Format File Bitmap RASTER GRAPHICS. Common Raster Formats. Raster Graphics GIF JPEG BMP PNG TIFF IF-UTAMA 4/4/2012

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Format File Bitmap

Dosen Pembina : Sriyani Violina, M.T. Danang Junaedi 1

RASTER GRAPHICS

2 alfeacamia.cmswiki.wikispaces.net/file/view/2.01+Raster+Graphics.ppt

Raster Graphics

• Also called bitmap

graphics

• Consist of grids of tiny

dots called pixels

• Have a fixed

resolution and cannot

be resized without

altering image quality

• Edited in paint

programs

Bitmap enlargement Notice the pixels

Image source: http://graphicssoft.about.com/od/aboutgraphics/a/bitmapvector.htm

Common Raster Formats

• GIF

• JPEG

• BMP

• PNG

• TIFF

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GIF – Graphics Interchange Format

Animation – Standard format for animation on the Internet.

Transparency – yes • Lossless compression • Colors = 256 (8-bit)

• Most common format for:

– Text

– Clip art, animations, icons, logos

– Simple diagrams, line drawings

– Graphics with large blocks of a single color

– Graphics with transparent areas

– Images displayed on computer screens and on websites.

Animated Gif

5

JPEG – Joint Photographic Experts Group

X Animation – No X Transparency – No • Lossy compression • Colors – 16.7 M (24-bit) • High quality but larger file

size than a GIF

• Commonly Used For:

– Desktop publishing photographs

– Photographs and natural artwork

– Scanned photographs – Emailing photographs – Digital camera photographs

6

BMP - Bitmap

X Animation – No

X Transparency – No

• Uncompressed

• 256 colors

• Large file size - not

well suited for transfer

across the Internet or

for print publications

• Commonly Used For:

– Editing raster graphics – Creating icons and

wallpaper

– On-screen display

Icons 7

PNG – Portable Network Graphics

X Animation – no

Transparency – yes

• Lossless

compression

• 256 colors

– Not suited for photographs

• Commonly Used For:

– Replacing GIF and TIFF images – Online viewing of images

• See examples at

http://graphicssoft.abo

ut.com/od/freedownlo

ads/l/blfreepng07.htm

8

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TIFF – Tagged Image File Format

X Animation – No X Transparency – No • Available in compressed and un-compressed formats • Compressed is advised • Colors – 16 M (24-bit)

• Commonly Used For:

– Storage container for faxes and other digital images – To store raw bitmap data

by some programs and devices such as scanners – High resolution printing – Desktop Publishing images

9

Demonstration of File Sizes

10

samsclass.info/131/pptF05/ch09.ppt

BITMAP

11

1. pages.towson.edu/hilberg/COSC109/Ch06.ppt

2. Referensi lain yang terkait

BMP File Bitmap

• The BMP file format, sometimes called bitmap or DIB file format (for

device-independent bitmap), is an image file format used to store bitmap

digital images, especially on Microsoft Windows and OS/2 operating systems.

• Bitmap is derived from the words ‘bit’, which means the simplest element in

which only two digits are used, and ‘map’, which is a two-dimensional matrix of these bits. A bitmap is a data matrix describing the individual dots or pixels (picture elements) of an image.

• Bitmapped images are known as paint graphics.

• Bitmapped images can have varying bit and color depths.

• Bitmaps are an image format suited for creation of:

– Photo-realistic images. – Complex drawings.

– Images that require fine detail.

• Many graphical user interfaces use bitmaps in their built-in graphics

subsystems;[1] for example, the Microsoft Windows and OS/2 platforms' GDI subsystem, where the specific format used is the Windows and OS/2

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Bitmaps

13

Available binary Combinations for Describing a Color

Bitmaps

1. 24 bit color (millions of colors)

2. 8 bit color (256 colors)

3. 8 bit color (Mac optimized palette)

4. 4 bits color (16 colors)

5. 8 bit gray scale (256 shades)

14

Bitmaps

Bitmaps can be inserted by:

– Using clip art galleries - an assortment of graphics, photographs, sound, and video. A popular alternative for users who do not want to create their own images.

– Using bitmap software such as Adobe's Photoshop and Illustrator, Macromedia's Fireworks, Corel's Painter, CorelDraw, Quark Express.

– Capturing and editing images.

• Capturing and storing images directly from the screen is another way to assemble images for multimedia.

• Image editing enables one to enhance and make composite images, alter and distort images and add and delete elements.

– Scanning images from conventional sources and make necessary alterations and manipulations.

15

Device-independent bitmaps and BMP file

format

BMP File Header Stores general information about the BMP file.

Bitmap Information

(DIB header)

Stores detailed information about the bitmap image.

Color Palette Stores the definition of the colors being used

for indexed color bitmaps.

Bitmap Data Stores the actual image, pixel by pixel.

16

• Microsoft has defined a particular representation of color bitmaps of different color depths, as an aid to exchanging bitmaps between devices and applications with a variety of internal representations. They called these device-independent bitmaps or DIBs, and the file format for them is called DIB file format or BMP file format. • A typical BMP file usually contains the following blocks of data:

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BMP file header

• This block of bytes is at the start of the file and is used to identify the file.

• A typical application reads this block first to ensure that the file is actually a

BMP file and that it is not damaged.

• Note that the first two bytes of the BMP file format (thus the BMP header) are

stored in big-endian order.

• This is the magic number 'BM'. All of the other integer values are stored in

little-endian format (i.e. least-significant byte first)

Offset# Size Purpose

0000h 2 bytes

the magic number used to identify the BMP file: 0x42 0x4D (Hex code points for B and M).

The following entries are possible: •BM - Windows 3.1x, 95, NT, ... etc •BA - OS/2 Bitmap Array •CI - OS/2 Color Icon •CP - OS/2 Color Pointer •IC - OS/2 Icon •PT - OS/2 Pointer 0002h 4 bytes the size of the BMP file in bytes

0006h 2 bytes reserved; actual value depends on the application that creates the image 0008h 2 bytes reserved; actual value depends on the application that creates the image 000Ah 4 bytes the offset, i.e. starting address, of the byte where the bitmap data can be

found.

17

Bitmap information (DIB header)

This block of bytes tells the application detailed information about the image, which will be used to display the image on the screen. The block also matches the header used internally by Windows and OS/2 and has several different variants.

Size Header Identified by Supported by the GDI of

12 OS/2 V1 BITMAPCOREH

EADER

OS/2 and also all Windows versions since Windows 3.0

64 OS/2 V2 BITMAPCOREH

EADER2

40 Windows V3 BITMAPINFOHE

ADER

all Windows versions since Windows 3.0

108 Windows V4 BITMAPV4HEAD

ER

all Windows versions since Windows 95/NT4

124 Windows V5 BITMAPV5HEAD

ER Windows 98/2000 and newer

18

BITMAPFILEHEADER

Offset Size Name Description 0 2 bfType ASCII “BM” 2 4 bfSize Size of file (in bytes) 6 2 bfReserved1 Zero

8 2 bfReserved2 Zero

10 4 bfOffBits Byte offset in files where image begins

14 4 biSize Size of this header (40 bytes)

18 4 biWidth Image width in pixels

22 4 biHeight Image height in pixels

26 2 biPlanes Number of image planes, must

be 1

28 2 biBitCount Bits per pixel: 1,4,8, or 24

30 4 biCompression Compression type

19

BITMAPINFOHEADER (Windows 3) (cont’d)

Offset Size Name Description

34 4 biSizeImage Size of compressed image (in bytes),

zero if uncompressed

38 4 biXPelsPerMeter Horizontal resolution (pixels/meter)

42 4 biYPelsPerMeter Vertical resolution (pixels/meter)

46 4 biClrUsed Number of colors used

50 4 biClrImportant Number of ‘important’ color

54 4*N bmiColors Color map

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Proses Pembacaan Citra 24 bit

21

Windows RGBQUAD

Offset Name Description

0 rgbBlue Blue value for color map entry

1 rgbGreen Green value

2 rgbRed Red value

3 rgbReserved Zero

22

Proses Penentuan Warna Ke Layar

• Untuk file 24 bit Informasi intensitas RGB sudah dapat langsung

diketahui dari bitmap data, sedangkan untuk file 1,4,8 bit informasi RGB diperoleh dari Color Map

23

Proses Penentuan Warna Ke Layar

• Pada umumnya setiap bahasa pemrograman telah

menyediakan fungsi untuk menghasilkan warna apabila kita telah mengetahui intensitas RGB:

– Contoh dalam delphi:

• Image1.canvas.pixel(1,1)=RGB(10,8,2);

– Contoh dalam Visual Basic:

• PicBaru.PSet (SbX, SbY), RGB(10, 8, 2)

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A

B

• Perlu diperhatikan bahwa dalam file data disimpan dari belakang ke depan secara sequential. Berarti bitmap data pertama adalah pixel pada posisi A dan bitmap data terakhir adalah pixel pada posisi B

Penentuan Posisi Pixel

25

Color map

• Citra 1, 4, dan 8 bit per pixel butuh color map

• Entri dalam color map (palette) biasanya 2, 16, atau 256 – Bisa lebih sedikit jika citra tidak membutuhkan semua

warna yang tersedia

– Jumlah warna yang digunakan = biClrUsed

– biClrUsed = 0 color map memuat semua warna

– 4 byte per entri

• Entri awal color map = warna penting

– Jumlah warna penting = biClrImportant jumlah

warna yang diperlukan untuk mendapat tampilan citra yang cukup bagus

26

Proses Pembacaan Citra 8 bit

• Citra dengan kedalaman 8 bit berarti 1 pixel diwakili oleh 1 byte dan memiliki kemungkinan warna sebanyak 8 bit • Prosesnya sama dengan pembacaan citra 24 bit dimana

kita membaca :

• FileHeader sebesar 14 byte • InfoHeader 40 byte • ColorMap

• Bitmap Data

Proses Pembacaan Citra 8 bit

Dengan mengetahui informasi mengenai OffBits maka kita bisa menghitung posisi offset dari ColorMap yaitu dimulai dari offset 54 sampai dengan nilai yang tersimpan didalam offbits(X)

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Proses Pembacaan Citra 8 bit

• Analogi Color Map adalah mengindex warna yang ada ke dalam tabel sehingga bitmap data tidak lagi berisi data intensitas RGB namun mengandung index warna • Untuk mengetahui warna pixel(x) maka kita mengakses

color map dengan index sesuai dengan nilai yang tersimpan pada bitmap data

29

Proses Pengambilan Warna dari Color Map

Berarti untuk pixel 1 intensitas RGB : 56 5 9

Berarti untuk pixel 2 intensitas RGB : 5 34 67

Berarti untuk pixel 3 intensitas RGB : 5 34 67 COLORMAP B G R 0 B G R 0 B G R 0 56 5 9 1 5 34 67 15 5 34 67 30

Menentukan Ukuran File dari Bitmap

• Yang membedakan antara citra 1,4,8,24 bit adalah

ukuran storage yang digunakan untuk menyimpan warna dari 1 buah pixel

• Misalkan: citra A :200 x 200 pixel

– Hitung berapa minimum byte dari file bitmap yang dihasilkan bila:

a. citra A disimpan dalam 8 bit b. citra A disimpan dalam 24 bit

– Solusi a. 200 x 200 x 1 + 54 + 256 * 3 = 40822 byte b. 200 x 200 x 3 + 54 = 120054 byte 31

EQUALISASI HISTOGRAM

SPESIFIKASI HISTOGRAM

32

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Dua Pendekatan Image Enhancement

• Metode-metode berbasis domain frekwensi

– Manipulasi terhadap representasi frekwensi dari citra – Contoh: operasi berbasis transformasi Fourier terhadap

citra

• Metode-metode berbasis domain spasial

– Manipulasi langsung terhadap pixel-pixel pada citra – Contoh: operasi histogram

33

Histogram citra

• Berlaku untuk nilai gray level; RGB per plane warna • Plotting dari persamaan:

– L: jumlah level

– pr(rk): probabilitas kemunculan level ke-k

– nk: jumlah kemunculan level k pada citra

– n: total jumlah pixel dalam citra

1 ,...,

1 ,

0 ;

1

0 ;

)

(

=

≤

r

≤

k

=

L

−

n

r

p

k _k k r 34

Contoh histogram

35

Equalisasi histogram

• Tujuan: melakukan transformasi terhadap histogram citra asli sedemikian sehingga didapat histogram citra hasil dengan distribusi lebih seragam (uniform) ≈ linearisasi • Dasar konsep: transformasi probability density function

menjadi uniform density bentuk kontinyu

• Agar dapat dimanfaatkan dalam pengolahan citra digital, diubah ke bentuk diskrit

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Equalisasi pada domain kontinyu

[ ]

1

0

1 )

(

1 )

(

)

(

:

1

0 ;

)

(

)

(

:

)

(

)

(

:

) ( ) ( 0 ) ( 1 1 1

≤

=













=

≤

=









=

− − − = = =

∫

s

r

p

r

p

s

p

Uniform

r

dw

w

p

s

T

s

si

Transforma

ds

dr

r

p

s

p

Histogram

s T r s T r r r s r r s T r r s 37

Ilustrasi equalisasi pada domain kontinyu

38

Bentuk diskrit fungsi transformasi

1

0 )

(

1 ,...,

1 ,

0

1

0 )

(

)

(

1 0 0

≤

=

−

=

≤

=

− = =

∑

k k k k k j k j j r j k k

s

T

r

L

k

r

p

n

r

T

s

39

Operasi equalisasi histogram

1. Buat histogram dari citra asli

2. Transformasikan histogram citra asli menjadi

histogram dengan distribusi seragam

3. Ubah nilai tiap pixel sesuai dengan nilai hasil

pemetaan (histogram asli

_uniform

histogram)

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Pseudo Code : citra 512 x 512 pixel 256 graylevel

Var x,y,i,j : integer;

HistEq : array[0..255] of integer; Hist : array[0..255] of real; Sum : real;

Begin

Histogram(image,Hist) {bentuk histogram dari citra asli} for i:= ∅∅∅∅to 255 do {transformasi ke uniform histogram}

sum := 0.0 for j:= ∅∅∅∅to i do

sum:= sum + hist[j] endfor

histEq[i]:=round(255 * sum); end;

for y:=0 to 511 do {ubah nilai tiap pixel pada citra} for x:=0 to 511 do image[x,y]:= HistEq[Image[x,y]]; end; end; end; 41

Contoh

Citra 64x64 pixel, 8 tingkat keabuan dgn distribusi: rk nk pr(rk)=nk/n r0=0 790 0,19 r1=1/7 1023 0,25 r2=2/7 850 0,21 r3=3/7 656 0,16 r4=4/7 329 0,08 r5=5/7 245 0,06 r6=6/7 122 0,03 r₇=1 81 0,02 Histogram citra: 0 0,05 0,1 0,15 0,2 0,25 0,3 0 1/7 2/7 3/7 4/7 5/7 6/7 1 gray level (rk) p ro b a b il it y ( p r (r k )) 42

Fungsi transformasi

00 . 1 ) ( ) ( 98 . 0 ) ( ) ( ; 95 . 0 ) ( ) ( 89 . 0 ) ( ) ( ; 81 . 0 ) ( ) ( 65 . 0 ) ( ) ( ) ( ) ( ) ( 44 . 0 ) ( ) ( ) ( ) ( 19 . 0 ) ( ) ( ) ( 7 0 7 7 6 0 6 6 5 0 5 5 4 0 4 4 3 0 3 3 2 1 0 2 0 2 2 1 0 1 0 1 1 0 0 0 0 0 = = = = = = = = = = = = = = = = + + = = = = + = = = = = = =

∑

= = = = = = = = j j r j j r j j r j j r j j r r r r j j r r r j j r r j j r r p r T s r p r T s r p r T s r p r T s r p r T s r p r p r p r p r T s r p r p r p r T s r p r p r T s 43

Fungsi transformasi: grafik

0 0,2 0,4 0,6 0,8 1 1,2 0 1/7 2/7 3/7 4/7 5/7 6/7 1 gra y le ve l (rk) tr a n s fo rm e d v a lu e ( sk ) 44

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Pembulatan

• 8 tingkat keabuan valid nilai Skdibulatkan ke nilai

valid terdekat [Normal (Skx (tingkat kedalaman-1))]

s0 = 0.19 ≅ 1/7 s1 = 0.44 ≅ 3/7 s2 = 0.65 ≅ 5/7 s3 = 0.81 ≅ 6/7 s4 = 0.89 ≅ 6/7 s5 = 0.95 ≅ 1 s6 = 0.98 ≅ 1 s7 = 1.00 ≅ 1 45

Pemetaan

• Hanya ada 5 level keabuan pada uniform histogram

– r0(790 pixel) s0= 1/7

– r1(1023 pixel) s1= 3/7

– r2(850 pixel) s2= 5/7

– r3(656 pixel), r4(329 pixel) s3= 6/7

– r5(245 pixel),r6(122 pixel),r7(81 pixel) s4= 7/7

46

Histogram dengan distribusi seragam

0 0,05 0,1 0,15 0,2 0,25 0,3 0 1/7 2/7 3/7 4/7 5/7 6/7 1 gra y le ve l (sk) p ro b a b il it y ( ps (sk ))

Karena histogram merupakan aproksimasi terhadap probability density function, sangat jarang didapat histogram hasil yang betul-betul rata

47

Tabel Histogram secara Lengkap

rk nk pr(rk)=nk/n Sk Sk x 7 Normal(Sk) r0=0 790 0,19 0,19 1,33 ≅≅≅≅1 s0=1/7 r₁=1/7 1023 0,25 0,44 3,08 ≅≅≅≅3 s₁=3/7 r2=2/7 850 0,21 0,65 4,55 ≅≅≅≅5 s2=5/7 r₃=3/7 656 0,16 0,81 5,67 ≅≅≅≅6 s₃=6/7 r4=4/7 329 0,08 0,89 6,23 ≅≅≅≅6 s4=6/7 r₅=5/7 245 0,06 0,95 6,65 ≅≅≅≅7 s₅=7/7 r6=6/7 122 0,03 0,98 6,86 ≅≅≅≅7 s6=7/7 r₇=1 81 0,02 1,00 7 s₇=1 48

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Hasil Equalisasi

rjsk nk ps(sk) r₀s0=1/7 790 0,19 r1s1=3/7 1023 0,25 r₂s2=5/7 850 0,21 r3,r4 s3=6/7 985 0,24 r5,r6,r7 s4=7/7 448 0,11 0 0 , 0 5 0 , 1 0 , 1 5 0 , 2 0 , 2 5 0 , 3 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 g r a y l e v e l (sk) p ro b a b il it y ( ps (sk )) 49

Contoh1 equalisasi histogram

50

Contoh 2 equalisasi histogram

51

Spesifikasi histogram

• Kelemahan equalisasi histogram:

histogram hasil tidak bisa dibentuk sesuai

kebutuhan

• Kadangkala dibutuhkan untuk lebih

menonjolkan rentang gray level tertentu

pada citra

_{spesifikasi histogram}

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Operasi spesifikasi histogram

1. Buat histogram dari citra asli

2. Transformasikan histogram citra asli

menjadi histogram dengan distribusi

seragam

3. Tentukan fungsi trasformasi sesuai

spesifikasi histogram yang diinginkan

4. Ubah nilai tiap pixel sesuai dengan nilai

hasil pemetaan (histogram asli

_histogram

equalisasi

_{histogram hasil)}

53

Algoritma:

citra 512 x 512 pixel 256 graylevel

Var x,y,i,minval,minj,j : integer; Histspec : array[0..255] of integer; Invhist : array[0..255] of integer; Sum : real;

Begin

Hist_Equalization(Image) {equalisasi histogram}

For i:= 0 to 255 do {histogram yang dispesifikasikan telah disimpan di

spec}

Sum:= 0.0;

For j:= 0 to i do Sum := sum + spec[j] Histspec[i] = round(255 * sum) Endfor {didapat fungsi transformasi} for i:= 0 to 255 do {pemetaan histogram}

minval := abs(i – histspec[0]; minj := 0; for j:= 0 to 255 do

if abs(i – histspec[j]) < minval then minval := abs(i – histspec[j]) minj := j

endif invhist[i]:= minj endfor

endfor

for y:= 0 to 511 do {ubah nilai tiap pixel pada citra} for x:= 0 to 511 do image[x,y] = invhist[image(x,y)]

54

Bentuk diskrit spesifikasi histogram: by

example

Citra 64x64 pixel, 8 tingkat keabuan dgn distribusi: rk nk pr(rk)=nk/n r0=0 790 0,19 r1=1/7 1023 0,25 r2=2/7 850 0,21 r3=3/7 656 0,16 r4=4/7 329 0,08 r5=5/7 245 0,06 r6=6/7 122 0,03 r7=1 81 0,02 Histogram citra: 0 0,05 0,1 0,15 0,2 0,25 0,3 0 1/7 2/7 3/7 4/7 5/7 6/7 1 gray level (rk) p ro b a b il it y ( pr (rk )) 55

Bentuk histogram yang diinginkan

zk pz(zk) z0=0 0,00 z1=1/7 0,00 z2=2/7 0,00 z3=3/7 0,15 z4=4/7 0,20 z₅=5/7 0,30 z6=6/7 0,20 z7=1 0,15 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0,35 0 1/7 2/7 3/7 4/7 5/7 6/7 1 gray level (zk) p ro b a b il it y ( pz (zk )) 56

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Langkah 1: equalisasi histogram

Didapat hasil: rjsk nk ps(sk) r₀s0=1/7 790 0,19 r1s1=3/7 1023 0,25 r₂s2=5/7 850 0,21 r3,r4 s3=6/7 985 0,24 r5,r6,r7 s4=7/7 448 0,11 0 0 , 0 5 0 , 1 0 , 1 5 0 , 2 0 , 2 5 0 , 3 0 1 / 7 2 / 7 3 / 7 4 / 7 5 / 7 6 / 7 1 g r a y l e v e l (sk) p ro b a b il it y ( ps (sk )) 57

Langkah 2: cari fungsi transformasi

∑

=

k j j z k k

G

z

p

z

v

0

)

(

)

(

v

₀

= G(z

₀

) = 0,00

v

1

= G(z

1

) = 0,00

v

₂

= G(z

₂

) = 0,00

v

₃

= G(z

₃

) = 0,15

v

4

= G(z

4

) = 0,35

v

₅

= G(z

₅

) = 0,65

v

₆

= G(z

₆

) = 0,85

v

₇

= G(z

₇

) = 1,00

58

Langkah 1 : Equalisasi

rk nk pr(rk)=nk/n Sk Sk x 7 Normal(Sk) r0=0 790 0,19 0,19 1,33 ≅ 1 s0=1/7 r₁=1/7 1023 0,25 0,44 3,08 ≅ 3 s₁=3/7 r2=2/7 850 0,21 0,65 4,55 ≅ 5 s2=5/7 r₃=3/7 656 0,16 0,81 5,67 ≅ 6 s₃=6/7 r4=4/7 329 0,08 0,89 6,23 ≅ 6 s4=6/7 r5=5/7 245 0,06 0,95 6,65 ≅ 7 s5=7/7 r6=6/7 122 0,03 0,98 6,86 ≅ 7 s6=7/7 r7=1 81 0,02 1,00 7 s7=1 59

Langkah 2: cari fungsi transformasi

zk pz(zk) Vk Vk x 7 Normal(Vk) z0=0 0,00 0,00 0,00 v0=0 z1=1/7 0,00 0,00 0,00 v1=0 z2=2/7 0,00 0,00 0,00 v2=0 z3=3/7 0,15 0,15 1,05 ≅ 1 v3=1/7 z4=4/7 0,20 0,35 2,45 ≅ 2 v4=2/7 z5=5/7 0,30 0,65 4,45 ≅ 4 v5=4/7 z6=6/7 0,20 0,85 5.95 ≅ 6 v6=6/7 z7=1 0,15 1,00 7 v7=1

Dengan kata lain, lakukan langkah-langkah equalisasi thd histogram yang diinginkan :

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Grafik fungsi transformasi

0 0,2 0,4 0,6 0,8 1 1,2 0 1/7 2/7 3/7 4/7 5/7 6/7 1 gra y le ve l (zk) tr a n s fo rm a ti o n ( vk ) 61

Langkah 3: terapkan inverse G pada

level histogram equalisasi

Pemetaan nilai skke G(zk) terdekat

s0= 1/7 ≈ 0.14 G(z3) = 0.15; z3= 3/7 s₁= 3/7 ≈ 0.43 G(z4) = 0.35; z4= 4/7 s₂= 5/7 ≈ 0.71 G(z5) = 0.65; z5= 5/7 s₃= 6/7 ≈ 0.86 G(z6) = 0.85; z6= 6/7 s4= 1 G(z7) = 1.00; z7= 1 62

Langkah 4: pemetaan dari r

_k

ke z

_k

• Dengan memperhatikan pemetaan histogram asli ke histogram equalisasi r₀= 0 z3= 3/7 r1= 1/7 z4= 4/7 r2= 2/7 z5= 5/7 r3= 3/7 z6= 6/7 r4 = 4/7 z6 = 6/7 r5 = 5/7 z7 = 1 r6 = 6/7 z7 = 1 r7 = 1 z7 = 1 63

Histogram hasil

zk nk pz(zk)=nk/n r₀=0 0 0 r1=1/7 0 0 r₂=2/7 0 0 r3=3/7 790 0,19 r₄=4/7 1023 0,25 r5=5/7 850 0,21 r₆=6/7 985 0,24 r7=1 448 0,11 0,00 0,05 0,10 0,15 0,20 0,25 0,30 0 1/7 2/7 3/7 4/7 5/7 6/7 1 gray level (zk) p ro b a b il it y ( p z (z k ))

Histogram hasil mungkin tidak sama persis dengan spesifikasinya transformasi hanya akan memberikan hasil yang persis pada kasus kontinyu