Physics, Psychophysics and Physiology of Vision Practical Two - Image Intensity
Distributions
10%, to be completed by 26/2/01 (MSc VIVE ONLY)
1. Objective
In the lectures, you have heard about different statistical models of images.
The aim of this practical is to illustrate some of these and to exercise
some of the techniques used earlier in the MSc VIVE programme, in particular
in the MMAI course.
2. Procedure
Carry out each of the steps listed below and, as in the first Physics,
Psychohysics and Physiology practical and the Machine Vision practicals
last term, write a brief report containing:
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a description of the techniques used, where appropriate in succinct
mathematical
terms
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a description of what was done, what data was used, how it was obtained,
what tools, library facilities etc were used
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the results obtained
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an analysis and critique of the results
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any conclusions you can draw from the exercise
Include any code you write yourself (suitably commented) in an appendix.
3. Exercises
Images, all in ppm format, may be copied as required from the following:
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/cs/research/vision/images/daedalus/Track1 (gravel path, near Lewes, East
Sussex),
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/cs/research/vision/images/daedalus/Track2 (a country farm lane in the
South Downs near Lewes, East Sussex),
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/cs/research/vision/images/daedalus/Track4 (South Downs Way, East Sussex),
and
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/cs/research/vision/images/daedalus/Track5 (a woody lane near Lewes, East
Sussex).
Select sample images from the sequences for the exercises below. For
some of the exercises below you will need to take several (for
example, five) samples from at least one sequence as well as images
from each sequence. If time permits, this will also allow you to check
consistency of your results more thoroughly. Note that if the images
are rather dark, it is best to view (but not process) the originals
after histogram equalisation, for example using xv.
3.1 Image Data
Use xv and IDL to convert image formats and to extract the image intensity
components so that the images can be accessed as matrices for processing
as described in sections 3.2-3.5 below. See the notes prepared earlier
by Ioannis Douros for the second MV practical on image
preparation for further details, in particular on how to set up image
matrices. As usual, it is probably best to perform all of the operations
indicated on one of the images or image sets first in order to be sure
that your implementation works and to minimise the number of images and
intermediate results you have to store.
3.2 The distribution of image intensities
Compute a histogram of the intensity for each image and use the maximum
likelihood method to fit a Gaussian to the distribution of image intensities
obtained. Discuss how well a Gaussian distribution may be used to model
the intensity distribution within each image by comparing the histograms
and Gaussian distributions obtained with each other and comment on the
extent to which the histograms and Gaussian distributions vary from image
to image for your chosen sequence and from track to track.
3.3 The distribution of image intensity within image regions
Select two regions in images in a sequence of your choice,
one from the track and one from part of the background in each case. Try
to choose your regions such that they are 64 pixels x 64 pixels or, if
this is not possible, use a rectangular region of similar area (eg. 32
pixels x 128 pixels, or vice-versa). As in 3.2 above, compute a histogram
of the intensity distribution and use the maximum likelihood method to
fit a Gaussian to it. Discuss how well a Gaussian now fits the intensity
distributions obtained and comment on the differences between the results
obtained (i) in the foreground (track), (ii) in background regions and,
by comparison with 3.2 above, (iii) over the whole of each of the
images in the samples you have chosen.
3.4 The distribution of image intensity along image rows
Select several (five may do, but if time permits, experiment a little) rows
within one of the images used in 3.3 above and a similar number of rows
within each of the foreground (track) and background regions defined in
3.3 above. Using the pixels on each of these three sets of rows as
samples, repeat
the calculation and comparison of the histograms and Gaussian distributions
and comment on the results obtained.
3.5 Power spectra
Use mathematica, or write your own program, to calculate the power
spectrum (modulus squared of the Fourier transform) for rows of pixels
such as those used in 3.4 above. Chose rows of pixels which lie on a
track, or similar fairly homogeneously textured area, and compare the
results obtained for each row and with rows from other parts of the
image, from other images, or other sequences as time permits. Describe
and, if possible, explain any systematic variations you find.
3.6 Fractal Behaviour
Compare the power spectra obtained with what you would expect for
power law (fractal) behaviour and, if they are similar, use a
log-log plot to estimate the power law and comment on the results
obtained. If necessary, average your spectra over several rows close
close to each other in order to smooth the spectra. Note that you
should only consider the tail of the power spectra at large wavenumber
when looking for fractal behaviour, so you will need to adopt a
suitable cut-off below which the specra should be ignored.
4. Reporting
As usual, beware of labouring long and hard to produce a pretty report.
There is a rapidly diminishing rate of return for such efforts. Evidence
that the exercise has been completed and content of the report is much
more important than presentation. Adequate presentation and analysis of
the original and normalised images should however, be included in your
report, as part of this evidence.
Bernard Buxton,
9 March 2000.