spatial processing
TRANSCRIPT
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Spatial Domain ImageProcessing
Dr. P. ArulmozhivarmanAssociate Processor
School of Electrical Sciences
VIT University
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Principal application areas
Improvement of pictorial information for
human interpretation
Processing of image data for storage,
transmission, and representation for
autonomous machine perception
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Gray-level Histogram
Spatial
DFT DCT
Spectral
Digital Image Characteristics
Point Processing Masking Filtering
Enhancement
Degradation Models Inverse Filtering Wiener Filtering
Restoration
Pre-Processing
Information Theory
LZW (gif)
Lossless
Transform-based (jpeg)
Lossy
Compression
Edge Detection
Segmentation
Shape Descriptors Texture Morphology
Description
Digital Image Processing
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Features of an image
Low Frequency Component
Smooth/uniform regions
Approximation component
High frequency Component
EdgesDetailed component
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Image processing
Low level processing :
primitive operation- enhance quality of
image as suitable for application.
Mid- level processing :
description of objects for computer
processing and classification.
High level processing :
making sense of recognized objects
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Image processing fundamentals
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Example of negative image
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Image Enhancement
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MRI IMAGING
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Image Encryption
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Normalized histogram
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Histogram Equalization
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Image Preprocessing
Enhancement Restoration
SpatialDomain
SpectralDomain
Point Processingimadjusthisteq
Spatial filteringfilter2
Filtering fft2/ifft2
fftshift
Inverse filtering Wiener filtering
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Image restoration attempts to restore images
that have been degraded
Identify the degradation process and attempt to
reverse it
Similar to image enhancement, but more objective
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Filtering to Remove Noise
We can use spatial filters of different kinds
to remove different kinds of noise
The arithmetic mean filter is a very simpleone and is calculated as follows:
This is implemented as the
simple smoothing filter Blurs the image to remove
noise
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tsgmn
yxf),(
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Other Means
There are different kinds of mean filters all of
which exhibit slightly different behaviour:
Arithmetic Mean
Geometric Mean
Harmonic Mean
Contraharmonic Mean
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Other Means (cont)
There are other variants on the mean which
can give different performance
Geometric Mean:
Achieves similar smoothing to the arithmetic
mean, but tends to lose less image detail
mn
Sts xy
tsgyxf
1
),(
),(),(
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Other Means (cont)
Harmonic Mean:
Works well for salt noise, but fails for pepper
noiseAlso does well for other kinds of noise such as
Gaussian noise
xyStstsg
mnyxf
),( ),(1
),(
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Other Means (cont)
Contraharmonic Mean:
Q is the order of the filter and adjusting its value
changes the filters behaviourPositive values of Q eliminate pepper noise
Negative values of Q eliminate salt noise
xy
xy
Sts
Q
Sts
Q
tsg
tsg
yxf),(
),(
1
),(
),(
),(
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Order Statistics Filters
Spatial filters that are based on ordering the
pixel values that make up the nieghbourhood
operated on by the filter
Useful spatial filters include Median filter
Max and min filter
Midpoint filter Alpha trimmed mean filter
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Median Filter
Median Filter:
Excellent at noise removal, without thesmoothing effects that can occur with othersmoothing filters
Particularly good when salt and pepper noiseis present
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tsgmeanyxfxySts
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Max and Min Filter
Max Filter:
Min Filter:
Max filter is good for pepper noise and min is
good for salt noise
)},({max),(),(
tsgyxf
xy
Sts
)},({min),(
),(
tsgyxfxySts
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Midpoint Filter
Midpoint Filter:
Good for random Gaussian and uniformnoise
)},({min)},({max2
1),(
),(),(tsgtsgyxf
xyxy StsSts
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Alpha-Trimmed Mean Filter
Alpha-Trimmed Mean Filter:
We can delete the d/2 lowest and d/2 highestgrey levels
So gr(s, t) represents the remaining mn
d pixels
xySts
r tsg
dmn
yxf),(
),(1
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Detection of Discontinuities
3 basic types of gray-level discontinuities:
Points
LinesEdges
Common method of detection: run a maskthrough the image.
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Filter Mask
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Point Detection
T: nonnegative threshold:
9
1992211
...i ii
zwzwzwzwR
R T
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Point Detection
A point has been detected at the location on
which the mask is centered if: |R|>T
The gray level of an isolated point will bequite different from the gray levels of its
neighbors
measure the weighted differences between thecenter point and its neighbors
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Line Detection
If at a certain point |Ri
|>|Rj
|, this point ismore likely associated with a line in thedirection of mask i.
R1 R2 R3 R4
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Edge Detection
Edge (a set of connected pixels):
the boundary between two regions with relativelydistinct gray-level properties.
Note: edge vs. boundary
Assumption:
the regions are sufficiently homogeneous, so thatthe transition between two regions can be
determined on the basis of gray-leveldiscontinuities alone.
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Image Segmentation
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Edge Detection Basic Idea:
A profile is defined perpendicularly to the edgedirection and the results are interpreted.
The magnitude of the first derivative is used todetect an edge (if a point is on a ramp)
The sign of the second derivative can determinewhether an edge pixel is on the dark or light side ofan edge.
Remarks on second derivative: It produces two responses for every edge
The line that can be formed joining its positive andnegative values crosses zero at the mid point ofthe edge (zero-crossing)
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Edge Detection
Computation of a local derivative operator
A profile is defined perpendicularly to the edgedirection and the results are interpreted.
The first derivative is obtained by using themagnitude of the gradient at that point.
The second derivative is obtained by using theLaplacian.
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Gradient Operators
y
fx
f
G
GF
y
x
The gradient vector points in the direction of
maximum rate of change of f at (x,y).
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Gradient Operators
Gradient: 2/122 ][)( yx GGFmagf
(maximum rate of increase of f(x,y) per unit distance)
|||| yx GGf
Direction angle off at (x,y):
x
y
G
G
yxa1
tan),(
Image Segmentation
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Image Segmentation
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Image Segmentation
I S t ti
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Image Segmentation
I S t ti
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Image Segmentation
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Image Segmentation
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Gradient Operators
Computation of the gradient of an image:
Soebel operators provide both a differencing &a smoothing effect:
)2()2( 321987 zzzzzzGx
)2()2( 741963 zzzzzzGy
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Summary: Gradient Operators
Smooth edges due toblurring (result of sampling)
Positive: leadingNegative: trailing
Zero: in constant gray levels
Positive: from dark sideNegative: from light side
Zero: in constant gray levels
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The magnitude of the first derivative detects
the presence of an edge and the sign of the
second detects whether the edge pixel lies on
the dark or light side of an edge.
The second derivative has a zero-crossing atthe mid-point of a transition.
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Laplacian
(of a 2-D function f(x,y)): 22
2
2
2
y
f
x
ff
A 3 x 3 discrete mask based on the above is:
)(4 864252
zzzzzf
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Laplacian
The idea:
Coefficient of center pixel should be positive
Coefficients of outer pixels should be negative
Sum of coefficients should be zero(the Laplacian is a derivative)
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Image Segmentation
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Laplacian
The Laplacian is seldom used in practice,
because:
It is unacceptably sensitive to noise (as second-order derivative)
It produces double edges
It is unable to detect edge direction
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Laplacian
An important use of the Laplacian:
To find the location of edges using its zero-crossings property.
Plus, the Laplacian plays only the role ofdetector of whether a pixel is on the darkor light side of an edge.
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Laplacian
Convolve an image with the Laplacian of a2D Gaussian function of the form:
h(x,y) exp x2 y
2
22
where is the standard deviation.
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Laplacian
The Laplacian of the above Gaussian is:
2h r2
2
4
exp
r2
22
where r2 = x2 + y2.
determines the degree of blurring that occurs.
Image Segmentation
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Image Segmentation
Image Segmentation
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Thank you!