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
Computer Memory & StorageComputer Memory & Storage
0 0
0 1
1 0
1 1
2x2 = 4 gray levels
2 gray levels
0
1
1 bitpixel
2 bitspixel
Computer Memory & StorageComputer Memory & Storage
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
Computer Memory & StorageComputer Memory & Storage
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
Computer Memory & StorageComputer Memory & Storage
3 bits/pixel: 8 gray levels
000 →→ 111
(0 →→ 7)
4 bits/pixel: 16 gray levels
0000 →→ 1111
(0 →→ 15)
Computer Memory & StorageComputer Memory & Storage
5 bits/pixel: 32 gray levels
00000 →→ 11111
(0 →→ 31)
8 bits/pixel: 256 gray levels
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, …]
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.
5 bits/pixel : 32 values
6 bits/pixel : 64 values
7 bits/pixel:128 values
8 bits/pixel : 256 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)
Grayscale ImagesGrayscale Images
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?
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
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”
u If we add red (which alonegives us 256 different reds): 0 255
0
255
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”
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
RGB Color Images: 24-bit colorRGB Color Images: 24-bit color
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”)
RGB Color Images: 24-bit colorRGB Color Images: 24-bit color
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
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
4 bits/pixel : 16 colors
5 bits/pixel:64 colors
8 bits/pixel : 256 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?
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