A short quiz on convolution and friends

Adrian F. Clark

1. What is a morphological grey-level expand?

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

   • taking the maximum 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.

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

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

   • it is proportional to the dimension of the mask
   • it is not affected by the dimension of the mask
   • it is proportional to the logarithm of 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.

3. The Laplacean mask is useful for:

   • locating edges
   • locating corners
   • locating dark regions

   • locating isolated white pixels

   The Laplacean is best at identifying isolated pixels in images.

4. What does a morphological opening tend to do?

   • find the boundary between dark and light regions

   • delete isolated light pixels within dark regions

   • find the skeleton of light regions
   • delete isolated dark pixels within light regions

   An opening is a shrink followed by an expand. The shrink reduces the size of light regions, so an isolated pixel (for a $3 \times 3$ mask) within a dark region will disappear. The expand then grows any light regions that remain.

5. Given a white feature on a black background, how could you find its boundary?

   • subtract the result of opening from the original image
   • subtract the result of expand from the original image
   • subtract the result of closing from the original image
   • subtract the result of opening from the original image

   • subtract the result of shrink from the original image

   A shrink using a $3 \times 3$ mask reduces the size of light regions by a single pixel around its boundary. Subtracting this from the original image leaves just the boundary.

6. 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.

7. What is a morphological grey-level shrink?

   • taking the standard deviation when performing a convolution

   • taking the minimum when performing a convolution

   • taking the maximum when performing a convolution
   • taking the mode 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.

8. What is matched filtering?

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

   • designing a mask that matches a desired image feature

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

9. What is the most popular use of median filtering?

   • execution speed
   • deblurring images
   • enhancing edges

   • noise reduction

   So-called 'salt and pepper noise' due to damaged sensors tends to deliver very bright or very dark pixel values. As a median involves sorting values, a very dark or very bright one sorts to the start or end of the values and has no real effect on the middle one -- so it is very useful for reducing noise.

10. What is a morphological opening?

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

    • a shrink followed by an expand

    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!