask where the central pixel is -4 and its neighbours to north, south, east and west are 1?

   • dark and light spots will be enhanced

   • the image will be lightened
   • X-shaped features will be enhanced
   • +-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.

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

   • it will enhance edges

   • it will blur edges

   • it will detect isolated points
   • it has no effect

   Averaging over a region will tend to blur an image.

5. 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.

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

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

   • it blurs the image less

   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.

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

   • 2

   • 4

   • 1
   • 3

   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.

8. What is a morphological opening?

   • a shrink followed by an expand

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

9. The Laplacean mask is useful for:

   • locating dark regions

   • locating isolated white pixels

   • locating edges
   • locating corners

   The Laplacean is best at identifying isolated pixels in images.

10. What is the effect of convolving an image with a +-shaped mask?

    • X-shaped features will be enhanced
    • light spots will be enhanced

    • +-shaped features will be enhanced

    • dark spots will be enhanced

    This produces a large output when the value below the middle of the mask lines at the centre of a light +-shaped feature.