Digital image basics

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Digital image basics

• Human vision perception system
• Image formation
• Human vision property and model
• Image acquisition
• Image transform
• Image quality
• Connected components
• Image sensing
• Image formats

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1. Human vision
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1. Human vision (contd)

• Two types of receptors
• -- Cones (fovea) sensitive to brightness
  and color
• - 7M
• - Cone-vision (photopic, bright-light
  vision)
• -- Rod (cell) sensitive to low-level
  illumination
• - 100M
• - Rod-vision (scopotic, dim-light
  vision)

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2. Image perception and formation
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3. Vision property
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3. Vision property (contd)

• Brightness adaptation
• -- There are a range of intensity levels
  that human eye can adapt
• - photopic 10(-3) (mL) 10(3) (mL)
• - scopotic 10(-3) (mL) 10(-1) (mL)
• -- Human eyes have brightness adaptation
  level,
• they cannot adapt the whole range
• simultaneously

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3. Vision property (contd)

• Brightness discrimination
• -- The ability to discriminate different
  intensity level
• - Weber ratio just noticeable
  difference of intensity versus the background
  intensity
• -- The intensity defined in the digital
  image is not the real intensity. It is a contrast
  scale (e.g., gray scale)

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3. Vision property (contd)

• Contrast
• -- Absolute contrast
• C Bmax / Bmin
• where Bmax is the maximum brightness intensity
• Bmin is the minimum brightness intensity
• -- Relative contrast
• Cr (B B0) / B0
• B is the brightness of object B0 is
  the background brightness
• -- Mach Band over-shooting effect

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3. Vision property (contd)

• Spatial discrimination (SD)
• -- minimum view angle which can
  discriminate two points on the object to be
  viewed
• d/(2 Pi L) theta / 360

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3. Vision property (contd)

• Spatial discrimination (SD)
• -- low illumination (SD decreases)
• -- low contrast (SD decreases)
• -- too high illumination (SD does not
  increase too much)
• -- SD of color is weaker than SD of
  brightness
• -- projection on fovea (SD increases)

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3. Vision property (contd)

• Human vision model
• -- g(x, y) T f(x, y)
• -- T transform input optical scene to
  output image
• - linear or non-linear transform
• - H(u,v) low pass filter (e.g., limited
  discrimination, linear)
• - log response to the brightness (e.g.,
  non-linear)
• - time-delay effect (e.g.,
  image-remain effect)

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4. Image acquisition

• Wavelength
• -- electromagnetic spectrum

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4. Image acquisition (contd)

• Principle of imaging sensor
• -- transform illumination energy into
  digital image
• -- output voltage waveform is proportional
  to light
• -- e.g., single sensor, group sensors
  (one-strip, CT/MRI), group sensors (2D array CCD)

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4. Image acquisition (contd)

• Image digitizing
• -- Sampling digitizing the coordinate
  values (spatially)
• - Nyquest rate 2F(max)
• - limited by the number of sensors
• - spatial sampling uniform and
  non-uniform
• (e.g., fovea-based, fish-eye
  based)
• -- Quantization digitizing the amplitude
  values
• - uniform
• - non-uniform (based on image
  characteristics)

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4. Image acquisition (contd)

• Image digitizing
• -- f(x, y) is the gray level at pixel
  location (x, y)
• -- Gray level is not real illumination
  intensity (it is an
• index of the gray scale)
• -- f(x, y) is in the range of 0, 255 for
  8-bit image
• -- the image with size of MN and k bits
  per pixel,
• has the total bits MNk

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4. Image acquisition (contd)

• Spatial resolution
• -- number of pixels with respect to the
  image size
• -- line pair smallest discernible detail
  per unit
• distance in an image
• - e.g., 100 lp/mm.

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4. Image acquisition (contd)

• Relationship between spatial resolution N and
  gray level resolution K
• -- N ? and K ? ? quality ?
• -- N ? and K ? ? contrast ?
• -- N (detail) ? ? K (number of gray level)
  can be ?
• (e.g., half-tone image)

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4. Image acquisition (contd)

• Aliasing problem
• -- JigJag or staircase effect.
• -- occurs in image acquisition (e.g.,
  image processing)
• -- occurs in display (e.g., computer
  graphics)
• -- Reasons
• The sampling or displaying resolution
  is lower than the
• minimum rate 2F(max), which is the
  Nyquest rate.
• -- Possible solution
• - Smooth image before sampling to
  reduce the F(max)
• - side-effect image blurred, quality
  ?

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5. Image transform

• Size change
• -- Zoom-in
• -- Zoom-out
• -- pixel replication
• -- pixel interpolation
• -- super-resolution
• Shape change
• -- geometric transformation

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6. Image quality

• Subjective
• -- Rating (e.g., R1, 2,, 5)
• where N is the number of evaluators Ji ?R
• -- application in image enhancement,
  restoration, compression, etc.

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6. Image quality

• Objective
• -- Mean square error
• -- dB value -10Log(E)
• -- f(x,y) is the image to be evaluated.
• f(x,y) is the reference image to be
  compared with.
• -- application in image coding, etc.

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7. Connected components

• Relationship of pixels
• -- Four neighbors of pixel P
• - N4(P) (strong neighbors)
• - ND(P) (weak neighbors)
• -- Eight neighbors of pixel P
• - N8(P) N4(P) ND(P)

P
Strong
weak
8-neighbor
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7. Connected components (contd)

• Adjacency
• -- 4-adjacency
• -- 8-adjacency
• -- m-adjacency (mixed-adjacency)

q
P
P
q
q
4-connected pq
is not m-connected 8-connected
m-adjacent if q is N4(p), or
q is Nd(p)
and N4(p) ?N4(q) ?
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7. Connected components (contd)

• Path
• -- If p and q is connected, there is a path
  between p and q.
• -- m path the path between p and q based on
  m-connected pixels.
• -- closed path starting p and ending q are
  connected

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7. Connected components (contd)

• Connected component
• -- set of pixels which are connected
• -- The set is also called connected set
• Concept
• -- R is a region if R is a connected set
• -- boundary of R is closed path
• -- edge gray-level discontinuity at a point
• - link edge points ? edge segment

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7. Connected components (contd)

• Distance
• -- D(p, q) is defined as the distance between
  p and q.
• D(p, q) gt0
• D(p, q) D(q, p)
• D(p, q) lt D(p,z) D(q,z)
• -- Euclidean distance (disk shape)
• De(p,q) sqrt(xp xq)(2) (yp
  yq)(2)

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7. Connected components (contd)

• Distance
• -- D4 distance (city-block distance) (diamond
  shape)
• D4(p,q) (xp xq) (yp yq)
• 2
• 2 1 2
• 2 1 0 1 2
• 2 1 2
• 2

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7. Connected components (contd)

• Distance
• -- D8 distance (chessboard distance) (square
  shape)
• D8(p,q) max((xp xq), (yp yq))
• 2 2 2 2 2
• 2 1 1 1 2
• 2 1 0 1 2
• 2 1 1 1 2
• 2 2 2 2 2

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7. Connected components (contd)

• Distance
• -- Dm distance (shortest m-path between two
  points)
• 1 - 1
• 1 - 1
• 1
• Dm 4

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8. Pixel operation

• Point-wise operation
• -- MN image bound matrix

t
r
(r,t) coordinates of upper-left component each
component is either defined (which is represented
by a certain intensity value), or undefined
(which is represented by ).
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8. Pixel operation (Contd)

• Arithmetic operation
• (1) ADDf, g(I,j)
• f(I,j) g(I,j) IF
  f(I,j) ? ? and g(I,j) ? ? (C1)
• ?
  otherwise
• (2) Multf,g(I,j)
• f(I,j) g(I,j) IF C1
• ?
  otherwise
• (3) SCALARt f(I,j)
• t f(I,j) IF
  f(I,j) ? ?
• ?
  otherwise

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8. Pixel operation (Contd)

• Arithmetic operation
• (4) Maxf,g(I,j)
• maxf(I,j), g(I,j) IF
  C1
• ?
  otherwise
• (5) Minf,g(I,j)
• minf(I,j), g(I,j) IF
  C1
• ?
  otherwise
• (6) Subf(I,j)
• -f(I,j) IF
  f(I,j) ? ?
• ?
  otherwise
• (6) SCALARt f(I,j)
• t f(I,j) IF
  C1
• ?
  otherwise

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8. Pixel operation (Contd)

• Arithmetic operation
• (7) EXTENDf,g(I,j)
• f(I,j) IF
  f(I,j) ? ?
• g(I,j)
  otherwise
• (8) EXTADDf,g(I,j)
• ADDf,g(I,j) IF C1
• f(I,j) IF
  f(I,j) ? ? and g(I,j) ?
  
• g(I,j) IF
  g(I,j) ? ? and f(I,j) ?
• both
  g and f on undefined domain

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8. Pixel operation (Contd)

• Arithmetic operation
• (9) THRESHf,t(I,j)
• 1 IF f(I,j) ?
  t
• 0 IF f(I,j) lt
  t
• ? IF f(I,j)
  ?
• (10) TRUNCf,t(I,j)
• f(I,j) IF f(I,j)
  ? t
• 0 IF f(I,j) lt
  t
• ? IF f(I,j)
  ?
• TRUNCf,g(I,j) Multf, THRESH(f, t)

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8. Pixel operation (Contd)

• Arithmetic operation
• (11) EQUALf,t(I,j)
• 1 IF f(I,j)
  t
• 0 otherwise
• on the
  undefined domain
• (12) similar definition for
• GREATERf,t(I,j)
• BETWEENf, t1, t2(I,j)
• (13) operation with masking
• AND, OR, NOT.

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8. Pixel operation (Contd)

• Arithmetic operation
• (14) PIXSUM(f) is the summation of all
  pixels on the
• defined domain
• (15) DOT(f,g) SUMf(I,j) ? g(I,j) on the
  common domain
• (16) Norm(f) SUMf(I,j)2(1/2)
• Norm(f) (DOT(f,f))(1/2)

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8. Pixel operation (Contd)

• Arithmetic operation
• (17) RESTf,g(I,j)
• f(I,j) IF
  g(I,j) ? ?
• ? IF
  g(I,j) ?
• (18) Note
• Linear operation H(af bg) aH(f)
  bH(g)
• otherwise non-linear operation
  (e.g., f-g operation)
• H operator
• f, g images
• a, b scale values

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Image Sensing

• Single Image Sensor
• Line Sensor (Sensor strip)
• Array Sensor

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Image Sensing

• Linear motion
• Rotation
• Sensing Ring for CT (x-ray) to create
  cross-sectional images

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Image Format

• TIF (LZW lossless coding)
• GIF
• JPEG
• BMP

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Image Format

• TIF (LZW lossless coding)
• Tagged image file format
• Image head
• field tags values
• image size
• compression
• color depth
• location of data
• bits per sample
• .

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Image Format

• JPEG
• 88 blocks ? DCT ? Coefficient quantization ?
  Huffman coding ? zig-zag run-length coding

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Demo
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Image Format

• BMP
• PBM - portable bitmap file format (binary)
• PGM portable greymap (grey scale)
• PPM portable pixmap (color)