A quiz on image representation and processing in software

Adrian F. Clark

1. In OpenCV, if Y indexes lines, X columns and C channels, the right nesting >of loops is

   • C inside Y inside X

   • C inside X inside Y

   • Y inside X inside C
   • X inside Y inside C

   The C subscript should cycle fastest in all languages you will use OpenCV with, followed by the X subscript. The Y subscript should cycle slowest. This order mimics the way in which the pixels are stored in memory and thus minimises cache misses etc.

2. Why is imagery with 8 bits per pixel commonly used in vision software?

   • 8-bit values fit into a byte
   • 8-bit values are faster to process than integers
   • computers don't have enough memory to use more than 8 bits/pixel

   • the human eye sees less than 8 bits worh of grey levels

   The underlying reason is that the eye sees less than 256 shades of grey, though they are not evenly spaced in intensity. It is a convenient coincidence that this matches one byte per pixel. Depending on the hardware involved, 8-bit values are processed at the same speed as integers. Unless it is extremely large (and some of those your lecturer processes are), images are small compared to the size of memory these days.

3. Why are digital images usually rectangularly-sampled?

   • because that is a better match for the human eye's rods and cones

   • because they are easier to process with a computer

   • because it is impossible to make hexagonally-spaced CCDs
   • because of the way images are formed on photographic film

   Digital images are most easily processed by computer if they are rectangularly-sampled, as ordinary 2D arrays can be used. The rods and cones in the human eye are tightly-packed, which makes them approximately hexagonally-sampled. Hexagonally-sampled CCDs are entirely feasible and are used, for example, on some Fujifilm digital cameras. Finally, photographic film forms images in a purely analogue way, so there is no sampling involved at all.

4. After contrast-stretching, an over-exposed image which has only a few grey levels occupied will have a histogram that

   • has all grey-level bins roughly equally occupied

   • tends to show small spikes across the entire range of grey levels

   • has a nice peak of grey levels in its middle region
   • has a concentration of large values near high grey-level values

   A poorly-exposed image (either under- or over-exposed) which is contrast-stretched will normally exhibit only a few occupied bins, and they will be equally-spaced across the entire range of grey levels, giving it a `spiky' appearance.

5. If a histogram has most of its values bunched together at its left, how does the image appear?

   • equally-exposed
   • well-exposed
   • over-exposed

   • under-exposed

   If the majority of pixels are are the left of a histogram, they have low values and so the image is dark and that normally means it is under-exposed.

6. Why does EVE use float values for pixels?

   • it should execute faster
   • that's the way images are stored in disk files

   • it reduces the number of places that the effects of rounding have to be considered

   • it supports a wider range of values

   The use of float values in EVE is largely to reduce the effects of rounding: there are fewer places in a typical piece of code where the effects of rounding need to be considered. There are other advantages too, such as representing a widrer range of values but the rounding one is the most important.

7. The correlation coefficient between two images tells us

   • the amount of noise in the images

   • how similar they are, ignoring gain or offset changes

   • whether or not two images are identical
   • whether there are gain or offset changes between them

   Correlation is a measure which is independent of the means of signals and is normalized by the variances of the two signals, so it is also independent of their relative scales -- it measures only whether the variations in two images relative to their means are in step. The correlation coefficient lies in the range -1 -- +1 and the value describes the similarity of the two images.

8. What is plotted along the abscissa (x-axis) of a histogram?

   • grey level

   • number of occurrences
   • standard deviation
   • mean value

   The x-axis of a histogram plots the grey level; the y-axis plots the number of occurrences of that grey level.

9. Why would you contrast-stretch an image?

   • to improve subsequent processing
   • to improve its exposure

   • to spread out the grey levels which are occupied

   • to equalize the image's histogram

   The real purpose of contrast-stretching an image is to improve its appearance when seen by a human, with a wider range of grey levels being occupied. This doesn't actually improve its exposure because if only 10 grey levels were occupied before stretching, only ten would be afterwards too, it's just that they are further apart. There are a few cases in which contrast-stretching might help processing (morphology springs to mind) but that's rarely the case. Contrast stretching definitely does not equalize the histogram!

10. When computing a histogram h, what operation do you do a pixel of value v?

    • h[v] = h[v] + v

    • h[v] = h[v] + 1

    • h[v] = h[v] - 1
    • h[v] = h[v] - v

    You're counting the number of times v occurs in the image, so you add unity to the current value of h[v].