binary images - rit center for imaging science images u the simplest digital images are binary...

Binary ImagesBinary Images

u The simplest digital images are binary images.Binary images contain only one bit per pixel, so theycan only represent two gray values. For example;

0 = black

1 = white

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 0 0 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 0 0 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

1 1 1 1 1 1 1 1 1 1 1 0 0 0 0

Computer Memory & StorageComputer Memory & Storage

u If we want an image that has more than two gray levels,we have to increase the number of ‘bits per pixel’

binary: just white or black grayscale: many shades of gray


0 0

0 1

1 0

1 1

2x2 = 4 gray levels

2 gray levels

0

1

1 bitpixel

2 bitspixel


2x2x2 = 8 gray levels

3 bitspixel

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1


0 0 0 = 0

0 0 1 = 1

0 1 0 = 2

0 1 1 = 3

1 0 0 = 4

1 0 1 = 5

1 1 0 = 6

1 1 1 = 7

. . . = .

u We started to look at the bits astokens to represent differentvalues, but we ended up with abinary counting system.

u The largest number we cancount to (and the number ofdifferent gray levels we canhave) depends on how manybits we use.

Grayscale imagesGrayscale images

u To get more than two gray values, we need a codewith more than one bit per pixel.

1 bit 2 bits 3 bits

0 00 000

1 01 001

(2 values) 10 010

11 011

(4 values) 100

101

110

111

(8 values)

Binary ArithmeticBinary Arithmetic

u In binary arithmetic, we can onlycount from 0 to 1 before we haveto ‘carry’

u To increase the number ofdifferent values that can berepresented with a binary number,(and the number of gray levels ina digital image) we have toincrease the number of bits

01

1011

100101110111

10001001101010111100110111101111

10000...

binary

0123456789

101112131415

16...

decimal

1 bit

2 bits

3 bits

4 bits


3 bits/pixel: 8 gray levels

000 →→ 111

(0 →→ 7)


0000 →→ 1111

(0 →→ 15)



00000 →→ 11111

(0 →→ 31)


00000000 →→ 11111111

(0 →→ 255)

Grayscale ImagesGrayscale Images

u The number of gray levels that can be represented isfixed by the bit depth, the number of bits per pixelused to store the gray value.

1 bit/pixel : 2 values (‘binary’) [0, 1]

2 bits/pixel : 4 values [00, 01, 10, 11]

3 bits/pixel : 8 values[000, 001, 010, …]

4 bits/pixel : 16 values[0000, 0001, 0010, …]


u The number of gray levels that can be represented isfixed by the bit depth, the number of bits per pixelused to store the gray value.

5 bits/pixel : 32 values


7 bits/pixel:128 values


Bit depth: bits per pixelBit depth: bits per pixel

u The number of possible gray levels is controlled by thenumber of bits/pixel, or the ‘bit depth’ of the image

gray levelsgray levels

22

44

88

1616

3232

6464

128128

256256

bits/pixel

1

2

3

4

5

6

7

8

Memory requirements: Bit depthMemory requirements: Bit depth

u Adding more gray levels is ‘cheap’ in terms of memoryrequirements. Every added bit doubles the number ofgray levels

Grayscale Values vs. Bit Depth

0

64

128

192

256

1 2 3 4 5 6 7 8

bits per pixel

gray levels

Digital images: FundamentalsDigital images: Fundamentals

39

56

45

75

62

99

64

101

228 178 106 193

183 143 84 162

u A digital image is an ‘ordered array’ of numbers

u Each pixel (picture element) in a grayscale digital image isa number that describe the pixel’s lightness

(e.g., 0 = black 255 = white)


u Grayscale images commonly have 256 different grayvalues, numbered 0 - 255. Each pixel can then be storedin 8 bits, or 1 byte. [00000000 Õ 11111111]

0 = black 255 = white

u Grayscale pixels are sometimes stored with as many as1024 gray values (10 bits) or 4096 gray values (12 bits)This doesn’t make the image ‘look better’ but it increasesthe lightness range that can be captured

Bit depth & spatial resolutionBit depth & spatial resolution

0

50

100

150

200

250

300

0 50 100 150 200 250 300

8 bit

3 bit

2 bit

The bit depth describes the ‘grayscale resolution’

- with what precision are gray values distinguished?

Bit depth & spatial resolutionBit depth & spatial resolution

Spatial resolution

- with what precision are spatial variations reproduced?

Image Resolution: Image Resolution: 4 x 3 Pixels4 x 3 Pixels

Image Resolution: Image Resolution: 1280 x 960 Pixels*1280 x 960 Pixels*

Spatial Sampling & File SizeSpatial Sampling & File Size

u Doubling the linear image sampling rate renders moreimage detail, but quadruples the file size.

64X

256X

1

1 2 3 4

5 6 7 8

9 10 11 12

13 14 15 16

1 2

3 4

RGB Color ImagesRGB Color Images

u Each one of the color images (‘planes’) is like a grayscaleimage, but is displayed in R, G, or B

=

u The most straightforward way to capture a color image isto capture three images; one to record how much red is ateach point, another for the green, and a third for the blue.

Color images: 24-bit RGBColor images: 24-bit RGB

u Color images also need to be coded

u The bit depth in a color image determines the numberof colors that can be assigned to a given pixel.

u One common format is the 24-bit RGB image, withthree 8-bit planes; Red, Green, and Blue; 16.7M colors

=

(256 x 256 x 256 = 16.7 million)

RGB Color Images: 24-bit colorRGB Color Images: 24-bit color

u Every pixel in each of the three8-bit color planes can have 256different values (0-255)

u If we start with just the blueimage plane, we can make 256different “colors of blue”

0

255




u If we add red (which alonegives us 256 different reds): 0 255

0

255




u If we add red (which alonegives us 256 different reds):

u We can make 256 x 256 =65,536 combination colorsbecause for every one of the 256reds, we can have 256 blues.

0 255

0

255


u When we have all threecolors together, there are256 possible values ofgreen for each onefor each one of the65,536 combinations ofred and blue:

u 256 x 256 x 256 = 16,777,216 (“> 16.7 million colors”)


u The numbers stored for each pixel in a colorimage contain the color of that pixel

Color Image = Red + Green + BlueColor Image = Red + Green + Blue

=

u In a 24-bit image, each pixel has R, G, & B values

u When viewed on a color display, the three images arecombined to make the color image.

212100139196

16375113149

37446372

95118155170

189

162

38

41608278

182

161

50

43576863

Indexed Color ImagesIndexed Color Images

u A small subset of the 16 million colors canoften be used instead of the full 24 bits --256 colors is often sufficient if the colorsare chosen carefully

u Indexed color images take advantage of thisfact to use less memory or work withdisplays that can’t show 24-bit images

Indexed Color imagesIndexed Color images

24 bit

8-bit“adaptive”8-bit “system”

Color images: Index ColorColor images: Index Color

u A more compact code can be created for color images bymaking a look-up-table of colors for use in an image.Indexed color images store a fixed number of colors limitedby the bit-depth:

3 bits/pixel : 8 colors


5 bits/pixel:64 colors


File Size CalculationFile Size Calculation

100 pixels

100 pixels

Bit depth = 8 bits per pixel (256 gray levels)

File size (in bits) = Height x Width x Bit Depth

100 x 100 x 8 bits/pixel = 80,000 bits/image80,000 bits or 10,000 bytes

u How much memory isnecessary to store an imagethat is 100 x 100 pixels with8 bits/pixel?

File Size CalculationFile Size Calculation

1280 pixels

960 pixels

Bit depth = 24 bits per pixel (RGB color)

File size (in bits) = Height x Width x Bit Depth

960 x 1280 x 24 bits/pixel = 29,491,200 bits/image29,491,200 bits = 3,686,400 bytes = 3.5 MB

u How much memory isnecessary to store an imagethat is 1280 x 960 pixelswith 24 bits/pixel?

JPEG - Adobe PhotoShop “10” 324 KBRaw image = 3,686 KB

compressed/raw ~ 9%


compressed/raw ~ 2%


compressed/raw ~ 1%

JPEG 324 KB

JPEG 70 KB

JPEG 32 KB

~ 9%

~ 2%

~ 1%

binary images - rit center for imaging science images u the simplest digital images are binary...

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