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Wavelets in image compression P. F. Góra Faculty of Physics, Astronomy and Applied Computer Sciences, Jagellonian University Kraków, 2009
Copyright © 2009, P.F.Góra2 Czyngis-chan
Copyright © 2009, P.F.Góra3
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.Góra5 oryginał, 420x480, 8bppJPEG, 0.19bpp
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
Copyright © 2009, P.F.Góra7 The FBI files A fingerprint fragment from FBI collection. The original has bytes. FBI has archived nearly 200 million fingerprints, with cards added everyday. In a typical case ~29 million cards are searched. Blow-up of the original card. JPEG compressed by a factor bytes.
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
Copyright © 2009, P.F.Góra9 An example
Copyright © 2009, P.F.Góra10 wavelet compression, 0.19bppJPEG, 0.19bpp
Copyright © 2009, P.F.Góra11 The FBI files: wavelet compression Blow-up of the original card. 13-to krotna kompresja falkowa bajtów.
Copyright © 2009, P.F.Góra12 Edge detection
Copyright © 2009, P.F.Góra13 Other applications Denoising (medical, astronomical, satellite,... images) Image enhancement
 AN ANALYSIS OF DIGITAL WATERMARKING IN FREQUENCY DOMAIN.
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Copyright © 2013, 2009, 2006 Pearson Education, Inc. 1 Section 5.4 Polynomials in Several Variables Copyright © 2013, 2009, 2006 Pearson Education, Inc.
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Chapter 2 Section 3. Objectives 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. More on Solving Linear Equations Learn and use the four steps for.
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Lecture 2 Concepts, Terms and Definitions. Display Devices They are divided into a lot of small squares called pixels (“PICture ELements”). Each pixel.
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