A short quiz on convolution and friends

Adrian F. Clark

1. 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.

2. 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

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

   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.

3. How do you perform template matching?

   • measure the similarity at each pixel with a pre-defined image region

   • emphasize edges of a region
   • design a mask to emphasize particular image features
   • convolve with a pre-defined image region

   Template matching means trying to find occurrences of a particular pattern within an image: the lecture notes show how this can be used to identifiy letters in a piece of text. You do this by measuring the similarity of the template with a region of an image at each possible location on the image.

4. What is a morphological opening?

   • subtracting the result of shrink from the original image

   • a shrink followed by an expand

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

5. 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 blur edges

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

   Averaging over a region will tend to blur an image.

6. 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 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 expand?

   • taking the maximum when performing a convolution

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

   • it is faster to calculate

   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.

9. 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 unchanged

   • the image is shifted down one pixel

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

   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.

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

    • execution speed
    • enhancing edges
    • deblurring images

    • 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.