Transcript Image enhancement

Image enhancement
Antti Tuomas Jalava
Jaime Garrido Ceca
Overview
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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.
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:
f    f1    f 2
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Sensitive to motion
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
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 soft-tissue
and hard tissue separately
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 Transform
Overview
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Gray-scale thresholding.
Gray-scale windowing.
Gamma correction.
Histogram transformation.
Histogram specification.
Limitation of global operations.
Local-area histogram equalization.
Adaptive-neighborhood histogram equalization.
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)
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Gray-scale thresholding.
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Problem:
Solution:
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new bi-level image.
Narrow range of gray levels.
Stretch the range of interest to the full range.
Gray-scale windowing.
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Gray level object > L
Linear transformation
Gamma correction.
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Non-linear transformations
0  f m, n   f1
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 f m, n   f 1
g m, n   
 f1  f m, n   f 2
f

f
2
1


1  f m, n   f 2
g m, n   f m, n
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Thresholding
Original image
L = 30
New Image
Gamma Curve
Gamma Correction
Original image
γ = 0.3
New image
Windowing
Original image
f1 = 5
f2 = 60
New image
Histogram Transformation
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Principle: maximal information is conveyed
when PDF is uniform.
Histogram transformation is used to enhance the
image.
Histogram-based methods:
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Histogram equalization.
Histogram specification.
Local-area histogram equalization (LAHE).
Adaptive-neighborhood histogram equalization.
Histogram Equalization
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pg  1
Goal:
0  s 1
s  T r    p f wdw
Properties of this function:
•Single value monotonically increasing.
•Maintain same range of values.

dr
1 
pg  p f r  
  p f r  

ds r T 1 s  
p f r 
1
r
0
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r T 1  s 
Discrete version:
k
k
ni
s k  T rk    p f ri   
i 0
i 0 P
0  s 1
Original image
Equalized image
Histogram of the original image
Equalized Histogram
Histogram Specification
Problem: H. Equalization provides only one output
image. Not satisfactory in many cases.
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Histogram Specification is a series of histogramequalization steps to obtain prespecified histogram.
Process:
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Specify the desired histogram and derive p d t 
2.
Derive the histogram-equalizing transform q  T2 t 
3.
Derive s  T1 r  from p r 
1
1
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Obtain t  T2 s  T2 T1 r 
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f
5.
Transform to image f.
Limitations of Global Operations
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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.
Local-area Histogram Equalization (LAHE)
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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.
Adaptive-neighborhood Histogram Equalization
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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.
Adaptive-neighborhood Histogram Equalization
Original
Equalization,
Background depth 5,
growth threshold 16
Convolution Mask Operators for Image
Enhancement
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2D convolution of images with 3 x 3
masks.
1.
Unsharp masking
2.
Subtraction Laplacian
Convolution Mask Operators
Unsharp Masking
Tackles blurring by an unknown phenomenon.
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Assumes that each pixel of original image contributes
also to neighboring pixels.
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Procedure:
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The original degraded image is blurred.
The blurred image is subtracted from the degraded
image.
1.
2.
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Results into a fog.
Removes the fog.
Mean filter
General form:
Where
is local mean in degraded image
.
Unsharp mask
Convolution Mask Operators
Subtraction Laplacian
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Assumption that degraded image is a result of diffusion process that
spreads intensity values over space as a function of time
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3 x 3 convolution mask form
of Laplacian (gradient):
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With weighting factor
set to 1
the subtraction Laplacian is:
Convolution Mask Operators
Problems
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Edge enhancement & high-frequency emphasis (Over
and under-shoot seen as halos around edges).
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Can lead to negative pixel values.
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While seeming sharper, some finer details might be lost.
Linear mapping back to display range can cancel any enhancing.
Fixed operators.
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No adaptivity to variability within image.
Original
Unsharp mask,
A = 1, B = 9,
Dynamic range
cut to original
Unsharp mask,
A = 1, B = 9,
Normalized
dynamic range
Subtracting
Laplacian,
A = 1, B = 5,
Normalized
dynamic range
High-frequency Emphasis
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Bad idea: Ideal highpass filter
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Introduces ringing artifacts.
Butterworth highpass filter
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Use of smooth transition from stopband to pass
band.
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Artifact reduction.
Extracts only edges.
Order n.
Butterworth high-emphasis filter
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Adds constant to frequency space.
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Preserves image and sharpens edges.
Homomorphic Filtering (I)
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Already known: Two images with different frequency composition that are added
together can be separated with linear filtering.
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Two images multiplied with each other?
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Take logarithm first.
(subscript l indicates that Fourier transform has
been applied to Fourier transformed image)
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Then filter, inverse Fourier transform
and reverse logarithm with exponent.
Homomorphic Filtering (II)
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Extension for convolved images (Chapter 10.3).
→ generalized
linear filtering.
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Operations are called homomorphic systems.
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With highpass filter used to achieve
simultaneous dynamic range compression
(brightness normalization) and contrast
enhancement.
Original
Butterworth
High-frequency
emphasis filter,
n = 1,
D = 0.6,
Ka = 0.1,
Kb = 0.5
Homomorphic
filtering
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
Adaptive-neighborhood Enhancement in
General
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Adaptive neighborhood (foreground):
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Interconnected segment of pixels with certain common property with a seed
pixel. (Found with seed fill.)
 Properly defined segments should correspond to image features.
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Found regions are extended to overlap with adjacent regions (background).
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Borders of few pixels wide.
Prevents edge artifacts like reversed intensity across border.
Enhancing algorithm is performed within the combined foreground and
background.
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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.
Adaptive-neighborhood Contrast
Enhancement
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Common property: Similar gray value
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To be exact: Growth tolerance
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→
.
If
, all pixels connected to seed pixel with gray value between 0.95 and 1.05
times the seed pixel’s gray value are included to foreground.
All grown regions have contrast higher than
gray value.
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independent of seed pixel’s
Worst case scenario
(From equation 2.7)
= average foreground pixel gray value
= average background pixel gray value
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Weber’s ratio of 2 % (for contrast of visible features)
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should be about 4 %.
Algorithm: Increase contrast to
by replacing seed pixel’s value with
(From equation 2.7)
Original
Adaptiveneighborhood
contrast
enhancement,
growth
tolerance
0.05,
background
depth 5
Objective Assessment of Contrast
Enhancement
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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
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Better contrast
sharpness of detail and
visibility of features
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are the targets for image enhancing.
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Results can vary with each approach and image.
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It can be beneficial to obtain several enhanced images with variety
of approaches (as with most fields of image analysis).
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Image restoration is presented in chapter 10.
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Image restoration: reversing the degradation when the exact
mathematical model of degradation is known.
Seed Fill - Foreground
Seed Fill - Background