Image Compression and Signal Processing Dan Hewett CS 525

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

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

Basics of DFT 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 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