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Assignment1_B31SE_Part2
School of Engineering and Physical Sciences
Electrical Electronic and Computer Engineering
Assignment 1 for Part 2 of B31SE (10 Marks)
ASSESSED EXERCISE: Submission deadline: March 14th
Problem 1: Implement the skeletonizing procedure described below and obtain skeleton of
the images. (5 marks)
Develop and test the following algorithm for thinning binary regions using the given images.
Here, region points are assumed to have value 1 and background points to have value 0. The
method consists of successive passes of two basic steps applied to the border points of the
given region, where a border point is any pixel with value 1 and having at least one
neighbour valued 0. With reference to the 8-neighbourhood notation described in your lecture
notes, Step 1 flags a contour point for deletion if the following conditions are satisfied:
a)
b)
c)
d) (1)
Where is the number of nonzero neighbours of ; that is,
(2)
Where is either 0 or 1, and is the number of 0-1 transitions in the ordered sequence
. For example, and as in Fig.1.
In Step 2, conditions (a) and (b) remain the same, but conditions (c) and (d) are changed to
(c´) (3)
(d´) (4)
Step 1 is applied to every border pixel in the binary region under consideration. If one or
more conditions (a)-(d) are violated, the value of the point in question is not changed. If all
conditions are satisfied, the point is flagged for deletion. However, the point is not deleted
until all border points have been processed. This delay prevents changing the structure of the
data during execution of the algorithm. After Step 1 has been applied to all border points,
those that were flagged are deleted (changed to 0). Then Step 2 is applied to the resulting data
in exactly the same manner as Step 1.
p9=0 p2=0 p3=1
p8=1 p1 p4=0
p7=1 p6=0 p5=1
Figure 1: illustration of conditions (a) and (b) in Eq (1). In this case and
.
Assignment1_B31SE_Part2_2022 2
Note that one iteration of thinning algorithm consists of (1) applying Step 1 to flag border
points for deletion 2) deleting the flagged points 3)applying Step 2 to flag the remaining
points for deletion and 4) deleting the flagged points. This procedure is applied iteratively
until no further points are deleted. At this point, you should see the skeleton of the region.
Solutions: With program and examples, a brief description of the process and observations
are expected. Some sample pictures:
Problem 2: Implement the Fourier descriptor scheme and apply your algorithm to a chosen image
in the image folder. Reduce the number of descriptors (frequency coefficients) to the minimum
required to keep the shape recognizable. (5 marks)
Solutions: With program and examples, a brief description of the process and observations
are expected. Testing of invariance and observations also expected. Some sample pictures:
Assignment1_B31SE_Part2_2022 3
In your report, please describe your experiments. Also include the results and matlab codes.
Finally try to address the following issues:
• Is the proposed skeletonizing procedure good for generating human chromosome?
• Is it difficult to find an appropriate number of iterations for any given image?
• Is your implementation of the skeletonizing procedure time-consuming?
• Propose possible applications for the procedure of Fourier descriptor.
• Describe the possible transformation/invariance properties of the Fourier descriptors
possibly by some experiments.
