Description
1. (25 points.) Write a function named myjpeg in Matlab that approximates the way the JPEG image compression
algorithm works, using the following steps:
• Input the source image and a positive number τ that determines the amount of compression (a bigger number means more compression).
• Make sure the image is a double in the range [0, 255].
• Subtract 128 from the image intensities (so they range between -128 and +127).
• Split the source image into 8×8 blocks, and take the 2D Discrete Cosine Transform of each block. Use the
functions dct2 and blockproc.
• For each block, set any coefficients that are less than τ in magnitude to 0.
• Take the inverse DCT of each 8×8 block to recover a compressed image.
• Add 128 to the resulting image intensities. Clip values to the [0, 255] range.
• Display the compressed image on the screen.
Turn in a code listing with your homework. (Note that your algorithm is doing threshold coding, while JPEG uses a
kind of zonal coding based on a normalization matrix.)
Test your routine on the image guardian.png provided in the zip file using τ = 10, τ = 25, and τ = 75. Include
a printout of each image with your homework. Explain what you see in each case (it will help to put the original
image side-by-side with the compressed one; look carefully at fine-detail regions of the image). Experiment to see
how large you can make τ before you see perceptible differences in the image. How does the saved filesize change
with τ?
2. (25 points.)
(a) Create a point spread function that simulates motion blur using the command
PSF = fspecial(‘motion’,21,11);. This creates a PSF that is roughly a line 21 pixels long oriented at an
angle of 11 degrees. Apply the motion blur filter to the image death.png using the imfilter command.
Remember to supply an appropriate 3rd argument so that array values outside the borders are assumed to be
white. You can should see that the image is blurred to the point that text and fine details are not readable.
(b) The image museum-blur.png was blurred with the same point spread function as above, and there was no
additional noise added to it (although be aware that saving the image as an 8-bit image actually introduces
a very small amount of quantization noise). Since we know the PSF exactly and there is no noise added to
the image, apply the inverse filter using deconvwnr to undo the blur. Discuss the restored image in terms of
sharpness, artifacts, readability of text, contrast, etc.
(c) You should still observe some problems that came from the inverse filter due to the quantization noise. Instead, supply deconvwnr with a very small noise-to-signal ratio of 0.00001. How does this restored image
look?
More fun on the next page −→
3. (25 points.)
(a) Consider the image clock2.png. Compute its Radon transform using θ ranging from 0◦
to 179◦
and ∆θ = 2
◦
.
Display the result in grayscale with axes labels (hint: use radon with full input and output arguments, and
clip the image intensities to [0, 255], don’t scale them). Interpret what you see, paying particular attention to
the ρ = 0 line. How are the θ value and bright spots in the Radom transform related to features of the original
image? Why is the image black at the top and bottom, and why is the non-zero region of the Radon transform
rectangular?
(b) Now recover an approximation to the original image using the inverse Radon transform. Remember that you
must supply the theta vector to iradon. Interpret what you see. Where does the result look good and where
are there visible artifacts? Repeat the experiment by taking the forward and inverse Radon transform using
∆θ = 1
◦
. How has the result improved? Are there still visible artifacts?
4. (25 points.) Consider the grayscale image guys.png. In this problem, you’ll look at four ways of rendering it in
black and white. For each method, include the black-and-white image produced by your code, and discuss its
qualitative appearance in some detail. Make sure to cast the input image as a double before starting!
(a) First, threshold the image at a value of 128.
(b) Next, apply uniform dithering by adding i.i.d. uniform random noise in the range [-50,50], then thresholding
the resulting image at a value of 128.
(c) Third, halftone the image by tiling the image into 4×4 blocks, adding the Bayer mask
16×
1 9 3 11
13 5 15 7
4 12 2 10
16 8 14 6
to each block, and thresholding the resulting image at a value of 256.
(d) Finally, use Matlab’s built-in dither command to apply Floyd-Steinberg dithering.