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Wavelets in image compression
P. F. GóraFaculty of Physics, Astronomy and Applied Computer
Sciences, Jagellonian University
Kraków, 2009
Copyright © 2009, P.F.Góra 2
Czyngis-chan
Copyright © 2009, P.F.Góra 3
Copyright © 2009, P.F.Góra 4
Principles of compression
• Compute the transform
• Kill off the weak
• Round up („quantize”) the coefficients
• JPEG:– divide the picture into 8x8 blocks– do a fast cosine transform in each block
Copyright © 2009, P.F.Góra 5
oryginał, 420x480, 8bpp JPEG, 0.19bpp
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The basis of JPEG representation
The picture in each 8x8 block is represented as a
combination of 64 „basic pictures”
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The FBI filesA fingerprint fragment from FBI collection. The original has 589824 bytes. FBI has archived nearly 200 million fingerprints, with 20000-30000 cards added everyday. In a typical case ~29 million cards are searched.
Blow-up of the original card. JPEG compressed by a factor 13. 45853 bytes.
Copyright © 2009, P.F.Góra 8
Wavelet image compressionWavelet transform over rows and columns;
Without dividing the image into blocks;
Each row acts as a filter bank; decimating the results.
Cascade of filters – the pyramide algorithm, faster tahn FFT.
Quantizing of coefficients.
JPEG2000 standard
Copyright © 2009, P.F.Góra 9
An example
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wavelet compression, 0.19bpp JPEG, 0.19bpp
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The FBI files:wavelet compression
Blow-up of the original card. 13-to krotna kompresja falkowa. 45621 bajtów.
Copyright © 2009, P.F.Góra 12
Edge detection
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Other applications
Denoising (medical, astronomical, satellite, ... images)
Image enhancement