A short quiz on convolution and friends

Adrian F. Clark

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

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

   • dark spots 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.

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

   • light spots will be enhanced
   • dark spots will be enhanced
   • 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 lies at the centre of a light +-shaped feature.

3. What is matched filtering?

   • finding matches by convolution

   • designing a mask that matches a desired image feature

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

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

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

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

   • 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.

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

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

   • +-shaped features will be enhanced

   • light 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.

6. 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.

7. What is a morphological grey-level expand?

   • taking the maximum when performing a convolution

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

8. The Laplacean mask is useful for:

   • locating isolated white pixels

   • locating dark regions
   • locating edges
   • locating corners

   The Laplacean is best at identifying isolated pixels in images.

9. What is a morphological opening?

   • subtracting the result of expand from the original image
   • subtracting the result of shrink from the original image

   • a shrink followed by an expand

   • an expand followed by a shrink

   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!

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 will detect isolated points
    • it will enhance edges
    • it has no effect

    • it will blur edges

    Averaging over a region will tend to blur an image.