Image enhancement

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Image enhancement

• Antti Tuomas Jalava
• Jaime Garrido Ceca

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Overview

• Digital subtraction angiography. Dual-energy and
  energy-subtraction X-ray imaging. Temporal
  subtraction.
• Gray-scale transform.
• Convolution mask operators.
• High-frequency enhancement.
• Adaptive contrast enhancement.
• Objective assessment of Contrast Enhancement.

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Digital Subtraction Angiography

• PROCESS
• Agent is injected to increase the density of the
  blood
• Number of X-ray images.
• An image taken before the injection of the agent
  is used as the mask or reference image.
• Subtracted from the live images to obtain
  enhanced images.
• Useful to detect sclerosis.
• The mathematical procedure involved may be
  expressed simply as
• Sensitive to motion

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Dual-energy and Energy-subtraction X-ray Imaging

• X-ray images at multiple energy levels
• Distribution of specific materials in the object
  or body imaged
• Weighted combinations of multiple-energy images
  
• soft-tissue and hard tissue separately

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Temporal Subtraction

• To detect normal or pathological changes occurred
  over a period of time.
• Detection of lung nodules
• Normal anatomic structures are suppressed and
  pathological are enhanced.

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Gray Scale TransformOverview

• Gray-scale thresholding.
• Gray-scale windowing.
• Gamma correction.
• Histogram transformation.
• Histogram specification.
• Limitation of global operations.
• Local-area histogram equalization.
• Adaptive-neighborhood histogram equalization.

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Gray-scale Transforms (I)

• Presence of different levels of density or
  intensity in the image.
• Histogram gray-scale transform.
• Improve the visibility of details.

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Gray-scale Transforms (II)

• Gray-scale thresholding.
• Gray level object gt L new bi-level image.
• Problem Narrow range of gray levels.
• Solution Stretch the range of interest to the
  full range.
• Gray-scale windowing.
• Linear transformation
• Gamma correction.
• Non-linear transformations

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Thresholding
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Gamma Curve
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Gamma Correction
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Windowing
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Histogram Transformation

• Principle maximal information is conveyed when
  PDF is uniform.
• Histogram transformation is used to enhance the
  image.
• Histogram-based methods
• Histogram equalization.
• Histogram specification.
• Local-area histogram equalization (LAHE).
• Adaptive-neighborhood histogram equalization.

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Histogram Equalization

• Goal
• Discrete version
• 
  

• Properties of this function
• Single value monotonically increasing.
• Maintain same range of values.

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Histogram Specification

• Problem H. Equalization provides only one output
  image. Not satisfactory in many cases.
• Histogram Specification is a series of
  histogram-equalization steps to obtain
  prespecified histogram.
• Process
• Specify the desired histogram and derive
• Derive the histogram-equalizing transform
• Derive from
• Obtain
• Transform to image f.

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Limitations of Global Operations

• Global operators (Gray-scale histogram
  transform) provides simple mechanisms to
  manipulate the image.
• Global approach to image enhancement ignores the
  nonstationary nature of images.
• Given wide range of details of interest in
  medical image, such as hard and soft tissues, it
  is desirable to design local and adaptive
  transform for effective image enhancement.

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Local-area Histogram Equalization (LAHE)

• Problem Gray levels with low probability are
  merged upon quantization of the equalizing
  transform lost in the enhanced image.
• 2D sliding window.
• Resulting transform is applied only to the
  central pixel.
• Computationally expensive.
• LAHE variation
• Not every pixel. Only nonoverlapping rectangular
  block spanning the image.

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Adaptive-neighborhood Histogram Equalization

• Limitation of LAHE no justification to the
  choice of the rectangular shape and the size of
  the window.
• Identification of shape and size neighborhoods
  for each pixel by region growing.
• Uniform region spans a limited range of gray
  levels by a specified threshold.
• Local area composed not only by foreground region
  growing but also by background one.
• Histogram of the local region equalizing
  transform to the seed pixel and all the pixels
  with the same value.

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Adaptive-neighborhood Histogram Equalization
Original
Equalization, Background depth 5, growth
threshold 16
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Convolution Mask Operators for Image Enhancement

• 2D convolution of images with 3 x 3 masks.
• Unsharp masking
• Subtraction Laplacian

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Convolution Mask OperatorsUnsharp Masking

• Tackles blurring by an unknown phenomenon.
• Assumes that each pixel of original image
  contributes also to neighboring pixels.
• Results into a fog.
• Procedure
• The original degraded image is blurred.
• The blurred image is subtracted from the degraded
  image.
• Removes the fog.
• General form
• Where is local mean in degraded image
  .

Mean filter
Unsharp mask
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Convolution Mask OperatorsSubtraction Laplacian

• Assumption that degraded image is a result of
  diffusion process that spreads intensity values
  over space as a function of time
• 3 x 3 convolution mask form
• of Laplacian (gradient)
• With weighting factor set to 1
• the subtraction Laplacian is

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Convolution Mask OperatorsProblems

• Edge enhancement high-frequency emphasis (Over
  and under-shoot seen as halos around edges).
• While seeming sharper, some finer details might
  be lost.
• Can lead to negative pixel values.
• Linear mapping back to display range can cancel
  any enhancing.
• Fixed operators.
• No adaptivity to variability within image.

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Unsharp mask, A 1, B 9, Normalized dynamic
range
Original
Unsharp mask, A 1, B 9, Dynamic range cut to
original
Subtracting Laplacian, A 1, B 5, Normalized
dynamic range
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High-frequency Emphasis

• Bad idea Ideal highpass filter
• Introduces ringing artifacts.
• Butterworth highpass filter
• Use of smooth transition from stopband to pass
  band.
• Artifact reduction.
• Extracts only edges.
• Order n.
• Butterworth high-emphasis filter
• Adds constant to frequency space.
• Preserves image and sharpens edges.

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Homomorphic Filtering (I)

• Already known Two images with different
  frequency composition that are added together can
  be separated with linear filtering.
• Two images multiplied with each other?
• Take logarithm first.
• (subscript l indicates that Fourier
  transform has
• been applied to Fourier transformed
  image)
• Then filter, inverse Fourier transform
• and reverse logarithm with exponent.

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Homomorphic Filtering (II)

• Extension for convolved images (Chapter 10.3).
• generalized linear filtering.
• Operations are called homomorphic systems.
• With highpass filter used to achieve simultaneous
  dynamic range compression (brightness
  normalization) and contrast enhancement.

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Original
Homomorphic filtering Butterworth High-frequency
emphasis filter, n 1, D 0.6, Ka 0.1, Kb
0.5
Butterworth High-frequency emphasis filter, n
1, D 0.6, Ka 0.1, Kb 0.5
Butterworth High-pass filter, n 1, D 0.6
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Adaptive-neighborhood Enhancement in General

• Adaptive neighborhood (foreground)
• Interconnected segment of pixels with certain
  common property with a seed pixel. (Found with
  seed fill.)
• Properly defined segments should correspond to
  image features.
• Found regions are extended to overlap with
  adjacent regions (background).
• Borders of few pixels wide.
• Prevents edge artifacts like reversed intensity
  across border.
• Enhancing algorithm is performed within the
  combined foreground and background.
• Result is applied to each seed pixel and each
  pixel within foreground with same value of
  property than seed.
• Other pixels in foreground grow their own
  neighborhood.

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Adaptive-neighborhood Contrast Enhancement

• Common property Similar gray value
• To be exact Growth tolerance .
• If , all pixels connected to seed
  pixel with gray value between 0.95 and 1.05 times
  the seed pixels gray value are included to
  foreground.
• All grown regions have contrast higher than
  independent of seed pixels gray value.
• Worst case scenario
• 
  
• average foreground pixel gray value
• average background pixel gray value
• Webers ratio of 2 (for contrast of visible
  features)
• should be about 4 .
• Algorithm Increase contrast to by
  replacing seed pixels value with

(From equation 2.7)
(From equation 2.7)
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Adaptive- neighborhood contrast
enhancement, growth tolerance 0.05, background
depth 5
Original
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Objective Assessment of Contrast Enhancement

• Contrast histogram
• Distribution of contrast of all possible regions
  obtained by seed fill algorithm.
• Enhanced image should contain more counts of
  regions at higher contrast levels.
• In practice same as more spread contrast
  histogram.
• The second moment is used to characterize the
  spread

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Image Enhancing- Ending Remarks

• Better contrast
• sharpness of detail and
• visibility of features
• are the targets for image enhancing.
• Results can vary with each approach and image.
• It can be beneficial to obtain several enhanced
  images with variety of approaches (as with most
  fields of image analysis).
• Image restoration is presented in chapter 10.
• Image restoration reversing the degradation when
  the exact mathematical model of degradation is
  known.

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Seed Fill - Foreground
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Seed Fill - Background