ECE547 Image Processing Sept 25, 2008
Exercise 3
Lecturer: Prof. Thomas Huang Due: Oct 9, 2008
Problem 1 Compression Ratio (2 points)
Compute the compression ratio that you achieved in MP3. Assume that it takes the original image
was 128 ×128 with 8 bits per pixel. Suppose that it takes 7 bits to encode each row and column
value, 3 bits to encode a, and 8 bits to encode b. What is the compression ratio for blocksize=4
and blocksize=8?
Regardless of the block size, we are encoding each block with 7 + 7 + 3 + 8 = 25 bits. For
blocksize=4, each block of the original image takes 4×4×8 = 128 bits to represent. This means
that our method gives us 128 : 25 = 5.12 : 1 compression. Similarly, for blocksize=8, each block
of the original image takes 8 ×8×8 = 512 bits to represent. This means that our method gives us
512 : 25 = 20.48 : 1 compression
Problem 2 Fractal Encoding
Cross (3 points)
Below is an image of a simple 2-D fractal. Find the corresponding IFS and its fractal (Hausdorff)
dimension.
−0.5 −0.4 −0.3 −0.2 −0.1 0 0.1 0.2 0.3 0.4
−0.5
−0.4
−0.3
−0.2
−0.1
0
0.1
0.2
0.3
0.4
w1:0.333 0
0 0.333x
y+0
0
w2:0.333 0
0 0.333x
y+0.333
0
w3:0.333 0
0 0.333x
y+−0.333
0
w4:0.333 0
0 0.333x
y+0
0.333
w5:0.333 0
0 0.333x
y+0
−0.333
1
3s
+1
3s
+1
3s
+1
3s
+1
3s
= 1
=⇒1
3s
=1
5
=⇒slog 1
3= log 1
5
=⇒s=log 5
log 3
E3-1
