1. Wavelets in image compression P. F. Góra Faculty of Physics, Astronomy and Applied Computer Sciences, Jagellonian University Kraków, 2009

2. Copyright © 2009, P.F.Góra2 Czyngis-chan

3. Copyright © 2009, P.F.Góra3

4. 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

5. Copyright © 2009, P.F.Góra5 oryginał, 420x480, 8bppJPEG, 0.19bpp

6. Copyright © 2009, P.F.Góra6 The basis of JPEG representation The picture in each 8x8 block is represented as a combination of 64 basic pictures

7. Copyright © 2009, P.F.Góra7 The FBI files A 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.

8. Copyright © 2009, P.F.Góra8 Wavelet image compression Wavelet 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

9. Copyright © 2009, P.F.Góra9 An example

10. Copyright © 2009, P.F.Góra10 wavelet compression, 0.19bppJPEG, 0.19bpp

11. Copyright © 2009, P.F.Góra11 The FBI files: wavelet compression Blow-up of the original card. 13-to krotna kompresja falkowa. 45621 bajtów.

12. Copyright © 2009, P.F.Góra12 Edge detection

13. Copyright © 2009, P.F.Góra13 Other applications Denoising (medical, astronomical, satellite,... images) Image enhancement