Computer Assisted Image Analysis II
HT 2011
Exam 2011-12-14
time:
8.00–13.00
place:
Polacksbacken, Skrivsal
tools:
pen or pencil and paper, 2 hand-written sheets of notes
grades:
0–17
18–24
25–32
33–40
OBS:
Please use drawings and figures to illustrate your answers when suitable. Use a new page
for each new question, make sure that you write your exam code (or name) on each page,
and remember that the top left corner will be hidden by the staple. You may write your
answers in English or Swedish, but not with red ink.
fail
3
4
5
Results will be forwarded to the student office no later than January 6.
GOOD LUCK!
1. Filtering (Cris)
a) What is the advantage (or advantages) of Gaussian derivatives over filters like Sobel?
(2p)
b) What is the frequency response of the Gaussian filter? (describe it, there is no need to give the
exact equation)
(1p)
d) How would you implement a 2D Gaussian filter? Describe the size of the convolution kernel, and
any potential tricks to speed up the calculation.
(2p)
2. Active Shape Models (Cris)
Active shape models (ASM) learn an average shape and different modes of variation from a set of
example shapes.
a) What type of object can be modelled by ASM?
(1p)
b) What type of shape changes can an ASM adapt to?
(2p)
c) How does the ASM method choose important shape changes and discard irrelevant ones? (Or:
how does the ASM method reduce the number of parameters that describe the shape variations?)
(2p)
3. Measurement (Cris)
The chain code describing the boundary of a binary object can be obtained easily, and be used to
estimate the perimeter of the object.
a) Why is counting the number of elements in the chain code (i.e. the number of boundary pixels) a
biased estimate of the object’s perimeter? (Hint: I’m not asking why it is imprecise!)
(1p)
b) How could you make the pixel counting method unbiased?
(1p)
c) Most commonly, people will use different weights for odd and even chain codes. Why are the
weights 1 and √2 not suitable?
(1p)
d) As an additional improvement, the “corner count” method also uses the number of times the
chain code changes. Why is this helpful? Does this improve accuracy or precision?
(1p)
e) The chain code representation is also used in many other analysis algorithms. Why do you think
this is? In what ways is the chain code more useful than other object representations?
(1p)
4. Mathematical morphology (Ida-Maria)
Top Hat is a useful mathematical morphology transform.
a) What sequence of transforms/operations constitutes the Top Hat transform? Divide the
operations into as simple building blocks as possible.
(2p)
b) Describe how a combination of Top Hat transforms could be used to filter out the cell nuclei
(diameter approx. 30 pixels) in the image below, removing the uneven background as well as the
small dots. How should the input parameters be chosen?
(3p)
5. Fuzzy connectedness (Robin)
Fuzzy affinity can be written
μK(c,d) = μω(c,d) g(μφ(c,d), μδ(c,d)) ,
where μω(c,d) is the fuzzy adjacency, μφ(c,d) is the homogeneity-based component, and μδ(c,d) is the
object-feature based component.
a) Explain what information the different factors utilize.
(2p)
b) Give an example of a fuzzy affinity function that utilizes the mean intensity value of the object
and background.
(1p)
c) What is absolute fuzzy connectedness, relative fuzzy connectedness, and iterative relative fuzzy
connectedness?
(2p)
6. Skeletonization (Robin)
a) Give an algorithm for computing a skeleton (in 2D).
(1p)
b) Which skeletal properties (topologically equivalent, centred, unit-wide, reversible) are fulfilled
by the skeleton obtained by the algorithm?
(1p)
In which of the configurations (only object voxels are shown) below is the centre (grey) voxel
simple if we use:
c) 26-connected object and 6-connected background?
(1p)
d) 6-connected object and 26-connected background?
(1p)
i
ii
e) How can the algorithm in (a) be adjusted for 3D images?
iii
(1p)
7. Registration (Anders)
a) What are the differences between the concepts image registration and template matching?
(1p)
b) Explain the differences and characteristics of the functionals: mean squared error, correlation and
mutual information.
(2p)
c) Derive the affine transformation that transforms the 2D landmarks (0,2), (5,6) and (3, 0) into
(0, 1), (1,1) and (1,0).
(2p)
8. Motion (Anders)
a) Describe two different algorithms for change detection and their characteristics.
(2p)
b) Explain how motion can be estimated using RANSAC.
(1p)
c) What is the aperture problem?
(1p)
d) What is motion compensation?
(1p)