Image Compression and Signal Processing Dan Hewett CS

Image Compression and Signal Processing Dan Hewett CS 525

Keys to Compression Lossless – Must find information redundancy Lossy n n Find information similarity Degrade quality

Types of source images Complex Noisy Line Drawing 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) n n Real valued inputs -> A single complex output Measures “how much is there” of a single frequency FFT (Fast Fourier Transform) n n Real inputs -> Complex Outputs (0. . fs/2) Measures “How much is there” of n/2 frequencies DCT (Discrete Cosine Transform) n Real inputs -> Real output

Basics of DFT compares sin/cos to wave Result is complex number (mag+phase)

Basics of DCT Real Inputs -> Real outputs JPG encodes each pixel based on an 8 X 8 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