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Image Formation (Acquisition)

Sensor Arrangements
Three principal sensor arrangements: – Single, line, and array

Generating a Digital Image
Continuous image
Digitizing coordinate values
Scan-line from A to B in continuous image

Generating a Digital Image
Continuous image
Scan-line from A to B in continuous image
Digitizing coordinate values
Digitizing amplitude values

Generating a Digital Image
Sampled & Quantised

Sampling and Quantisation
Continuous colours mapped to a finite discrete set of colours

Sampling and Quantisation

Sampling and Quantisation

Sampling and Quantisation
Real image Sampled Quantised Sampled & Quantised

Representing Digital Images
Representing as an M×N numerical array

Spatial and Intensity Resolution
Spatial resolution
• A measure of smallest discernible detail in an image
• stated with line pairs per unit distance, dots (pixels) per
unit distance, dots per inch (dpi)
Intensity resolution
• A measure of smallest discernible change in intensity level • stated with 8 bits, 12 bits, 16 bits, etc.

Spatial Resolution
Under-sampling: lose some image details

Spatial Resolution
1024×1024
512
64 128
256

Spatial Resolution
1024×1024 512×512 256×256
128×128 64×64 32×32

DPI & PPI
Digital Image Size
measurements (width × height) of a digital photo in pixels
• PPI (Pixel Per Inch): number of pixels per inch; image digitizing devices (e.g., camera, scanner)
• DPI (Dots Per Inch): number of printed points (dots) per inch; printers (hard copy of image)
High DPI (more pixels in an inch)
Low DPI (fewer pixels in an inch)

Example: A poster with the size 90x60cm should be printed with 150 DPI. What is minimum size of digital photo?
Quiz

Example: A poster with the size 90x60cm should be printed with 150 DPI. What is minimum size of digital photo?
Height Width
90𝑐𝑚
2.54 𝑐𝑚 𝑖𝑛𝑐h
60𝑐𝑚
2.54 𝑐𝑚 𝑖𝑛𝑐h
× 150 𝑝𝑖𝑥𝑒𝑙𝑠= 5315 pixels 𝑖𝑛𝑐h
× 150 𝑝𝑖𝑥𝑒𝑙𝑠= 3543 pixels 𝑖𝑛𝑐h
Quiz
 image size of the digital photo must add up to at least 5315×3543 Pixels (~18,8 Megapixel)

DPI & PPI
• A 1000 × 1000 pixel image, at 72dpi would print out at … inches by … inches.
• A 1000 × 1000 pixel image, at 100dpi would print out at … inches by … inches.
• A 1000 × 1000 pixel image, at 200dpi would print out at … inches by … inches.
• A 1000 × 1000 pixel image, at 300dpi would print out at … inches by … inches.

Sampling
Uniform Sampling
same sampling frequency everywhere
Adaptive Sampling
higher sampling frequency in areas with greater detail (not very common)

Spatial and Intensity Resolution
Spatial resolution
• A measure of smallest discernible detail in an image
• stated with line pairs per unit distance, dots (pixels) per
unit distance, dots per inch (dpi)
Intensity resolution
• A measure of smallest discernible change in intensity level • stated with 8 bits, 12 bits, 16 bits, etc.

Intensity Resolution
Common quantisation levels, f(x,y) is given in integer values [0 – max], max = 2n – 1

Intensity Resolution
Common quantisation levels, f(x,y) is given in integer values [0 – max], max = 2n – 1
• n=1 [0–1]binaryimage
• n = 5 [0 – 31] maximum human eye can resolve
• n=8 [0–255]1byte,verycommon
• n = 16 [0 – 65535] common in research
• n = 24 [0 – 16.2×106] common in colour images (i.e. 3×8 bytes for RGB)
Intensity Resolution
number (n) of bits used to quantise intensity

Intensity Resolution
256 levels 8 levels 2 levels n= 8 n= 3 n= 1

Intensity Resolution

Continuous image projected onto a sensor array
Result of image sampling and quantization
Image Sampling and Quantization

Interpolation
Process of using known data to estimate unknown values at other locations
e.g., zooming, shrinking, rotating, and geometric correction
An imaging method to increase (or decrease) the number of pixels in a digital image (sometimes called resampling) Some digital cameras use interpolation to produce a larger image than the sensor captured or to create digital zoom

f1(x2,y2) =
f(round(x2), round(y2)) = f(x1,y1)
f(x1,y1)
• Assigns to each new location the intensity of its nearest neighbour in the original image
• Produce undesirable artefacts, such as severe distortion of straight edges
Nearest Neighbour Interpolation
f1(x3,y3) =
f(round(x3), round(y3)) = f(x1,y1)

Nearest Neighbour Interpolation
top-left
Original: 200 × 200
top-right
Resampled from 128 × 128
bottom-left
Resampled from 64 × 64
bottom-right
Resampled from 32 × 32

Bilinear Interpolation
(x,y)

Bilinear Interpolation
Use weighted averages of 4 neighbouring pixels
The weight depends on a relative distance between pixels in two grids

Bilinear Interpolation
top-left
Original: 200 × 200
top-right
Resampled from 128 × 128
bottom-left
Resampled from 64 × 64
bottom-right
Resampled from 32 × 32

Interpolation

Recommended Reading
“Digital Image Processing”, R.C. Gonzalez and R.E. Woods, 3rd edition, Pearson Prentice Hall, 2008
Chapter 2