Image Compression and

pancakesbootAI and Robotics

Nov 24, 2013 (3 years and 7 months ago)

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Image Compression and
Signal Processing

Dan Hewett

CS 525

Keys to Compression

Lossless


Must find information redundancy

Lossy


Find information similarity


Degrade quality

Types of source images

Complex



Line Drawing





Noisy Simple

Simple Lossless Compression

(GIF)

Low number of colors (Uses a color map)

Compression is based on repeated
elements (LZW)

Does not work on a wide variety of source
images


Compression in Frequency/Spatial
domain

Takes advantage of spatial relationships

Compression may decrease color
resolution

May take advantage of human perception

May use further encoding (Huffman/RLE,
etc) on frequency data

Frequency Transforms (cont)

Information content is not gained/lost

Compressibility is due to
redundancy/similarity in the new domain.

DFT/FFT/DCT


How do they work?

Frequency Transforms

Looks at the sinusoidal behavior of the
color in each row and column


How do they work

DFT (Discrete Fourier Transform)


Real valued inputs
-
> A single complex output


Measures “how much is there” of a single frequency

FFT (Fast Fourier Transform)


Real inputs
-
> Complex Outputs (0..f
s
/2)


Measures “How much is there” of n/2 frequencies

DCT (Discrete Cosine Transform)


Real inputs
-
> Real output


Basics of DFT

DFT compares sin/cos to wave



Result is complex number (mag+phase)

-1
-0.5
0
0.5
1
0
2
4
6
8
10
12
reference
sin(x)
cos(x)
Basics of DCT

Real Inputs
-
> Real outputs



JPG encodes each pixel based on an 8X8
matrix of DCTs

Results of the DCT are then discretized
and compressed

Quality of compression

Low frequency lends to high compression
with less loss

Impulses (non
-
smooth) source can lead to
unpleasant artifacts

Conclusion

Redundancy/similarity is key to
compression

Find the domain where
redundancy/similarity occur

Discretize/quantize for further reduction