Wavelets in image compression P. F. Góra Faculty of Physics, Astronomy and Applied Computer...

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


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


oryginał, 420x480, 8bpp JPEG, 0.19bpp


The basis of JPEG representation

The picture in each 8x8 block is represented as a

combination of 64 „basic pictures”


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.


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


An example


wavelet compression, 0.19bpp JPEG, 0.19bpp


The FBI files:wavelet compression

Blow-up of the original card. 13-to krotna kompresja falkowa. 45621 bajtów.


Edge detection


Other applications

Denoising (medical, astronomical, satellite, ... images)

Image enhancement

Wavelets in image compression P. F. Góra Faculty of Physics, Astronomy and Applied Computer...

Documents

Transcript of Wavelets in image compression P. F. Góra Faculty of Physics, Astronomy and Applied Computer...