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EE4206 Digital Image Processing Course Intended Learning Outcomes (CILOs)

Number CILOs

1 Describe principles of different digital imaging systems

2 Analyse and design digital filters for two-dimensional (2-D) signals

3 Perform the 2-D discrete Fourier transform (DFT)

4 Implement image processing algorithms on computers

5 Apply computer algorithms to practical problems

Teaching and Learning Activities (TLAs)

CILOs 1, 2, 3 Lectures, tutorials, on-line learning

CILOs 4, 5 Computer projects

Assessment Tasks/Activities

Type of assessment tasks Weighting

Continuous assessment Written assignments, quizzes, computer projects 30%

Examination Written examination 70%

Grading of Student Achievement

Letter Grade Grade Point Grade Definitions

A+ A A-

4.3 4.0 3.7

Excellent

B+ B B-

3.3 3.0 2.7

Good

C+ C C-

2.3 2.0 1.7

Adequate

D 1.0 Marginal

F 0.0 Failure

EE4206 Digital Image Processing Tutorial #1

Assume that a video system has

- Each frame size 512 by 512;

- 30 frames/second;

- 8 bits for each color component.

(1) What is the minimum data rate needed to transmit the

video if the data are uncompressed?

(2) What compression ratio is needed to transmit the data

through a modem with the speed of 56K bit/s?

(3) Suppose that we can down-sample the image to reduce the

amount of data. For a compression ratio of 100, what is

the maximum image size the above modem can handle?

EE4206 Digital Image Processing

Tutorial #2

1. Estimate the diameter of the smallest dot on a page that the eyes can discern if the page is 0.2m away from the eyes. Assume: The retina has a diameter of 28 mm. The fovea is a square area of 1.5mm by 1.5 mm. The fovea has 580 by 580 receptors equally spaced in the square area. The

eyes cannot resolve a dot whose image on the fovea is less than a receptor in size.

2. Suppose that a flat area with center at (x0, y0) is illuminated by a light source with

intensity distribution

])()[( 20

20),( yyxxKeyxi

Assume that the reflectance of the area is 1, and let K = 255. If the resulting image is digitized with m bits of intensity resolution, and the eye can detect an abrupt change of eight shades of intensity between adjacent pixels, what value of m will cause visible false contours?

Left image: m is too small (too few gray levels); right image: m is enough.


Tutorial #3

1. Suppose that a flat area with center at (x0, y0) is illuminated by a light source with intensity distribution

])()[( 20

20),( yyxxKeyxi

Assume that the reflectance of the area is 1, and let K = 255. Assume that the resulting image is digitized with m = 2 bits of intensity resolution with a uniform quantiser. Determine the decision and output levels of the quantizer and sketch the quantized image.

2. Red and green lights can be considered as radio waves with two different frequencies. Explain why we get yellow if we mix red and green. (Hint: A radio wave can be modeled using a sine function sin(2vx), where is the frequency of the wave).


Tutorial #4

1. Convert the following 4-path to an 8-path.

2. Design a method to determine whether each connected component in the diagram below

a. touches the boundary of the image; b. contains one or more holes.

Image boundary


Tutorial #5

1. Propose a set of gray-level slicing transformations capable of producing all the individual bit planes of an 8-bit monochrome image.

Hint: the transformation for bit 7 is shown below:

2. Consider all bit planes in an image

(a) How would the histogram of the image change if we set the least significant

bit of each pixel to zero? (b) How would the histogram of the image change if we set the most significant

bit of each pixel to zero?

1

0128 255


Tutorial #6

1. In local image enhancement equalization, we need to compute the histogram of a small sliding window in an image. Propose a method to efficiently update the local histogram.

2. An image with intensities in the range [0, 1] has the gray scale level PDF pr(r)

shown in the following diagram. It is desired to transform the gray levels of this image so that they will have the specified pz(z) shown. Assume that r and z are continuous variables. Find the transformation in terms of r and z to accomplish this.

0 1 r

pr(r)

2

0 1z

pz(z)

2


Tutorial #7

1. Show that the Laplacian operator 2

2

2

22

y

f

x

ff

is isotropic. That is, if we

rotate the coordinate system (x, y) by an angle , then the Laplacian for the rotated coordinate system is the same as that before the rotation.

Hint: Coordinate rotation can be described by

cossin

sincos

yxy

yxx

2. Consider unsharp masking and highboost filtering

yxgkyxfyxg

yxfyxfyxfyxg

,,,

image blurred, ,,,

mask

mask

Design a 3 3 filter mask to perform the above operation.


Tutorial #8

1. A real function f(x) can be decomposed as the sum of an even function and an odd

function.

(a) Show that

)()(2

1)( and )()(

2

1)( xfxfxfxfxfxf oddeven

(b) Show that

)(Im)( and )(Re)( xfFjxfFxfFxfF oddeven

2. Assume that x and y are continuous variables, that )()( FxfF and that

),(),( vuFyxfF . Determine the Fourier transforms of

(a) )(xfdx

d

(b) ),(),( yxfy

yxfx

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