Chapter 3' Image Enhancement

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Chapter 3. Image Enhancement

• Objective - process an image so that the result
  is more suitable than the original image for a
  specific application.
• Approaches
• Spatial Domain (image plane) direct manipulation
  of pixels in an image.
• Frequency Domain Modify FT of an image.
• Combination

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• 3.1 BACKGROUND
• Spatial Domain Method
• a(gain), b(brightness)
• g(x,y)Tf(x,y)afb
• f(x,y) input image,
• g(x,y) processed image
• T operator

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• 3.2 Enhancement by Point Process
• A. Intensity Modifications

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• 3.2 Enhancement by Point Process
• A. Intensity Modifications
• (1) Image negatives
• Applications medical images, slides
• Reverse the order from black to white so that the
  intensity of output decreases as the intensity of
  input increases.

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(2) Contrast stretching

• low-contrast images can result from poor
  illumination, lack of dynamic range in the image
  sensor, or even wrong setting of a lens.

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• Locations of points control the shape of
  transformation function

• The function is single valued and monotonically
  increasing. The condition preserves the order of
  gray levels.

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• (3) Compression of Dynamic Range
• The dynamic range of a processed image far
  exceeds the capability of display device. Only
  the brightest parts of the image are visible on
  screen. Ex. Display of FT.
• To compress the dynamic range
• sc log (1r)
• (c scaling constant)
• Ex Fourier spectrum
• 0,R0, 2500000
• log(1r) 0, 6.4 --gt 0, 255
• scaling factor c255/6.4

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(4) Gray-level Slicing

• Highlighting a specific range of gray levels.
• Applications enhance features such as masses of
  water in satellite imagery and flaws in x-ray
  images.
• Display a high value for all gray levels in the
  range of interest. Others low value or same.

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• (5) Bit-plane Slicing
• Highlighting the contribution made to total image
  appearance by specific bits.
• Only the five highest order bits contain visually
  significant data, others more subtle details.

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An example of bit-plane slicing
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• B. Histogram Processing
• Histogram a discrete function
• Histogram Equalization
• r the gray levels to be enhanced.
• Assume r continuous in 0,1
• sT(r) inverse

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• Cumulative Distribution Func (CDF)

s
1
T(r)
r
0
1
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• In discrete form
• The resulting histogram in discrete form after
  equalization is not flat.
• The gray levels are spread out.
• This process increases dynamic range.

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An example of histogram equalization
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• Histogram Specification
• HE only generates one result, not allow
  interaction.
• If desired image were available

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• Algorithm
• 1. Equalize levels of original image
• 2. Specify desired and obtain G(z)
• 3. Apply inverse
• Combine two funcs into one

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An example of Histogram Specification
(1) Apply Histogram Equalization to the original
image
The expected grayscale specification is 0 10,
1 30, 2 5, 3 5, 4 5 , 5 5,
6 30, 7 10
(2) Apply Histogram Equalization to the
desired image.
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(3) Find the matching between the grayscale
levels of original and desired image based
on the grayscale levels of histogram
equalization.
Histogram Specification
Final Image
Original Image
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• Local Enhancement
• The two histogram processing methods are global.
• It is necessary to enhance details over small
  areas.
• Procedure Define a square or rect. neighborhood
  and move the center from pixel to pixel. At each
  location, histogram is processing and map the
  center pixel.

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• Another approach
• Use non-overlapping regions, but produces an
  undesirable checkerboard effect.
• A typical local transformation
• g(x,y)A(x,y)f(x,y)-m(x,y)m(x,y)

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• Image Subtraction
• The difference between two images
• g(x,y)f(x,y)-h(x,y)
• Application medical imaging (mask mode
  radiography)
• Mask h(x,y), x-ray image of a region of a
  patients body
• f(x,y) image acquired after injection of a dye
  into the bloodstream.

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• Image Averaging
• Reduce the noise effects by adding a set of noisy
  images.
• Let noise A noisy image
• Assume
• Noise uncorrelated, zero average

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• It follows that
• E expected value, variances.
• As M increases, variability decreases.
• approaches f(x,y) as the
  of noisy images used in the averaging process
  increases.

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• 3.3 SPATIAL FILTERING
• Low-pass Eliminate high-frequency components
  (edges or sharp details) in the Fourier domain.
  Net effect blurring
• High-pass Eliminate low-frequency.
• Band-pass Remove selected freq. Regions.

Demo Program
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• To sum the products between mask coefficients and
  pixel intensities.
• Non-linear filters
• median
• max
• min

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• 3.3.2 Smoothing Filters
• For blurring and noise reduction.
• Low-pass All mask coef. positive
• Ex a sampled Gaussian function
• Ex neighborhood averaging (all 1)
• Median Achieve noise reduction rather than
  blurring.
• Sort the pixel value and neighbors, determine
  median, assign the value.

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• 3.3.3 Sharpening Filters
• To highlight fine detail or to enhance detail
  that has been blurred.
• Basic High-pass Filtering
• Positive coefficient near center and negative in
  the outer periphery.
• The sum of the coeffs. is 0.
• The results involve scaling and/or clipping to
  span the range 0,L-1.

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• High-boost filtering
• Highpass Original - Lowpass
• High-boost (high-freq-emphasis) Multiply the
  original image by an amplification factor.
• High boost (A)(Original) - Lowpass
• (A-1)(Original) Original - Lowpass
• (A-1)(Original) Highpass
• A1, standard high-pass
• Agt1, edge enhancement

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• Derivative Filters
• Averaging blur Differentiation sharpen.
• Gradient For a function f(x,y)
• The magnitude
• Approximated at

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• Instead of squares, using absolute
• Roberts cross-gradient operators (2x2)
• Prewitt operators (3x3)
• Sobel operators (3x3) more weight on pixels
  closer to center.

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• A 3x3 region Prewitt
• Roberts Sobel

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• 3.4 Enhancement in Freq Domain
• Compute FT, multiply the result by a transfer
  func, inverse FT.
• 3.4.1 Lowpass Filtering
• G(u,v)H(u,v)F(u,v)
• H Filter transfer funcs that affect real and
  imaginary parts in the same way.
  (zero-phase-shift)

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• Ideal filter
• A 2-D ideal lowpass filter (ILPF)
• Ideal all freqs inside a circle of radius are
  passed, whereas all freqs outside are completely
  removed.

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• Cutoff frequency ( ) The point of transition
  between H1 and H0.
• The sharp cutoff cannot be realized with
  electronic components.
• Ex The total power
• Taking u,v to enclose percent of power

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• ILPF refer to convolution G(u,v)H(u,v)F(u,v)
• Lead in the spatial domain

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• Butterworth Filter (BLPF)
• When D(u,v) H(u,v)0.5, but prefer to use

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• 3.4.2 Highpass Filtering Ideal Filter (IHPF)

Butterworth Filter (BHPF)
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