Compression: Why? Shannon! H = ²log S^n = n log S H: information S: number of symbols n:...

Transcript of Compression: Why? Shannon! H = ²log S^n = n log S H: information S: number of symbols n:...

Compression: Why? Shannon!

H = ²log S^n = n log S

H: informationS: number of symbolsn: messagelength

But what if we know what to expect?So S = 2, n = 4 has same info content as S = 16, n = 1Because 4 log 2 = 1 log 16So we can e.g. code 4 bits as one hexadecimal number

Entropy:m: a possible messagep: probability

H = -Σ p(m) ²log p(m)

4 random bits (16 r. messages):H = - 16 * 1/16 ²log 1/16 = 4 bit

Image compression: Fourier

Freq.

Time

http://www.google.nl/url?sa=i&rct=j&q=image%20compression%20fourier&source=images&cd=&cad=rja&docid=QfI7P6U5epmkbM&tbnid=vhY2mdS2hDHZCM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.sciencedirect.com%2Fscience%2Farticle%2Fpii%2FS0262885604002276&ei=GOJFUYOsIenA0QWSuYG4Ag&bvm=bv.43828540,d.d2k&psig=AFQjCNFnAN1lPj8VVUPzdw-EUjhxEcavIw&ust=1363620690621469

Fourier: filter out high spatial frequencies

http://www.google.nl/url?sa=i&rct=j&q=image%20compression%20fourier&source=images&cd=&cad=rja&docid=DgKMos0oreDjaM&tbnid=y4xZgmmn130t1M:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.mathworks.com%2Fmatlabcentral%2Ffileexchange%2F9554-a-numerical-tour-of-signal-processing%2Fcontent%2Fnumerical-tour%2Fcs_fourier%2Findex.html&ei=ZuNFUb_rEsiG0AWm4YGoDQ&bvm=bv.43828540,d.d2k&psig=AFQjCNE1oCEGOwXgymyx6uYjAHtQnCH2jg&ust=1363621070031755

Blockwise Fourier: blocking artefact

Quantisation artefact

Vector quantisation

http://www.google.nl/url?sa=i&rct=j&q=image%20compression%20vector%20quantisation&source=images&cd=&cad=rja&docid=Gr8TV59z-5hsAM&tbnid=sv7J2yn4WQsK1M:&ved=0CAUQjRw&url=http%3A%2F%2Fblog.vene.ro%2Ftag%2Fscikit-learn%2F&ei=kuZFUZrSDqy20QXl14DwDA&bvm=bv.43828540,d.d2k&psig=AFQjCNE8ii_aALbPnaU1hrcRkBayjI7O-g&ust=1363621879144499

http://www.google.nl/url?sa=i&rct=j&q=image%20compression%20vector%20quantisation&source=images&cd=&cad=rja&docid=Javpf0LoN3-4QM&tbnid=7KQ5CiSsaTuZOM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.squeezechart.com%2Fpeople.html&ei=rOZFUZL1MMnH0QXQoIGwAw&bvm=bv.43828540,d.d2k&psig=AFQjCNE8ii_aALbPnaU1hrcRkBayjI7O-g&ust=1363621879144499

Inter-frame compression

http://www.google.nl/url?sa=i&rct=j&q=image%20compression%20interframe&source=images&cd=&cad=rja&docid=GGNPicREg1kR9M&tbnid=gpxTJnCvvsIe1M:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.intechopen.com%2Fbooks%2Fdigital-video%2Fbuilding-principles-and-application-of-multifunctional-video-information-system&ei=NOdFUdawNcqq0QWUx4HgDg&bvm=bv.43828540,d.d2k&psig=AFQjCNGrcwGqpIi70yhvjUfuFTy7cFjcgw&ust=1363622047381741

Inter-frame compression artefacts

Segmentation: Use most bandwith for important parts

http://www.google.nl/url?sa=i&rct=j&q=image%20compression%20segmentation%20model&source=images&cd=&cad=rja&docid=nDDX8JloG1HI-M&tbnid=ZO9RJKwR31FHiM:&ved=0CAUQjRw&url=http%3A%2F%2Fwww.merl.com%2Fprojects%2Fcompress-segment%2F&ei=f-hFUe-kK-bI0QWEkIH4Dg&bvm=bv.43828540,d.d2k&psig=AFQjCNGn92k9j54WdeAm5IQ9LXt8YtX9eQ&ust=1363622388040316

Compression: Why? Shannon! H = ²log S^n = n log S H: information S: number of symbols n:...

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Transcript of Compression: Why? Shannon! H = ²log S^n = n log S H: information S: number of symbols n:...

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