# 代做 R – Image Representation

### Image Representation ``````Rynson W.H. Lau
``````
``````CS4185/CS5185 Multimedia Technologies and Applications
``````

#### Pixels

``````Pixel: comes from the words picture and element. A pixel corresponds to the smallest unit in a digital picture.

``````
``````Image resolution refers to the number of pixels in a digital image. For example, HDTV has a resolution of 1920
``````
``````1080 pixels.
``````
``````pixel
``````
``````Rynson W.H. Lau:
``````

#### Binary Images

``````Each pixel is represented by a single bit (0 or 1).

``````
``````Such an image is also called a monochrome image since it contains only a single foreground color on a single background color (usually black/white).
``````
``````Rynson W.H. Lau:
``````
``````original image
``````
``````binary image
``````

#### 8-Bit Gray-Level Images

``````Each pixel is represented by an 8-bit black and white value, i.e., between 0 and 255, where 0 corresponds to the smallest value (completely black) while 255 corresponds to the highest value (maximum brightness).
``````
``````Rynson W.H. Lau:
``````
``````original image 8-bit gray-level image
``````

#### Example Images

``````1-Bit Binary Image
``````
``````8-Bit Gray-Level Image
``````
``````1 0
``````
``````255 0
``````
``````Rynson W.H. Lau:
``````

#### Number of Bits per Pixel

``````Bits per pixel (color depth)
``````
``````Number of different gray values that can be specified by a fixed number of bits in a pixel of a digital image.
``````
``````
``````
``````As the number of bits per pixel increases by one, the number of gray values is doubled.

``````
``````As the number of different gray values increases, the boundary between any two adjacent values becomes less visible.
``````
``````Rynson W.H. Lau:
``````

#### Gamma Correction

``````To display an image, we typically need to convert each RGB value to a voltage to drive the display screen.

``````
``````However, the mapping between the driving voltage and the amount of light emitted is typically non-linear for most display devices, such as CRTs and LCDs. The light emitted is roughly proportional to the voltage
``````
``````raised to a power
``````
``````; and
``````
``````this power is called
``````
``````gamma
``````
``````, with symbol
``````
``````.
``````
``````Hence, if a pixel value in the red channel is R, the screen emits light proportional to R
``````
``````. For
``````
``````CRTs, the gamma value is about 2.2.
``````
``````GammaCorrection
``````
``````CRTSystem
``````
``````RR = R
``````
``````1 /
``````
``````(R
``````
``````)= R
``````
``````CRTSystem
``````
``````R
``````

R Image with Gamma Correction Image without Gamma Correction

``````Rynson W.H. Lau:
``````

#### Histogram

``````A histogram shows the number of occurrences,
``````
``````p(
``````
``````g), of
``````
``````each individual gray-level value,
``````
``````g, in an image.
``````
``````Rynson W.H. Lau:
``````

The distribution of pixel values tells the quality of the image. For examples: If majority of the pixels have small gray values, the image

``````will appear dark.
``````
• If majority of the pixels have large gray values, the image
``````will appear bright.
``````
``````Rynson W.H. Lau:
``````

If majority of pixel values are within a small range, the

``````image will appear to have a low contrast. (The previous two images are also considered as low contrast images.)
On the contrary, a high contrast image covers a wide range
``````
``````of gray values.
``````
``````Rynson W.H. Lau:
``````

#### Brightness

``````original image
``````
``````image with
increased brightness
``````
``````Brightness of the image can be adjusted as follows:
``````
``````pixel
``````
``````(x
``````
``````, y
``````
###### ) =
``````pixel
``````
``````(x
``````
``````, y
``````
###### ) +
``````brightness
``````
``````If the sum or difference exceeds the range (0, 255), the output value is clipped to the minimum/maximum value.

``````
``````This brightness adjustment is equivalent to shifting the histogram horizontally.
``````

#### Contrast

``````Contrast of an image can be adjusted as follows:
``````
``````pixel
``````
``````(x
``````
``````, y
``````
###### ) =
``````contrast
``````
###### * (
``````pixel
``````
``````(x
``````
``````, y
``````
###### )
``````gmean
``````
###### ) +
``````gmean
``````
``````where
``````
``````gmean
``````
``````is the mean gray value of the original image.
``````
``````If
``````
###### X
``````and
``````
###### Y
``````represent the horizontal and vertical resolutions
``````
``````of the image,
``````
``````gmean
``````
``````can be computed as:
``````
``````Again, if an output value exceeds the range (0, 255), it is clipped to the minimum/maximum value.
``````
``````Rynson W.H. Lau:
``````
###### X
``````y
x
``````
``````pixel
``````
``````g
``````
``````X x
``````
``````Y y
``````
``````mean
``````
###### (
``````0
``````
``````0
``````
``````=
``````
``````=
``````
``````=
``````
``````original image
``````

Contrast correction is similar to scaling the histogram distribution. We reduce the contrast of an image by setting contrast

``````(in the equation) to smaller than 1 and increase it
``````
``````by setting
``````
``````contrast
``````
``````to larger than 1. image with
increased contrast
``````
``````Rynson W.H. Lau:
``````

#### Inversion (Negative)

``````Image inversion can be achieved as follows:
``````
``````pixel(x, y) = 255  pixel(x, y)
``````
``````Films are negative, while photographs are positive.Original image
``````
``````negative Image
``````
``````Rynson W.H. Lau:
``````

#### Quantization

``````This is to uniformly quantize the gray values of an image into a smaller number of levels.original image(256 levels)
``````
``````quantized Image
``````
``````(16 levels)
``````
``````Rynson W.H. Lau:
``````

#### Thresholding (Binarization)

``````original image
``````
``````binary image(threshold = 128)
``````
``````This is to convert a gray-level image into a binary image:
``````
``````pixel(x, y) = 0
``````
``````if pixel(x, y) < threshold
``````
``````pixel(x, y) = 255
``````
``````if pixel(x, y) >= threshold
``````

#### Dithering

``````In existing black-and-white printers, each pixel can only have 2 levels of intensity (1 bit), i.e., with or without ink.

``````
``````Color printers provide 15 levels (or 15 different colors), by combining four types of inks, cyan, magenta, yellow and black.

``````
``````Dithering
``````
``````is a technique to print more intensity (or color)
``````
``````levels by reducing the printing resolution, i.e., trading off spatial resolution for intensity resolution.

``````
``````The idea is to replace and print each image pixel with a pixel pattern (using multiple pixels) such that the average intensity (or color) of the pixel pattern approximates the original image pixel intensity.
``````

Consider printing an 8-bit gray-level image on a black-and-whit

e

``````laser printer. We may replace each image pixel with, say, a 2
``````
``````^2
``````
``````pixel pattern. A 2
``````
``````2 matrix produces a total of 5 possible pixel
``````
``````patterns:
image pixel value
``````
``````0  50
``````
``````51  101
``````
``````102  152 153  203 204  255
``````
``````code to represent the range
``````
``````abcde
``````
``````pixel pattern for printing

``````
``````Given an image pixel, we first
``````
``````map its value (between 0 and 255
``````
``````)
``````
``````into a new value (between 0 to 4). We then map the new pixel value to one of the above 5 pixel patterns.

``````
``````An example:
``````
``````
``````
``````
``````
``````240
180
``````
``````69
122
``````
``````
``````
``````
``````
``````W
W
W
B
``````
``````W
W
W
W
``````
``````B
B
W
B
``````
``````B
W
B
W dithered binary image for printing
``````
``````a 2
``````
``````2 image
``````
``````map each pixel value to a code
``````
``````

``````
``````B
B
``````
``````B
B
``````
``````

``````
``````B
B
``````
``````B
W
``````
``````

``````
``````W
B
``````
``````B
W
``````
``````

``````
``````W
B
``````
``````W
W
``````
``````

``````
``````W
W
``````
``````W
W
``````
``````map each code to a pixel pattern
``````

A dithered example image:

``````magnification of a dithered region
``````
``````dithered binary image
``````
``````original gray-level
``````
``````image
``````
``````Rynson W.H. Lau:
``````

Printer dithering (also called halftoning) examples:

``````Rynson W.H. Lau:
``````
``````black-and-white
``````
``````dithering
``````
``````Color dithering
``````

#### Pixel Per Inch (PPI)

``````PPI is a measure of the pixel density. It refers to the display
or printing resolution of an input image.

``````
``````As suggested by Fotomax (
``````
``````http://www.fotomaxonline.com/serv
``````
``````ice.asp?lang=en&page=175
``````
###### ),
``````the PPI requirement for digital photo printing is 300 PPI for best resolution, or 180 PPI for minimum resolution.
``````
``````Product
``````
``````Image Size(Inch)
``````
``````The Best Resolution
``````
``````(Pixels)
``````
``````Minimum Resolution
``````
``````(Pixels)
``````
``````1.5"x2" ID Photo 8 pcs
``````
``````1.5 x 2
``````
``````450 x 600
``````
``````270 x 360
``````
``````2R
``````
``````2.5 x 3.5
``````
``````750 x 1050
``````
``````450 x 630
``````
``````3R
``````
``````3.5 x 5
``````
``````1050 x 1500
``````
``````630 x 900
``````
``````4D (4.5"x6")
``````
``````4.5 x 6
``````
``````1350 x 1800
``````
``````810 x 1080
``````
``````4R
``````
``````4 x 6
``````
``````1200 x 1800
``````
``````720 x 1080
``````
``````5R
``````
``````5 x 7
``````
``````1500 x 2100
``````
``````900 x 1260
``````
``````6R
``````
``````6 x 8
``````
``````1800 x 2400
``````
``````1080 x 1440
``````
``````8R
``````
``````8 x 10
``````
``````2400 x 3000
``````
``````1440 x 1800
``````
``````8F
``````
``````8 x 12
``````
``````2400 x 3600
``````
``````1440 x 2160Rynson W.H. Lau:
``````

#### Dot Per Inch (DPI)

``````DPI refers to the printer resolution. It controls the printing quality.

``````
``````It specifies the number of droplets of ink that can be printed on one inch of the paper.

``````
``````Typical printer DPIs include 360DPI, 720DPI, 1440DPI and 2880DPI, but the differences among these setting may be small and not visible to naked eyes. Changing the DPI setting has no effect on the size of the print.

``````
``````To print an image, the PPI of the image file is mapped to the DPI of the printer  based on the dithering method that we have discussed.
``````
``````Rynson W.H. Lau:
``````

#### Light and Spectra

``````Light is an electromagnetic (EM) wave.

``````
``````Human visible light ranges from 400nm to 700nm.
``````
``````Rynson W.H. Lau:
``````

Spectral Power Distribution (SPD), or

spectrum

(

###### ),
``````shows the relative amount of light energy at each wavelength
``````
``````.
``````
``````
``````
``````E(
``````
``````)
``````
``````Spectrum of Daylight
``````
``````Rynson W.H. Lau:
``````

#### Human Vision

``````Retina consists of an array of rods and three kinds of cones Rods are for night vision Cones are for color vision
``````
1. L-cone: most sensitive to red light 2. M-cone: most sensitive to green light3. S-cone: most sensitive to blue light

#### Spectral Sensitivity of the Eye

``````
``````
``````The eye is most sensitive to li
``````
``````ght in the middle of the visible
``````
``````spectrum.
``````
``````
``````
``````The response in each color channel in the eye is proportional t
``````
``````o the
``````
``````corresponding number of cones: Red Receptor Sensitivity
``````
``````qR
``````
``````()
``````
• Green Receptor Sensitivity
``````qG
``````
``````()
``````
• Blue Receptor Sensitivity
``````qB
()
``````
``````
``````
``````Luminous-efficiency function
``````
``````V(
``````
``````):
``````
``````q(R
``````
``````)
``````
``````q(G
``````
``````)
``````
``````q(B
``````
``````)
``````
``````V(
)
``````
``````
``````
``````overall sensitivity formed by the sum of the response curves for Red, Green and Blue.
``````
``````The Blue receptor sensitivity is not shown to scale because it is much smaller than the curves
``````
``````for Red or Green.
``````

Total response on each channel is given by:

``````R
``````
``````=
``````
``````E(
``````
``````)
``````
``````qR
``````
``````()
``````
``````d
``````
``````G
``````
``````=
``````
``````E(
``````
``````)
``````
``````qG
``````
``````(
) d
``````
``````
``````
``````B
``````
``````=
``````
``````E(
``````
``````)
``````
``````qB
``````
``````()
``````
``````d
``````
``````q(R
``````
``````)
``````
``````q(G
``````
``````)
``````
``````q(B
``````
``````)
``````
``````V(
)
``````
``````
``````
``````
``````
``````E(
``````
``````)
``````
``````Spectrum of Daylight
``````
``````Source:
``````
``````http://escience.anu.edu.au/lecture/cg/Color/index.en.html
``````

#### Image Formation

``````Light from the illuminant (light source) with SPD
``````
###### E(
``````)
``````
``````impinges on a surface, with surface spectral reflectance function
``````
###### S(
``````), is reflected, and then is filtered by the eye's
``````
``````cone functions
``````
``````q(
``````
``````).
``````
``````The
``````
``````color signal, C
``````
``````(
``````
``````), is defined by
``````
###### C(
``````) =
``````
###### E(
``````)
``````
###### S(
``````).
``````
``````Total response on each channel is now given by:
``````
``````R
``````
``````=
``````
``````E(
``````
``````)
``````
``````S(
``````
``````)
``````
``````qR
``````
``````()
``````
``````d
``````
``````=
``````
``````C(
``````
``````)
``````
``````qR
``````
``````(
) d
``````
``````
``````
``````G
``````
``````=
``````
``````E(
``````
``````)
``````
``````S(
``````
``````)
``````
``````qG
``````
``````()
``````
``````d
``````
``````=
``````
``````C(
``````
``````)
``````
``````qG
``````
``````()
``````
``````d
``````
``````B
``````
``````=
``````
``````E(
``````
``````)
``````
``````S(
``````
``````)
``````
``````qB
``````
``````(
) d
``````
``````=
``````
``````C
``````
``````(
) q
``````
``````(B
) d
``````
``````
``````

#### RGB Color Space

``````Different combinations of the red, green, blue channel values result in different colors.
``````
``````RGB Color Cube
``````
``````Red Channel
``````
``````Blue Channel
``````
``````Green Channel
``````
``````Rynson W.H. Lau:
``````

#### 24-Bit Color Images

``````In a 24-bit color image, each pixel is represented by three bytes, usually in RGB format.  With 1 byte each for R, G, and B, this representation provides
``````
``````a total of 256
``````
``````^256
``````
``````256 (or 16,777,216) possible colors.
``````
• However, this will consume a lot of memory. A single HD
``````image of 1920
``````
``````1080, without any compression, will require
``````
``````5.93MB to store.
``````
``````
``````
``````Many 24-bit color images are actually stored as 32-bit images. The extra byte in each pixel is used to store an alpha
``````
``````value representing some special effect information
``````
``````(e.g., transparency).
``````
``````Rynson W.H. Lau:
``````

An example

``````24-Bit Color Image
``````
``````R Channel B Channel
``````
``````G Channel
``````
``````Rynson W.H. Lau:
``````
• Another example
``````24-Bit Color Image
``````
``````R Channel
``````
``````B Channel
``````
``````G Channel
``````
``````Rynson W.H. Lau:
``````

#### Color Models

``````In the previous discussion, we assume that each image is represented by the RGB channels.

``````
``````Such a representation is called the
``````
``````RGB color model
``````
###### .
``````Another two popular models are the YUV and YIQ models.

``````
``````The YUV color model is used in PAL color TV broadcasting, while the YIQ is used in NTSC color TV broadcasting.

``````
``````(PAL was developed by the UK and NTSC by the US. PAL and NTSC are two popular analog video broadcasting standards.)
``````
``````Rynson W.H. Lau:
``````

#### The YUV Model

``````In YUV,
``````
###### Y
``````is the luminance signal and is computed as:Y = 0.299R + 0.587G + 0.114B
``````
###### U
``````and
``````
###### V
``````are the chrominance signals and are computed as:U = B  YV =  R  Y
``````
``````As human eyes are more sensitive to the luminance signal, a high percentage of the bandwidth can then be allocated to carry the luminance signal in the PAL system.
``````
``````Rynson W.H. Lau:
``````

An example:

``````Rynson W.H. Lau:
``````
``````original color image
``````
``````YUV
``````

#### The YIQ Model

``````In YIQ,
``````
###### Y
``````is again the luminance signal and computed in
``````
``````the same way as in YUV.

``````
``````Iand
``````
###### Q
``````are also the chrominance signals, but rotated by
``````
###### 33
``````oas: I = 0.877(R  Y)cos33
``````
``````o 0.492(B  Y)sin33
``````
``````o
``````
###### = 0.596R 0.275G 0.321B
``````Q = 0.877(R  Y)sin33
``````
``````o 0.492(B  Y)cos33
``````
``````o
``````
###### = 0.212R 0.523G 0.311B
``````Similar to PAL, a high percentage of the bandwidth can be allocated to carry the Y signal in the NTSC system.
``````
``````Rynson W.H. Lau:
``````

An example:

``````Rynson W.H. Lau:
``````
``````original color image
``````
``````YI
``````
``````Q
``````

``````When two light beams hit the same point, their colors add together.

``````
``````When two nearby LCD points are turned on, their colors also add together.

``````
``````Hence, RGB (and so as YUV and YIQ) is referred to as an additive color model.
``````
``````Rynson W.H. Lau:
``````

However, in color printing, the opposite situation occurs.

``````When depositing a drop of yellow ink, it subtracts blue color from the white paper. Hence, it reflects red and green colors. As a result, it appears yellow.

``````
``````So, instead of red/green/blue, we have -red/-green/-blue. These subtractive color primaries then become Cyan (C), Magenta (M) and Yellow (Y).
``````
``````Rynson W.H. Lau:
See
``````
``````video
``````