Data Compression: The Complete Reference

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4.19 FELICS 409A BPA B PBA PProbability10... 0... 11...LH(a)(b)Figure 4.125: (a) The Two Neighbors. (b) The Three Regions.2. The intensity of P is lower than L (P is in the left region). The code assigned to Pin this case starts with 10.3. P’s intensity is greater than H. P is assigned a code that starts with 11.When pixel P is in one of the outer regions, the probability that its intensity willdiffer from L or H by much is small, so P can be assigned a long code in these cases.The code assigned to P should thus depend heavily on whether P is in the centralregion or in one of the outer regions. Here is how the code is assigned when P is inthe central region. We need H − L + 1 variable-size codes that will not differ much insize and will, of course, satisfy the prefix property. We set k = ⌊log 2 (H − L +1)⌋ andcompute integers a and b bya =2 k+1 − (H − L +1), b =2(H − L +1− 2 k ).Example: If H − L = 9, then k =3,a =2 3+1 − (9+1)=6,andb =2(9+1− 2 3 )=4.We now select the a codes 2 k − 1, 2 k − 2,...expressed as k-bit numbers, and the b codes0, 1, 2,... expressed as (k + 1)-bit numbers. In the example above, the a codes are8 − 1 = 111, 8 − 2 = 110, through 8 − 6 = 010, and the b codes, 0000, 0001, 0010, and0011. The a short codes are assigned to values of P in the middle of the central region,and the b long codes are assigned to values of P closer to L or H. Notice that b is even,so the b codes can always be divided evenly. Table 4.126 shows how ten such codes canbe assigned in the case L = 15, H = 24.When P is in one of the outer regions, say the upper one, the value P − H shouldbe assigned a variable-size code whose size can grow quickly as P − H gets bigger. Oneway to do this is to select a small nonnegative integer m (typically 0, 1, 2, or 3) and toassign the integer n a 2-part code. The second part is the lower m bits of n, and thefirst part is the unary code of [n without its lower m bits] (see Exercise 2.3 for the unarycode). Example: If m =2,thenn = 1101 2 is assigned the code 110|01, since 110 is theunary code of 11. This code is a special case of the Golomb code (Section 2.4), wherethe parameter b is a power of 2 (2 m ). Table 4.127 shows some examples of this code form =0, 1, 2, 3andn =1, 2,...,9. The value of m used in any particular compression jobcan be selected, as a parameter, by the user.
410 4. Image CompressionPixel Region PixelP code codeL=15 0 000016 0 001017 0 01018 0 01119 0 10020 0 10121 0 11022 0 11123 0 0001H=24 0 0011Table 4.126: The Codes for the Central Region.Pixel Regionm =P P–H code 0 1 2 3H+1=25 1 11 0 00 000 000026 2 11 10 01 001 000127 3 11 110 100 010 001028 4 11 1110 101 011 001129 5 11 11110 1100 1000 010030 6 11 111110 1101 1001 010131 7 11 1111110 11100 1010 011032 8 11 11111110 11101 1011 011133 9 11 111111110 111100 11000 10000... ... ... ... ...... ... ... ... ...Table 4.127: The Codes for an Outer Region.2 5 7 123 0 11 102 1 8 154 13 11 9Figure 4.128: A 4×4 Bitmap.⋄ Exercise 4.4: Given the 4×4 bitmap of Figure 4.128, calculate the FELICS codes forthe three pixels with values 8, 7, and 0.
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Data CompressionThird Edition
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David SalomonData CompressionThe Co
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To the many readers, whose question
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viiiPreface to the Third Editionthe
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xPreface to the Third Editionhttp:/
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xiiPreface to the Second EditionThe
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xivPreface to the Second Editionema
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xviAcknowledgmentsPreface to the Fi
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xviiiContents3 Dictionary Methods 1
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xxContents6 Video Compression 6376.
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2 Introductionstream) that has a sm
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4 Introductionalready compressed an
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6 IntroductionChar. Freq. Prob. Cha
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16 1. Basic TechniquesA B C D E•
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762 8. Other Methods# of guesses: 1
Page 785 and 786:
764 8. Other Methods2. It has been
Page 787 and 788:
766 8. Other MethodsWhile text is i
Page 789 and 790:
768 8. Other Methods...s|wiss␣mis
Page 791 and 792:
770 8. Other Methods...your␣|swis
Page 793 and 794:
772 8. Other Methodscontext file. T
Page 795 and 796:
774 8. Other MethodsEquation (8.2).
Page 797 and 798:
776 8. Other MethodsS[1 ...0] = λS
Page 799 and 800:
778 8. Other Methodssuch a drawing
Page 801 and 802:
780 8. Other Methodsand subtract8.5
Page 803 and 804:
782 8. Other Methodsthat the probab
Page 805 and 806:
784 8. Other MethodsThis section an
Page 807 and 808:
786 8. Other Methodstoken is a pref
Page 809 and 810:
788 8. Other Methodsinto a three-di
Page 811 and 812:
790 8. Other MethodsThe LZW algorit
Page 813 and 814:
792 8. Other MethodsS:=empty string
Page 815 and 816:
794 8. Other Methodsimage, since it
Page 817 and 818:
796 8. Other MethodsMark: A visible
Page 819 and 820:
798 8. Other Methodsthe index is ba
Page 821 and 822:
800 8. Other MethodsA finite-state
Page 823 and 824:
802 8. Other MethodsThe DMC algorit
Page 825 and 826:
804 8. Other MethodsThis suggests t
Page 827 and 828:
806 8. Other Methods10 2 5 00 01011
Page 829 and 830:
808 8. Other MethodsThe main princi
Page 831 and 832:
810 8. Other Methods×ZS 1S 2×YPX
Page 833 and 834:
812 8. Other Methodswhere it compre
Page 835 and 836:
814 8. Other MethodsNew symbol the
Page 837 and 838:
816 8. Other Methodsthe pair (1, 2)
Page 839 and 840:
818 8. Other Methodsregions, each w
Page 841 and 842:
820 8. Other Methods5. The half-edg
Page 843 and 844:
822 8. Other MethodsH=H|C;% append
Page 845 and 846:
824 8. Other Methodsis the number o
Page 847 and 848:
826 8. Other MethodsC C R R R S L C
Page 849 and 850:
828 8. Other MethodsThe Unicode Sta
Page 851 and 852:
830 8. Other Methodsmode). The tags
Page 853 and 854:
832 8. Other MethodsThe encoder the
Page 855 and 856:
Page 857 and 858:
836 BibliographyBanister, Brian, an
Page 859 and 860:
838 BibliographyCormack G. V., and
Page 861 and 862:
840 BibliographyFrank, Amalie J., J
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842 BibliographyNorwell, MA, 85-112
Page 865 and 866:
844 BibliographyLangdon, Glen G. (1
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846 BibliographyNahin, Paul J., (19
Page 869 and 870:
848 BibliographyRFC1950 (1996) ZLIB
Page 871 and 872:
850 BibliographyStarck, J. L., F. M
Page 873 and 874:
852 BibliographyWilliams, Ross N. (
Page 875 and 876:
Page 877 and 878:
856 GlossaryASCII Code. The standar
Page 879 and 880:
858 GlossaryCircular Queue. A basic
Page 881 and 882:
860 Glossaryfunction (which has to
Page 883 and 884:
862 Glossarybackground is a continu
Page 885 and 886:
864 GlossaryGolomb Code. The Golomb
Page 887 and 888:
866 GlossaryJBIG2. A recent interna
Page 889 and 890:
868 GlossaryLifting Scheme. A metho
Page 891 and 892:
870 GlossaryMPEG. This acronym stan
Page 893 and 894:
872 GlossaryQM Coder. This is the a
Page 895 and 896:
874 GlossaryStatistical Methods. Th
Page 897 and 898:
876 Glossaryredundancy. A typical t
Page 899 and 900:
Page 901 and 902:
880 IndexAES, see association of au
Page 903 and 904:
882 Indexcodec, 7, 858codesASCII, 8
Page 905 and 906:
884 Indexlists, 860queues, 172, 860
Page 907 and 908:
886 Indexcausal, 553deriving coeffi
Page 909 and 910:
888 IndexIMA ADPCM compression, 436
Page 911 and 912:
890 Indexas the information functio
Page 913 and 914:
892 Indexvertical, 244parrots (imag
Page 915 and 916:
894 IndexReynolds, Paul, 167RGB col
Page 917 and 918:
896 Indexterabyte, 616textcase flat
Page 919 and 920:
898 IndexD4, 551, 558, 560D8, 558di
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