Digital Image Processing: Homework #1

EE 569 Digital Image Processing: Homework #1

EE 569: Homework #1

General Instructions:
1. Read Homework Guidelines and MATLAB Function Guidelines for the information about homework
programming, write-up and submission. If you use the C/C++ programming language, you will get
5% of your total score as the bonus points.
2. If you make any assumptions about a problem, please clearly state them in your report.
3. You need to understand the USC policy on academic integrity and penalties for cheating and
plagiarism. These rules will be strictly enforced.
Problem 1: Basic Image Manipulation (30%)
In this problem, you will conduct a series of simple manipulations on grayscale and color images to get
familiar with image data access, processing and output.
(a) Color Space Transformation (Basic: 18%)
Different color spaces are adopted for different applications. In this problem, you will examine a couple
of color spaces that are employed in image processing.
1. Color-to-Grayscale Conversion
Each color pixel of an image is described by a triple (R, G, B) for red, green, and blue color intensities.
There are many ways to convert a color image to its grayscale image. The lightness method averages
the most prominent and least prominent colors: (max(R, G, B) + min(R, G, B)) / 2. The average
method simply averages the values: (R + G + B) / 3. The luminosity method is a more sophisticated
version of the average method. It also averages the values, but it forms a weighted average to account
for human perception. The formula for luminosity is 0.21 R + 0.72 G + 0.07 B. Convert the color
Tiffany image in Figure 1 to its gray scale images using the above three methods. Show the three gray
scale images and discuss which method works best overall.
Figure 1: Color Tiffany image
2. CMY(K) Color Space - The Cyan-Magenta-Yellow-(Black) (CMY(K)) colorspace isfrequently used
in image printing. It is defined by:
EE 569 Digital Image Processing: Homework #1
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(1)
What is the CMY representation for test images Bear and Dance in Figure 2? For each input color
image, produce 3 output grayscale images, corresponding to the cyan, magenta, yellow three channels
and show these three grayscale images in your report.

Figure 2: Bear and Dance images
(b) Image Resizing via Bilinear Interpolation (Advanced: 12%)
Use the bilinear interpolation to re-size the input color image airplane of size 512x512 in Figure 3 to an
output image of size 650x650. An image re-sizing example for the House image is given in Figure 4.
Figure 3: Airplane
C =1− R
M =1− G
Y =1− B
⎧
⎨
⎪
⎩
⎪
EE 569 Digital Image Processing: Homework #1
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(a) house image of size 512x512 (b) resized house image of size 650x650
Figure 4: Original and resized House images.
Problem 2: Histogram Equalization (40 %)
(a) Histogram Equalization (Basic: 12%)
Implement two histogram equalization techniques:
• Method A: the transfer-function-based histogram equalization method,
• Method B: the cumulative-probability-based histogram equalization method
to enhance the contrast of the Desk image in Figure 5 below.
(1) Plot the histograms of the red, green and blue channels of the original image. The figure should have
the intensity value as the x-axis and the number of pixels as the y-axis.
(2) Apply Method A to the original image and show the enhanced image. Plot the transfer function for
each channel.
(3) Apply Method B the original image and show the enhanced image. Plot the cumulative histogram for
each channel.
(4) Discuss your observations on these two enhancement results. Do you have any idea to improve the
current result?
Figure 5: Desk image
(b) Image Filtering – Creating Oil Painting Effect (Advanced: 16%)
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An exemplary oil-painting effect for the Barn image is shown in Figure 7. This effect can be implemented
as a filter with the following two steps.

(a) Barn (b) Barn with a reduced color set
Figure 6: Barn images with a full and a reduced color sets
Step 1: Quantize all colors of the input color image, denoted by I0, into an image containing only 64 colors,
denoted by I1. In other words, each channel should have only 4 values. The original and truncated Barn
images are shown in Figs. 6 (a) and (b), respectively.
Step 2: For each pixel of image I1, select the most frequent color in its NxN neighborhood (N is an odd
number, usually ranging from 3 to 11), as the representative color for this pixel in another output image
denoted by I2. The result of N = 5 is shown in Figure 7.
Figure 7: Barn with the Oil-Painting Effect
Implement and apply the oil-painting filter to the Star_Wars and Trojans images as shown in Figs. 8 and
9.
(1) Show the 64-color version of both images by following Step 1. Discuss how you choose the threshold.
(2) Implement the oil painting process as described in Step 2 with several different values of N. Which N
gives a better result? Discuss your observations.
(3) What happens to this filter when the input image has 512 colors instead? Show the corresponding
results for both images and explain your observation.
EE 569 Digital Image Processing: Homework #1
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Figure 8: Star_Wars Figure 9: Trojans
(c) Image Filtering – Creating Film Special Effect (Advanced: 12%)
Design an algorithm to achieve the film special effect. An example is shown in Figure 10. Describe your
algorithm step by step and apply your algorithm to test image Girl given in Figure 11. Show the film
special effect result in your report.
Hint: investigate the color channel relationship between the input and output images in Figure 10, which
will give your ideas about the film special effect.
Figure 10: An exemplary film special effect: the input (left) and the output (right).
Figure 11: Girl
EE 569 Digital Image Processing: Homework #1
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Problem 3: Noise Removal (30 % + 10 %)
In this problem, you will implement a set of denoising algorithms to improve image quality. You can use
the PSNR (peak-signal-to-noise-ratio) quality metric to assess the performance of your denoising
algorithm. The PSNR value for R, G, B channels can be, respectively, calculated as follows:
(a) Mix noise in color image (Basic: 15%)
Perform noise removal on a color image corrupted by a “mix” type of noise. The original and noisy Lena
images are shown in Figure 12.

Figure 12: The original and noisy Lena images.
1. Identify noise types in the noisy Lena image, and answer the following questions.
(1) Do all channels have the same noise type?
(2) Should you perform filtering on individual channels separately for both noise types?
(3) What filters would you like use to remove mixed noise?
(4) Can you cascade these filters in any order? Justify your answer.
(5) Discuss the effect of different filter window sizes.
2. Get the best results in removing mixed noise. Include the following in your report:
(1) Describe your method and show its results.
(2) Discuss its shortcomings.
(3) Give some suggestions to improve its performance.
EE 569 Digital Image Processing: Homework #1
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(b) Principal component analysis (PCA) (Advanced: 15%)
Principal component analysis (PCA) is a dimensionality reduction algorithm, yet it can also be used as a
tool for noise filtering. In this part, please read carefully the reference paper [1].
1. Explain why PCA can be used as a filtering approach for noisy data. What do the components mean
and how to choose the number of components in image denoising.
2. Describe and implement the patch-based local PCA (PLPCA) in [1]. (Use any available online source
code but include the source in your reference).
3. Apply the PLPCA to House_noisy.raw (Gaussian noise, � = 25) in Figure 13. Optimize different
parameters, e.g. patch size, the number of components, etc., and discuss their effect on the denoising
process. State the best PSNR and your optimized parameters in your report.
4. Apply the approach in part (a) to House_noisy.raw and compare the performance of the PCA approach
with those of filters used in part (a). Please explain the advantages of the PCA approach and why.
DO NOT quote statements directly from [1] or any other online source. Try and explain in your own
words. Reports and source codes are subject to verification for any plagiarism.
Figure 13: The grey-level original and noisy House images
(c) Block matching and 3-D (BM3D) transform filter (Bonus: 10%)
In this part, you will get familiar with another state-of-the-art denoising algorithm proposed in [2].
1. Please explain the BM3D algorithm in your own words, and implement the BM3D filter (Use any
available online source code but include the source in your reference) to denoise the noisy image:
House (Figure 13). Discuss the effects of several tunable parameters on the denoising result.
Note: It is recommended that you use the code provided by the authors on their website [3]. Their code is
written in MATLAB; so that it is okay to use MATLAB for this part (You still qualify for 5% bonus points
if you have used C/C++ everywhere else).
2. Why does the author utilize block matching? What is the motivation of step 2 (block matching and
Wiener filtering) and compare the denoising performance with and without step 2.
3. How would you classify BM3D - spatial domain filter, frequency domain filter, or both? Justify your
answer.
4. Conduct qualitative performance comparison between the algorithms developed for Problem 3(b) and
BM3D.
EE 569 Digital Image Processing: Homework #1
Professor C.-C. Jay Kuo Page 8 of 8
Appendix:
Problem 1: Simple Image Manipulation
Tiffany.raw 512x512 24-bit color(RGB)
Bear.raw 854x480 24-bit color(RGB)
Dance.raw 854x480 24-bit color(RGB)
Airplane.raw 512x512 24-bit color(RGB)
Problem 2: Histogram Equalization
Desk.raw 400x300 24-bit color(RGB)
Barn.raw 380x275 24-bit color(RGB)
Barn_64.raw 380x275 24-bit color(RGB)
Barn_oil.raw 380x275 24-bit color(RGB)
Star_Wars.raw 600x338 24-bit color(RGB)
Trojans.raw
Original.raw
Film.raw
Girl.raw
1800x1200
1000x750
1000x750
256x256
24-bit
24-bit
24-bit
24-bit
color(RGB)
color(RGB)
color(RGB)
color(RGB)
Problem 3: Noise Removal
Lena.raw 512x512 24-bit color(RGB)
Lena_mixed.raw 512x512 24-bit color(RGB)
House.raw 256x256 8-bit grey
House_noisy.raw 256x256 8-bit grey
Reference Images
All images in this homework are from Google images [4] or the USC-SIPI image database [5].
References
[1] Deledalle, Charles-Alban, Joseph Salmon, and Arnak S. Dalalyan. "Image denoising with patch
based PCA: local versus global." BMVC. Vol. 81. 2011.
[2] K. Dabov, A. Foi, V. Katkovnik, and K. Egiazarian, “Image denoising by sparse 3-d transformdomain collaborative filtering,” Image Processing, IEEE Transactions on, vol. 16, no. 8, pp. 2080–2095,
2007.
[3] [Online]. Available: http://www.cs.tut.fi/~foi/GCF-BM3D/
[4] [Online] http://images.google.com/
[5] [Online] http://sipi.usc.edu/database/