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Chapter3 Image Enhancement in the Spatial Domain

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Title: Chapter3 Image Enhancement in the Spatial Domain


1
Chapter3Image Enhancement in the Spatial Domain
  • 3.0 Introduction
  • 3.1 Background
  • 3.2 Some Basic Gray Level Transformations
  • 3.3 Histogram Processing
  • 3.4 Enhancement Using Arimethic/Logic Operations
  • 3.5 Basics of Spatial Filtering
  • 3.6 Smoothing Spatial Filters
  • 3.7 Sharpening Spatial Filters
  • 3.8 Combining Spatial Enhancement Methods

2
3.0 INTRODUCTION
  • 1. Objective
  • to process an image so that the result is more
    suitable for specific applications.
  • 2. Categories
  • a. spatial domain methods.
  • b. frequency domain methods.
  • c. combinations of above two types.

3
3.1 BACKGROUND
  • 1. Operate directly on an image f by the
    following way
  • g(x, y) T f (x, y)
  • where g is the processed image and T is an
    operator over an n ? n neighborhood of f
  • For simplicity in notation
  • S T(r)
  • r and s is the gray level of f(x,y)and g(x,y)

4
3.1 BACKGROUND
5
3.1 BACKGROUND
  • 2. Point processing -- for n 1, i.e.,
  • neighborhood the pixel itself
  • 3. Mask processing -- also called filtering
  • for n ? 1 neighborhood n ? n pixels using
    masks.

6
4.2 ENHANCEMENT BY POINT PROCESSING
  • 4.2.1 Some Simple Intensity Transformations
  • 4.2.2 Histogram Processing
  • 4.2.3 Image Subtraction
  • 4.2.4 Image Averaging

7
4.2.1 Some Simple Intensity Transformations(1)
  • 1. Image negatives
  • given a pixel gray level ( g. l. ) r, output
    pixel g. l. s is

L-1
T
s
L-1 largest g. l.
r
L-1
0
8
4.2.1 Some Simple Intensity Transformations(2)
  • 2. Contrast stretching
  • (1) Stretching is useful for improving image
    contrast.
  • (2) General transformation diagram.

L-1 largest g. l.
9
4.2.1 Some Simple Intensity Transformations(3)
  • (3) cases
  • a. no change -- if r1 s1 , r2 s2 .
  • b. thresholding -- if r1 r2, s1 0, and s2
    L-1
  • threshod value r1 r2.
  • c. stretching -- if r1? r2 s1? s2 ( to keep
    monotonicity of transformation )
  • d. Why dies stretching improve image contrast?
  • e. How to stretch is problem - dependent

10
4.2.1 Some Simple Intensity Transformations(4)
Mappings AgtT(A) (longer gt smaller)
L-1 largest g. l.
B gt T(B) (smaller gt larger ) CONTRAST IMPROVED)
C gt T(C) (larger gt smaller)
11
4.2.1 Some Simple Intensity Transformations(5)
  • 3. Compression of dynamic ranges
  • (1) Gray levels may be out of the display range
    after certain transformations.
  • (2) One way to compress is
  • S T( r ) c log(1 r )
  • where c is a constant to make s to lie between 0
    and L-1

12
4.2.1 Some Simple Intensity Transformations(6)
  • 4. Gray level slicing
  • (1) Highlighting a specific g. l. range
  • (2) Useful for many applications.
  • (3) Two approaches
  • a. use high values for desired ranges and low
    values for others
  • b. use high values for desired ranges and keep
    the values for others.
  • (4) See Fig 4.7

13
Fig 4.7
14
4.2.1 Some Simple Intensity Transformations(7)
  • 5. Bit-plane slicing
  • (1) Highlighting contributions made by specific
    bits to image appearance.
  • (2) More important information is included in
    higher- order bit planes details in others (see
    Fig. 4.8 )
  • (3) Bit - plane 7 ( highest - order ) result
    of thresholding with threshold 128
  • (4) See Fig. 4.9

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18
4.2.2Histogram Processing(1)
  • 1. Definition and properties of histogram
  • (1) the histogram of a given image f is a
    function
  • P( rk ) nk / n
  • where rk the kth g. l.
  • nk the no. of pixels with g.l. rk
  • n the total no. of pixels in f.
  • (2) Diagram of histogram

19
4.2.2Histogram Processing(2)
  • (3) Concept
  • histogram p.d.f ( probability density
    function )
  • (4) A histogram gives the global appearance of an
    image .
  • (5) Histograms of images with high and low
    contrasts (see Fig. 4.10 )

20
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21
4.2.2Histogram Processing(3)
  • 2. Histogram equalization
  • (1) Equalization transformation of a given image
    f
  • where Pr(w) is the histogram of f
  • (2) S above is exactly the c. d. f. of r ( c. d.
    f. cumulative distribution function )

22
4.2.2Histogram Processing(4)
  • (3) It can be shown by probability theory (see
    textbook) that the new image with g. l. s has a
    uniform distribution, i.e.,
  • (4) the transformation illustration

Pr(r)
Ps(s)
Equalization
r
S
Image with low contrast
Image with higher contrast
23
4.2.2Histogram Processing(5)
  • (5) Read the example in pp. 176-177.
  • (6) Histogram equalization is also called
    histogram flatting or linearization.
  • (7) Discrete form of histogram equalization

24
4.2.2Histogram Processing(6)
  • (8) A computation example

1
3
9
17
23
24
25
4.2.2Histogram Processing(7)
  • (9) A major advantage of histogram equalization
    for image contrast enhancement is that it can be
    applied automatically.
  • (10) See Fig. 4.14 for a real example.
  • 3. Histogram specification
  • See textbook
  • 4. Local enhancement
  • See textbook

26
4.2.3Image Subtraction
  • 1. Computes the difference g of two images f and
    h
  • 2. For application example, see Fig. 4.17

27
4.2.4Image Averaging
  • 1. Reduces noise by averaging several copies of
    and identical image
  • 2. Method
  • where gi(x, y) is one of copies of origin image
  • 3. Why work ? Noise standard deviation can be
    reduced to 1/n of origin
  • 4. See Fig. 4.18

28
4.3Spatial Filtering
  • 4.3.1 Background
  • 4.3.2 Smoothing Filtering
  • 4.3.3 Sharpening Filtering

29
4.3.1 Background(1)
  • 1. Spatial filtering is also called mask
    processing.
  • 2. Masks ( also called spatial filters ) are used
  • 3. High - frequency components in images
  • noise, edges, sharp details, etc.
  • 4. Low - frequency components in images
  • uniform regions, slow - changing background g.
    l., etc.
  • 5. Type of spatial filtering
  • (1) lowpass filtering
  • useful for image blurring (smoothing)

30
4.3.1 Background(2)
  • (2) Highpass filtering
  • useful for image sharpening
  • (3) Bandpass filtering
  • mostly used in image restoration
  • 6. See Fig 4.19 for the above 3 types.
  • 7. Linear mask operation

31
4.3.1 Background(2)
  • Operation replace z5 by
  • R M?N z1?w1 z2?w2 . z9?w9
  • 8. Nonlinear mask operation
  • R is computed nonlinearly using information of
    the neighborhood of current pixel as well as the
    mask.

Z5 g. l. of current pixel
Mask M
Neighborhood N
32
4.3.2Smoothing Filters(1)
  • 1. Used for image blurring noise reduction.
  • 2. Useful for removing small details and bridging
    small gaps in lines or curves.
  • 3. Lowpass spatial filtering
  • (1) Mask for 3?3 neighborhood

33
4.3.2Smoothing Filters(2)
  • (2) Operation -- replace z5 by
  • (3) Also called neighborhood averaging
  • (4) See Fig. 4.22 for effect
  • 4. Median filtering
  • (1) Reducing noise without blurring images

34
4.3.2Smoothing Filters(3)
  • (2) Operation --
  • replace g. l. at (x, y) with the median of all
    the g. l. of neighborhood.
  • (3) Meaning of median
  • value r such that
  • (i.e., r (1/2)tile of the p.d.f. )

P(x)
r median
x
Area 1/2
35
4.3.2Smoothing Filters(4)
  • (4) An example
  • given
  • g. l. z5 15 is replaced by median 20
  • (5) For effect of median filtering, see Fig. 4.23

36
4.3.3Sharpening Filters(1)
  • 1. Objective
  • highlighting or enhancing fine details in images.
  • 2. Applications
  • (1) electronic printing
  • (2) medical imaging
  • (3)industrial inspection
  • (4) target detection
  • etc.

37
4.3.3Sharpening Filters(2)
  • 3. Basic highpass spatial filtering (HPSF)
  • (1) Mask for 3?3 neighborhood
  • (2) See Fig. 4.25 for effect of filtering
  • 4. High best filtering
  • (1) Also called high-frequency emphasis
    filtering.

38
4.3.3Sharpening Filters(3)
  • (2) Method
  • high-best A ? (original) - lowpass
  • (A-1)(original) original - lowpass
  • (A-1)(original) highpass
  • where A is a selected weight.
  • (3) Note that part of the original image is added
    back.
  • (4) Equivalent mask
  • (5) See Fig. 4.27 (A1.1 is enough)

Where w9A-1 (A 1 ? basic HPSF)
39
4.3.3Sharpening Filters(4)
  • 5. Derivative filters
  • (1) Concept -
  • (2) The most common differentiation operation is
    the gradient

40
4.3.3Sharpening Filters(5)
  • (3) Gradient
  • a. definition -- the gradient of a function f at
    a pixel (x0, y0) is
  • b. magnitude of gradient --

41
4.3.3Sharpening Filters(6)
  • (4) Approximation of gradient magnitude
  • a. Assume the neighborhood (nbhd) g. l. of the
    pixel at (x, y) are
  • b. in continuous form

With g. l. at (x, y) z5
or
42
4.3.3Sharpening Filters(7)
  • C. in absolute difference form
  • d. Roberts operators for 2 ? 2 nbhd
  • operation N ? MR1 N ? MR2 z5-z9
    z6 - z8

or
MR1
MR2
43
4.3.3Sharpening Filters(8)
  • d. Prewitt operators for 3 ? 3 nbhd
  • operation N ? MP1 N ? MP2
  • (z7z8z9) - (z1z2z3) (z3z6z9) -
    (z1z4z7)
  • e. Sobel operators for 3 ? 3 nbhd
  • operation N ? MS1 N ? MS2
  • (z72?z8z9) - (z12?z2z3)
  • (z32?z6z9) - (z12?z4z7)

MP1
MP2
MS1
MS2
44
4.4 Enhancement in Frequency Domain
  • 4.4.1 Lowpass Filtering
  • 4.4.2 Highpass Filtering
  • 4.4.3 Homomorphic Filtering

45
4.4.1 Lowpass Filtering(1)
  • 1. Use
  • image blurring ( smoothing )
  • 2. Goal
  • Want to find a transfer function H(u, v) in the
    frequency domain to attenuate the high frequency
    in the FT F(u, v) of a given image f using the
    inverse FT

46
4.4.1 Lowpass Filtering(2)
  • 3. Ideal lowpass filter (ILPF)
  • (1) Definition --
  • H(u, v) 1 if D(u, v) ? D0
  • 0 otherwise
  • where D(u, v) distance from (0, 0) to (u, v)
  • and D0 is a constant ( called cutoff frequency )
  • (2) See Fig 4.30 for the filter shape in 3-D and
    2-D
  • (3) The ILPF cannot be implemented by analog
    hardware ( but can be implemented by software )
  • (4) Before seeing effects of the ILPF, we need to
    review more properties of the FT first.

47
4.4.1 Lowpass Filtering(3)
  • 4. Additional review of the Fourier transform
  • See sec.3.23.4 for FT, DFT, FFT
  • See Fig. 4.31 for an example of Fourier spectrum
    ( or simply called spectrum )
  • 5. See Fig. 4.32 for effects of applying the ILPF
    using different cutoff frequencies.
  • 6. The ILPF produces ringing effects see Fig.
    4.32(d) for an example and see Fig. 4.33 for the
    reason. Note Fig. 4.33(a) is equivalent to the
    top view of a 2-D sinc function.

48
4.4.1 Lowpass Filtering(4)
  • 7. Butterworth lowpass filter ( BLPF )
  • (1) A BLPF of order n with cutoff frequency at D0
    is defined as
  • where A 1 or 0.414
  • (2) See Fig. 4.34 for the shape of the BLPF.
  • (3) See Fig. 4.35 for the effects of applying the
    BLPF with n 1 for 5 D0 values.
  • 8. The BLPF produces no ringing effect due to the
    smoothness of its transfer function where A1 or
    0.414

49
4.4.2 Highpass Filtering(1)
  • 1. Use
  • Image sharpening
  • 2. Ideal highpass filter (IHPF)
  • (1) Transfer function
  • H(u, v) 0 if D(u, v) ? D0
  • 1 otherwise
  • (2) See Fig. 4.37 for shapes of the IHPF.

50
4.4.2 Highpass Filtering(2)
  • 3.Butterworth highpass filter (BHPF)
  • (1) Transfer function
  • where A 1 or 0.414
  • (2) See Fig. 4.38 for shapes of the BHPF.
  • 4.4.3 Homomorphic Filtering
  • 4.5 Generation of spatial masks from frequency
    domain specifications
  • Read the textbook

51
4.6Color Image Processing
  • 4.6.0 Introduction
  • 4.6.1 Color fundamentals
  • 4.6.2 Color models
  • 4.6.3 Pseudo-color image processing
  • 4.6.4 Full color image processing

52
4.6.0Introduction
  • 1. Motivation
  • (1) Color is a powerful descriptor for automated
    image analysis.
  • (2) The human eye can discern thousands of color
    shades and intensities ( but about only a dozen
    of grey levels )
  • 2. Study areas
  • (1) full color image processing
  • still in infancy
  • (2) Pseudo - color image processing
  • assigning color shades to monochrome intensity
    images

53
4.6.1Color Fundamentals(1)
  • 1. Colors of light
  • (1) Primary -- red (R), green (G), and blue (B)
  • (2) Secondary -- magenta (RB),
  • cyan (GB)
  • yellow (RG)
  • (3) See plate III(a) for illustration.
  • 2. Colors of pigments (colorants) --
  • (1) Primary -- magenta, cyan, and yellow
  • (2) Secondary -- red, green, and blue
  • (3) See plate III(b) for illustration.

54
4.6.1Color Fundamentals(2)
  • 3. Characteristics of color
  • (1) Three basic characteristics
  • a. brightness -- chromatic notion of intensity
  • b. hue -- dominant wavelength (color) perceived
    by human eyes
  • c. saturation -- amount of white light mixed with
    hue
  • (2) Chromaticity -- hue saturation
  • (3) trimulus values
  • amounts of red, green, and blue (denoted as X, Y,
    and Z, respectively ) for a color

55
4.6.1Color Fundamentals(2)
  • (4) trimulus coefficients -- x, y, z, with
  • x X / (X Y Z)
  • y Y / (X Y Z)
  • z Z / (X Y Z)
  • (5) Chromaticity diagram -- Plate IV

56
4.6.2Color models(1)
  • 1. Models
  • (1) RGB (red, green, blue ) model
  • useful for hardware e. g., color monitors, TV
    cameras, etc
  • (2) CMY ( cyan, magenta, yellow ) model
  • useful for color printers
  • (3) YIQ ( luminance, inphase, quatrature ) model
  • useful for color TV broadcasting
  • (4) HSI (hue, saturation, intensity ) model
  • useful for color image manipulation
  • (5) HSV (hue, saturation, value ) model
  • useful for color image manipulation

57
4.6.2Color models(2)
  • 2. Models most frequently used in image
    processing
  • RGB, YIQ, HIS
  • 3. RGB model
  • (1) Good for analysis of aerial satellite
    multispectral image data ( including 4 images of
    G, R and two infrared ).
  • (2) No good for natural scene image processing if
    R, G, B are treated separately ( e. g., human
    face processing ).
  • (3) See Fig. 4.44 for RGB color cube.

58
4.6.2Color models(3)
  • 4. YIQ model
  • (1) Y represents the luminance component.
  • (2) Y and color information ( i.e., I Q ) are
    decoupled.
  • (3) Contrast enhancement of an image in the YIQ
    model can be achieved by applying histogram
    equalization to the Y component only.
  • 5. HSI model
  • (1) I represents intensity.
  • (2) advantages
  • a. I and color information ( i.e., H S ) are
    decoupled

59
4.6.2Color models(4)
  • b. color information represented by H S is
    close to the color observed by eyes.
  • (3) Good for human color inspection works.
  • 6. Model conversions
  • (1) RGB ? YIQ -- use Eq. 4.6-6
  • (2) RGB ? HSI -- use Eq. 4.6-11, 18, 21 for I, H,
    S
  • (3) HSI ? RGB -- for detail, see pp 236-237 of
    the textbook.

60
4.6.3 Pseudo - color image processing(1)
  • 1. Purpose
  • to assign color to monochrome images based on
    properties of gray - level content of images.
  • 2. Method
  • (1) Intensity slicing
  • (2) Gray level to color transformation
  • (3) Filtering
  • 3. Intensity slicing
  • (1) slicing into two colors means the following
    transformation

61
4.6.3 Pseudo - color image processing(2)
  • (2) General slicing means the following
    transformation

Color
cM
c2
c1
L
I1
I2
IM
62
4.6.3 Pseudo - color image processing(3)
  • 4. Gray level to color transformation
  • (1) More general than intensity slicing.
  • (2) Method
  • feed image gray level into three (RGB)
    independent transformation functions and display
    the results in a color monitor ( see Fig. 4.50
    for illustration )
  • (3) For example, see Fig. 4.51 and Plate VI.
  • (4) Advantages
  • specific details in images may be emphasized.

63
4.6.3 Pseudo - color image processing(4)
  • 5. A filtering approach
  • (1) The principle is the same as that of gray
    level to color transformation except that the
    transformation are performed in the frequency
    domain.
  • (2) See Fig. 4.52 for illustration.
  • (3) Various forms of bandreject filters are used
    here ( see the textbook

64
4.64 Full Color Image Processing
  • 1. Only color image enhancement is discussed
    here.
  • 2. When the HIS model is used, intensity is
    decoupled from color information. So, we can
    enhance the I component using any enhancement
    technique for monochrome images.
  • 3.Detail procedure when the RGB model is used
  • RGB HSI HIS RGB
  • 4. See Plate IX for an example.
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