Transcript faculty.petra.ac.id

Image enhancement in
the spatial domain
Human vision for dummies
Anatomy and physiology
Wavelength sensitivity
Human vision for dummies (2)
Visual perception of the image
 Contrast (local change in brightness)
eye has logarithmic perception
of brightness
 Acuity (details)
best resolution: 500 lux, 40 cm
=> 0.16 mm
 Object border
Borders are important and
also context-dependent
 Color
The human eye is more sensitive
to color than brightness
Optical illusions
http://www.optillusions.com/
Image enhancement
T
f(x,y)
Original image
g(x,y)
New image
We want to create an image which is ”better” in some sense.
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Transformation is pointwise
Helps visual interpretation (brightening, sharpening…)
=> SUBJECTIVE
Pre-processing for a subsequent image analysis algorithm
=> PERF = PERF of IA TASK
Make the image more ”specific”
=> APPLICATION DEPENDENT
Image (pre-) Processing
Image processing can be performed in the
► Spatial domain
► Frequency domain that is after Fourier transform
(next two lectures)
We have three types of transforms in the spatial domain :
► Pixel brightness transforms, point processing
(depend only on the pixel value itself)
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Spatial filters, local transforms or local processing
(depend on a small neighborhood around the pixel)
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Geometric transforms
Pixel brightness transforms
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Each pixel in the output image depends directly on the
corresponding pixel in the input image
One-to-one transform: pointwise
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Common transforms
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inverse
contrast stretching
logarithmic
exponential
With more than one input image:
 sums, mean images
 statistical operations (variance, t-test…)
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Pixel brightness transforms are easy to generalize to 3D
Grey scale histogram
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A grey scale histogram shows how many pixels there are of
each grey level (intensity level).
original image
(neutral transform)
inverse transform
logarithmic transform
How is the histogram changed?
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Explains the terms
- compression
- expansion
you find sometimes in
the textbooks.
Example : the inverse transform
original image
brightness
(addition/subtraction)
contrast
= histogram stretching
Paint Shop Pro example
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What do the function do?
How to use them to get the best results? And why it is best.
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Implementation: Look Up Table (LUT)
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Note: MATLAB V6.0 with IP Toolbox 3.0, also has these tools
Histogram equalization
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Contrast / Brightness adjustments sometimes
need to be automatized
What can be “optimal” contrast for an image?
=> FLAT histogram
It can also be useful to do histogram normalization
i.e.: to get a given shape for the histogram (see GW 3.3.2)
Histogram Equalization, example
quantization interval [0 7], image size 256x256
rk
0/7=0
1/7=0.14
2/7=0.29
3/7=0.43
4/7=0.57
5/7=0.71
6/7=0.86
7/7=1
nk
24979
21636
10865
3122
1411
656
2583
284
pr(rk)
0.38
0.33
0.17
0.05
0.02
0.01
0.04
0.00
sk
0.38
0.71
0.88
0.93
0.95
0.96
1.00
1.00
output
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original image
histogram equalization
transformation by probability
density function - see black board
notes
Adaptative / localized
histogram equalization
Relations between pixels
A picture element (pixel) has 4 or 8 neighbors in 2D depending on
neighbor definition:
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4-neihgborhood - each neighbor must share an edge with the
pixel
8- neighborhood - each neighbor must share an edge or a
corner with the pixel
4- neighborhood
8- neighborhood
Spatial filtering
In spatial filtering, the pixel in the output image is given a value
calculated from a local neighborhood in the input image.
The local neighborhood is described by a mask, or spatial filter
(typical sizes 3x3, 5x5, 7x7… pixels)
Filtering is performed by letting the mask move over the image. The
center pixel in the output image is given a value that depends on
the input image and the weights of the mask.
Several types of spatial filters:
► Linear filters
► Fractile filters
► Adaptative filters (steerable)
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Convolution
Filtering: implementation
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Generic code
for P(x,y) in image
for F(u,v) in filter
Q(x,y) += F(u,v)  P(x-u,y-v)
end
end
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(-1,-1)
(0,-1)
(1,-1)
(-1,0)
(0,0)
(1,0)
(-1,1)
(0,1)
(1,1)
Managing the border
 Outside pixel value set to zero
 Mirroring of the border pixel values
 Changing filter size along the border (BEST, but slower)
Spatial filtering
original image
mean filter =
”smoothing”
Laplace filter
Laplace + original
image = ”sharpening”
Spatial filters
Linear filters:
Smoothing filters
mean filters
Gauss filters
Edge enhancing filter
Sobel operator
Prewitt operator
Laplace operator
For details, see
next lecture…
Fractile filters**
Median, Min, Max
**have no correspondence in frequency domain
Mean filtering
original image
mean 3x3
mean 5x5
mean 11x11
Edge enhancing filters
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The Sobel operator:
detection of horizontal edges
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Edge enhancing filters
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The Laplace operator: detection of
edges independent of direction
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