Spatial Processing

8/14/2019 Spatial Processing

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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

xySts

tsgmn

yxf),(

),(1),(

1

/9

1

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1

/9

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1/91/9

1/91/91/9


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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

)},({),(),(

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!

Documents

Spatial Processing