Question 1: (1×15 = 15 marks)
1) What is Monochromatic (or achromatic) light?
Monochromatic (or achromatic) light: The only attribute of monochromatic light is its intensity or amount.
Because the intensity of monochromatic light is perceived to vary from black to grays and finally, to
white, the term gray level is used commonly to denote monochromatic intensity
2) In Gaussian filter what does the parameter 𝜎 determin.
Sigma determines how fast the weights decay
3) What is the difference between global threshold and local threshold?
If the threshold depends only on gray-level values, it is the global threshold.
If the threshold depends on gray-level values and its neighbors, it is the local threshold
4) Describe the limitation of the average filter.
Thresholding; Boundary based; Region based; Hybrid
5) List four types of segmentation techniques?
The Median filter is a non-linear filter that is most commonly used as a simple way to reduce noise in
an image. It claims to fame (over Gaussian for noise reduction) is that it removes noise while keeping
edges relatively sharp
6) What is one main advantage of using a median filter over using a Gaussian filter for smoothing?
1. Gaussian smoothing 2. Compute the gradient and the orientation 3. Nonmaximal-suppresion 4.
Hysteresis thresholding
7) Briefly describe the main steps of Canny edge detector.
Signal frequencies shared with noise are lost, resulting in blurring. Impulsive noise is diffused but not
removed. It spreads pixel values, resulting in blurring. Impulsive noise is diffused but not removed.
8) Discuss the factors or parameters that could affect the detection and location of edges.
Sigma (Gaussian kernel size) determines the amount of smoothing; large Sigma detects large scale
edges while small Sigma detects fine features.
9) List two applications of the erosion.
1. We can also use erosion for edge detection by taking the erosion of an image and then subtracting
it away from the original image, thus highlighting just those pixels at the edges of objects that were
removed by the erosion.
2. Erosion can also be used to remove small spurious bright spots (`salt noise’ ) in images
10) Briefly describe the visibility of x-rays.
bones contain heavy atoms -> with many electrons, which act as an absorber of x-rays
commonly used to image gross bone structure and lungs
excellent for detecting foreign metal objects
main disadvantage -> lack of anatomical structure
all other tissue has very similar absorption coefficient for x-rays
11) What is the application of thinning?
Used to remove selected foreground pixels from binary images
12) In K-means clustering algorithm, what is the meaning of “K”?
Number of centers
13) In Laplacian of Gaussian operator, the edge kernel [1 -2 1] is meant to approximate which
order derivative?
2nd order derivative
14) Which one of the following statements about mean SHIF is NOT true? (1 mark)
c
a) It is based on Robust Statistics.
b) It is a non-parametric technique.
c) It translates the search window to the median.
d) It finds a peak of a given histogram.
15) You want to remove salt-and-pepper noise from a picture. Which filter is the best one to
achieve that?
a/c
a) Median filter
b) Average filter
c) Gaussian filter
Question #2 - Answer All the Questions (5 marks)
For each of the following concept, give a brief definition in 2 to 3 sentences.
1.
2.
3.
4.
5.
Fourier Transform
Mean Shift
Harris Detector
Corner Point
Opening Operation
1. In mathematics, a Fourier transform (FT) is a mathematical transform that decomposes functions
depending on space or time into functions depending on spatial or temporal frequency, such as the
expression of a musical chord in terms of the volumes and frequencies of its constituent notes.
2. Mean shift is a non-parametric feature-space analysis technique for locating the maxima of a
density function, a so-called mode-seeking algorithm.
3. Harris Corner Detector is a corner detection operator that is commonly used in computer vision
algorithms to extract corners and infer features of an image.
4. The corner points are the vertices of the feasible region.
5. An opening is defined as an erosion followed by a dilation using the same structuring element
for both operations
Question #3 - Image Processing (6 marks)
1. Suppose that a gray scale image patch shown below is in the range [0, 7] instead of [0, 255].
Please compute the following (2 marks):
(a) The output of a 3 × 3 mean filter at x=3, y=2 28/4=7
(b) The output of a 3 × 3 median filter at x=3, y=2. 2
2. A binary image is shown in Figure 1 (a). Clearly state the structure element(s) and the
morphological operation(s) that produced the image in Figure 1 (b) (4 marks).
Hint: 1. Use 3 by 3 structuring element. 2. Pixel value outside boundary is 0.
erosion
Question #4 – Hough Transform (12 marks)
1. Consider an image of 5 x 5 pixels identified by their coordinates between 0 and 4. P1 is the
pixel coordinate (2,3). We use the parameters m and c to represent the equation of a line in the
form y = mx + c. Give an equation of the line representative point P1. (2 points)
c=3-2m
2. If we apply the Hough Transform on the image below, what would be the maximum value for
the accumulator cell in the Hough space (2 marks)? What is the ρ and θ value when the
accumulator cell reaches the maximum (4 marks)? Please explain the reasons.
Note: each black square denotes a point and the numbers are the coordinates.
8, ρ = 5 and θ = 90
4. Briefly explain the basic steps of circle fitting algorithm using Hough transform (2 marks).
Discuss the parameters that could affect the detection result (2 marks).
Question #5 – KNN and K-means (12 marks)
1. The KNN classifier identify an unknown sample (testing point) with K nearest training patterns.
The Euclidean distance is used to measure the distance. Suppose we have two classes of
samples, true (+) and false (-), and we have another testing point (o). The samples have twodimensional feature vector (X, Y). Please answer the following questions (6 marks).
(a) What would be the label of this testing point if K=1? False (-)
(b) What would be the label of this testing point if K=3? True (+)
(c) What would be the label of this testing point if K=5? True (+)
2. Cluster the following instances that have two attributes using the K-means algorithm and
Euclidean similarity measure. Input instances:
𝐴 = (2,10), 𝐵 = (2,5), 𝐶 = (8,4), 𝐷 = (5,8), 𝐸 = (6,4), 𝐹 = (1,2), 𝐺 = (7,5), 𝐻 = (4,9).
For the clustering steps, consider 𝐾 = 3 and the initial cluster centroids are: 𝐴, 𝐷, and 𝐹. Now,
compute the cluster centers (6 points).
Ans: The answer can be similar to:
Initialization: A(2,10) B(2,5) C(8,4)
0
5
8.49
D0
3.61
4.24
5
8.06
3.16
7.28
G0
Iteration 1:
D1
G0
D(5,8)
3.61
0
7.21
E(6,4)
7.21
4.12
5.39
F(1,2)
8.06
7.21
0
G(7,5)
7.07
3.61
6.71
H(4,9)
2.24
1.41
7.62
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
0
1
0
0
5.67
6.52
5
4.12
1.58
8.49
2.83
6.52
3.61
2.24
5.7
7.21
2
4.53
8.06
6.40
1.58
7.07
1.41
5.7
2.24
3.61
6.04
1
0
0
0
0
1
0
1
0
0
1
0
0
1
0
0
0
1
0
1
0
1
0
0
C1=(2,10)
C2=(6,6)
C3=(1.5, 3.5)
C1=(3,9.5)
C2=(6.5,5.25)
C3=(1.5, 3.5)