Description

Digital Halftoning, Frequency Domain
Please read the submission guideline carefully before getting started. All images in this homework are in PNG format and can be downloaded from our NTU COOL website. Details of all files offered are listed in the appendix. You are NOT allowed to use other functions except I/O, plotting and basic functions.
Problem 1: DIGITAL HALFTONING
sample1.png is given in Figure 1.(a) Please apply several halftoning methods to the given image and provide discussions about the detail of the results.
(a) (5 pt) Perform dithering using the dither matrix I2 in Figure 1.(b) and output the result as result1.png.
(b) (10 pt) Expand the dither matrix I2 to I256 (256 × 256) and use it to perform dithering. Output the result as result2.png. Compare result1.png and result2.png along with some discussions.
(c) (15 pt) Perform error diffusion with two different filter masks. Output the results as result3.png, and result4.png, respectively. Discuss these two masks based on the results. You can find some masks here (from lecture slide 06. p23)

1 2
3 0

(a) sample1.png (b) Dither Matrix I2 (c) sample1 dotted.png
Figure 1: The image and dither matrix for digital halftoning.
Problem 2: FREQUENCY DOMAIN
(a) (10 pt) Perform Fourier transform on sample2.png to obtain its frequency spectrum and output it as result5.png. (Please take the log magnitude of the absolute value and center the low frequency part at the origin for visualization.)
(b) (15 pt) Based on the result of part (a), design and apply a low-pass filter in the frequency domain and transform the result back to the pixel domain by inverse Fourier transform. The resultant image is saved as result6.png. Please also design a low-pass filter in the pixel domain which behaves similarly to the one you design in the frequency domain. Output the result as result7.png and provide some discussions.
(c) (15 pt) Based on the result of part (a), design and apply a high-pass filter in the frequency domain and transform the result back to the pixel domain by inverse Fourier transform. The resultant image is saved as result8.png. Please also design a high-pass filter in the pixel domain which behaves similarly to the one you design in the frequency domain. Output the result as result9.png and provide some discussions.
(d) (10 pt) Perform Fourier Transform on sample3.png and output it as result10.png. Please discuss what you observe in sample3.png and result10.png.
(e) (10 pt) Try to remove the undesired pattern on sample3.png and output it as result11.png.

(a) sample2.png (b) sample3.png
Figure 2: Images for Fourier transform.
Appendix
Problem 1: DIGITAL HALFTONING sample1.png: 256 × 256 gray-scale
Problem 2: FREQUENCY DOMAIN
sample2.png: 480 × 640 gray-scale
sample3.png: 480 × 640 gray-scale
Recommended tools for Fourier transform
scipy.fftpack.fft2 scipy.fftpack.ifft2 scipy.fftpack.fftshift scipy.fftpack.ifftshift numpy.fft.fft2 numpy.fft.ifft2 numpy.fft.fftshift numpy.fft.ifftshift