digital image processing - scut.edu.cn · there are two broad categories of image enhancement...

Xiangyu Yu

School of Electronic and Information Engineering,

South China University of Technology, P. R. China

[email protected]

DIGITAL IMAGE PROCESSING

LECTURE 3INTENSITY TRANSFORMATION

INTRODUCTION

Images may suffer from the following degradations: Poor contrast due to poor illumination or finite sensitivity of the imaging device

Electronic sensor noise or atmospheric disturbances leading to broad band noise

Aliasing effects due to inadequate sampling

Finite aperture effects or motion leading to spatial

3/13/2019 DIGITAL IMAGE PROCESSING 3

IMAGE ENHANCEMENT DEFINITION

Image Enhancement: is the process that improves the quality of the image for a specific application

Enhancement : To “improve” the usefulness of an image by using some transformation on the image.

Often the improvement is to help make the image “better” looking, such as increasing the intensity or contrast.

The principal objective of enhancement is to process an image so that the result more suitable than the original image for a specific application

–Image enhancement is subjective (problem/application oriented)


IMAGE ENHANCEMENT


The reasons for doing this include:Highlighting interesting detail in images

Making images more visually appealing

Enhance otherwise hidden information

Filter important image features

Removing noise from images

Discard unimportant image features

PREPROCESSING

Why we need image enhancement? Un-necessary noises

Defects caused by image acquisition

Uneven illumination: non-uniform

Lens: blurring object or background

Motion : blurring

Distortion: geometric distortion caused by lens

registration


7

INTUITIVELY

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IMAGE ENHANCEMENT EXAMPLES

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IMAGE ENHANCEMENT EXAMPLES (CONT…)

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IMAGE ENHANCEMENT METHODS

There are two broad categories of image enhancement techniques

Spatial Domain Methods (Image Plane)Techniques are based on direct manipulation of pixel(the intensity values) in an image(on the image plane itself)

Point-based processing

Mask-based processing (neighbor-based processing) (spatial filters)

Frequency Domain MethodsTechniques are based on modifying the transform coefficients of the Fourier transform or wavelet transform of the image, not directly process the intensity values of the image plane

Frequency domain filters

Combination MethodsThere are many enhancement techniques based on various combinations of methods from the first two categories

For the moment we will concentrate on techniques that operate in the spatial domain


13

IMAGE ENHANCEMENT

Two main categories: Point operations: pixel’s gray value is changed without the knowledge of its

surroundings. E.g. thresholding.

Neighborhood processing: The new gray value of a pixel is affected by its small neighborhood. E.g. smoothing.

The intensity (or gray-level) transformations & spatial filtering approaches for neighborhood processing, or spatial convolution.

We start with point operations.


CONTENTS

In this lecture we will look at image enhancement point processing techniques: What is point processing?

Negative images

Thresholding

Logarithmic transformation

Power law transforms

Grey level slicing

Bit plane slicing


A NOTE ABOUT GRAY LEVELS

So far when we have spoken about image gray level values we have said they are in the range [0, 255]

Where 0 is black and 255 is white

There is no reason why we have to use this range

The range [0,255] stems from display technologies

For many of the image processing operations grey levels are assumed to be given in the range [0.0, 1.0]


IMAGE TRANSFORMATIONS

Transformation is a function. It maps one set to another set after performing some operations.

• Digital Image Processing system performs

the transformation.3/13/2019 DIGITAL IMAGE PROCESSING 16

SPATIAL DOMAIN METHODS

As indicated previously, the term spatial domain refersto the aggregate of pixels composing an image. Spatialdomain methods are procedures that operate directlyon these pixels. Spatial domain processes will bedenoted by the expression:

g(x,y) = T [f(x,y)]

Where f(x,y) in the input image, g(x,y) is the processedimage and T is as operator on f, defined over someneighborhood of (x,y)

In addition, T can operate on a set of input images.

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The principal approach for defining spatial neighborhoods about a point (x, y) is to use a square or rectangular region centered at (x, y).

The center of the pixel is moved from pixel to pixel starting, say , at the top, left, corner, and, it moves, it encompasses different neighborhoods. Operator T is applied at each location (x, y) to yield the output, g, at that location. Only the pixels in the neighborhood computing the values of g at (x, y).


POINT PROCESSING(INTENSITY TRANSFORMATION)

s(x,y) = T{ r(x,y)}

Transformed

Gray LevelOriginal

Gray Level

Transformation

Function

>>imadjdemo

>>imadjust


BASIC CONCEPTS

Pixel/point operation: Neighborhood of size 1x1: g depends only on f at (x,y)

T: a gray-level/intensity transformation/mapping function

Let r = f(x,y) s = g(x,y)

r and s represent gray levels of f and g at (x,y)

Then s = T(r)

Local operations:g depends on the predefined number of neighbors of f at (x,y)

Implemented by using mask processing or filtering

Masks (filters, windows, kernels, templates) :

a small (e.g. 3×3) 2-D array, in which the values of the

coefficients determine the nature of the process


NEIGHBORHOOD ABOUT A POINT


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neighbourhood about a point 0 0x ,y in an image. The

neighborhood is moved from pixel to pixel in the image to generate an output image.

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EXAMPLES OF ENHANCEMENT TECHNIQUES

Larger neighborhoods allow considerable more flexibility. The general approach isto use a function of the values of f in a predefined neighborhood of (x,y) todetermine the value of g at (x,y).

One of the principal approaches in this formulation is based on the use of so-calledmasks (also referred to as filters)

So, a mask/filter: is a small (say 3X3) 2-D

array, such as the one shown in the

figure, in which the values of the mask

coefficients determine the nature of the

process, such as image sharpening.

Enhancement techniques based on this

type of approach often are referred to as

mask processing or filtering.3/13/2019 DIGITAL IMAGE PROCESSING 22

MASK PROCESSING FILTERING


g(x,y) = T [ f(x,y) ]

f(x,y) g(x,y)

1

0

0

-1

0

0

0

0

0

T

OPERATION ON THE SET OF IMAGE-PIXELS


6 8 2 0

12 200 20 10

3 4 1 0

6 100 10 5

(Operator: Div. by 2)

OPERATION ON THE SET OF ‘NEIGHBORHOODS’ N(X,Y) OF EACH PIXEL


6 8 2 0

12 200 20 10

226

6 8

12 200

(Operator: sum)

OPERATION ON A SET OF IMAGES F1,F2,…


6 8 2 0

12 200 20 10

5 5 1 0

2 20 3 4

11 13 3 0

14 220 23 14

(Operator: sum)

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INTENSITY TRANSFORMATION / POINT OPERATION

Map a given gray or color level u to a new level v

Memory-less, direction-less operation

output at (x, y) only depend on the input intensity at the same point

Pixels of the same intensity gets the same transformation

Does not bring in new information, may cause loss of information

But can improve visual appearance or make features easier to detect

input gray level u

outp

ut

gra

y le

ve

l

v


INTENSITY TRANSFORMATION / POINT OPERATION

Two examples we already saw

Color space transformation

Scalar quantization


Grey-level transformation functions (also called, intensity functions), are considered the simplest of all image enhancement techniques.

Point processes are the simplest of basic image processing operations.

A point operation takes a single input image into a single output image in such a way that each output pixel's gray level depends only upon the gray level of the corresponding input pixel.

Thus, a point operation cannot modify the spatial relationships within an image.

Point operations transform the gray scale of an image.

POINT PROCESSING

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POINT PROCESSING

The simplest spatial domain operations occur when the neighbourhood is simply the pixel itself(when the neighborhood in of the smallest possible size 1 x 1)

In this case, the value of g at (x, y) depends only on the intensity of f at that point, and T is referred to as a intensity(gray-level transformation)function or a point processing operation (or mapping)

Point processing operations take the form

s = T (r)

where s refers to the processed image pixel value and r refers to the original image pixel value(before processing), both at any corresponding point (x, y) in the images.

When dealing with color images, the term intensity is used to denote a color image component in certain color spaces.

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Linear and nonlinear point operations

Examples:

Contrast Stretching

Image Negatives

Intensity-level Slicing

Bit-plane Slicing

Other Intensity Transformations

POINT OPERATIONS


POINT OPERATIONS

Point operations affect the way images occupy greyscale.

A point operation transforms an input image, producing an output image in which each pixel grey level is related in a systematic way to that of the corresponding input pixel.

Unchanged Stretch

Compress

Output

grey level

Inputgrey level

A point operation will

never alter the spatial

relationships within an

image.


EXAMPLES OF POINT OPERATIONS

Input

Output

t Input

Output

t t1 2

(a) Threshold (b) Window Threshold

Input

Output

(c) Contrast Stretch

Input

Output

(d) Contrast Compression

Input

Output

(e) Combination

Input

Output

(f) Contouring


POINT PROCESSING,GRAY-LEVEL TRANSFORMATION FUNCTION

Point processing techniques (e.g. contrast stretching, thresholding)


Contrast Stretching Thresholding

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The function shown in fig. (a) is called contrast stretching transformation. Because

it compresses the input levels lower than m, into narrow range of dark levels in

output image. Similarly greater than m into a narrow band of light levels in the

output. And fig. (b) is thresholding transformation for binary image.

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Contrast Stretching:

If T(r) has the form as shown in the figure below, the effect of applying thetransformation to every pixel of f to generate the corresponding pixels in g would:

Produce higher contrast than the original image, by:

Darkening the levels below m in the original

image

Brightening the levels above m in the

original image

So, Contrast Stretching: is a simple image

enhancement technique that improves the contrast

in an image by ‘stretching’ the range of intensity values it contains to span adesired range of values. Typically, it uses a linear function


MATLAB IMPLEMENT FOR CONTRAST STRETCHING

The notation introduced here for fig (a) has the form:

Where r represents the intensities of the input image, s thecorresponding intensity value in the output image, and E controls theslope of the function. The equation is implemented in MATLAB foran entire image as:

g = 1./(1+(m./(double(f)+eps)).^E)

3/13/2019 36DIGITAL IMAGE PROCESSING

EXAMPLE CODE IN MATLAB FOR CONTRAST STRETCHING

I=imread('tire.tif'); I2=im2double(I); m=mean2(I2) contrast1=1./(1+(m./(I2+eps)).^4); contrast2=1./(1+(m./(I2+eps)).^5); contrast3=1./(1+(m./(I2+eps)).^10); imshow(I2) figure,imshow(contrast1) figure,imshow(contrast2) figure,imshow(contrast3)



Thresholding

Is a limited case of contrast stretching, it produces a two-level (binary) image.

Some fairly simple, yet powerful, processing approaches can be formulated withgrey-level transformations. Because enhancement at any point in an image dependsonly on the gray level at that point, techniques in this category often are referredto as point processing.

g(x,y) =L if f(x,y) > t,

0 else

t = ‘threshold level’


POINT PROCESSING EXAMPLE: THRESHOLDING

Thresholding transformations are particularly useful for segmentation in which we want to isolate an object of interest from a background or contrast enhancement.

s = 1.0

0.0 r <= threshold

r > threshold

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Original

image


SOME BASIC INTENSITY TRANSFORMATION FUNCTIONS

There are many different kinds of grey level transformations

Three of the most common are shown here Linear function

Negative/Identity transformation

Logarithmic function

Log/Inverse log transformation

Power-law function

nth power/nth root transformation


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BASIC INTENSITY TRANSFORM FUNCTIONS

monotonic, reversible

compress or stretch certain range of gray-levels


Some basic intensity transformation functions. Each curve was scaled independently so that all curves would fit in the same graph. Our interest here is on the shapes of the curves, not on their relative values.

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LINEAR FUNCTIONS

Identity FunctionOutput intensities are identical to input intensities

This function doesn’t have an effect on an image, it was included in the graph only for completeness

Its expression:

s = r


LINEAR FUNCTIONS

Image Negatives (Negative Transformation) The negative of an image with gray level in the range [0, L-1], where L = Largest value in an image, is obtained by using the negative transformation’s expression:

s = L – 1 – r

Which reverses the intensity levels of an input image, in this manner produces the equivalent of a photographic negative.

The negative transformation is suitable for enhancing white or gray detail embedded in dark regions of an image, especially when the black area are dominant in size

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IMAGE NEGATIVES

Let the range of gray level be [0, L-1], then

s =T(r) = (L - 1) - r

Function reverses the order from black to white so that the intensity of the output image decreases as the intensity of the input increases.

Used mainly in medical images and to produce slides of the screen.


Input gray level

Out

put

gra

y leve

l

T(f)= L-1-r

POINT PROCESSING EXAMPLE: NEGATIVE IMAGES

Negative images are useful for enhancing white or grey detail embedded in dark regions of an image, esp. when black areas are dominant in size

Note how much clearer the tissue is in the negative image of the mammogram below

s = L-1 - rOriginal

Image

Negative

Image

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Small

lesion

(a) A digital mammogram. (b) Negative image obtained (Image (a) Courtesy of General Electric Medical Systems.)

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NEGATIVE TRANSFORMATION

Original Negative

s = (L – 1) – r


IMAGE NEGATIVES EXAMPLES

50


the appearance of photographic negatives

Gray Scale (256 levels) Negative

IMAGE NEGATIVES EXAMPLES(CONT..)




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Figure X-ray image of a human hand, viewed as a positive and a negative.

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IMAGE SCALING


s =T(r) = a.r (a is a constant)

LOGARITHMIC TRANSFORMATIONS

The general form of the log transformation:

s = c log (1+r)

Where c is a constant, and r ≥ 0 Log curve maps a narrow range of low intensity values in theinput image into a wider range of the output levels. The oppositeis true for higher values of input levels.

Used to expand the values of dark pixels in an image whilecompressing the higher-level values.

It compresses the dynamic range of images with large variationsin pixel values.

The inverse log transformation performs the oppositetransformation


G3C-P.64-65

Properties of log transformations

–For lower amplitudes of input image the range of gray levels is expanded

–For higher amplitudes of input image the range of gray levels is compressed

Application:

This transformation is suitable for the case when the dynamic range of a processed image far exceeds the capability of the display device (e.g. display of the Fourier spectrum of an image)

Also called “dynamic-range compression / expansion”


LOGARITHMIC TRANSFORMATIONS

LOGARITHMIC TRANSFORMATIONS (CONT…)

Log functions are particularly useful when the input grey level values may have an extremely large range of values

In the following example the Fourier transform of an image is put through a log transform to reveal more detail

s = log(1 + r)

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Pixel

values

dynamic

range=[

0 -

1.5×106

]

From the

range 0-

to the

range 0

to 6.2

6105.1

(a) Fourier spectrum displayed as a grayscale image. (b) Result of applying the log transformation with c = 1. Both images are scaled to the range [0, 255]. G3C-P.65-66

LOGARITHMIC & CONTRAST-STRETCHING TRANSFORMATIONS:

Logarithmic & contrast-stretching transformations are basic tools for dynamic range manipulations. Logarithmic transformations are implemented using the expression:

g = c * log(1+double(f))

where c is a constant. The shape of this transformation is similar to the gamma curve with the low values set at 0 and the high values set to 1 on both scales. Note, however, that the shape of gamma curve is variable, whereas the shape of the log function is fixed.

mat2gray(g) function brings the values to the range [0,1]

im2uint8 brings them to the range [0, 255]


One of the basic principal uses of the log transformations is to compress dynamic range. When performing a logarithmic transformation, it is often desirable to bring the resulting compressed values back to the full range of display. For 8 bits, the easiest way to do this in MATLAB is with the statement:

gs = mat2gray(g);

If image is of double data class:

gs = im2uint8(mat2gray(f));

Log Transformation g=mat2gray(log(1+double(f)));

g=im2uint8(mat2gray(log(1+double(f)));

imshow(g)


DIGITAL IMAGE PROCESSING3/13/2019 61

Figure Applying exponential and logarithmic point operators.

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LOG TRANSFORM

im = imread(‘lena.png’)

a = abs(fftshift(fft2(double(im))));

c = log(1+double(im)); c = range_normalize(c);

b = log(1+a); b=b/max(b(:));

lena

FFT(lena)stretch:

u 2 [0, .5] v 2 [0, .59]

compress:u 2 [.5, 1] v 2 [.59, 1]


I=imread('tire.tif');

imshow(I)

I2=im2double(I);

J=1*log(1+I2);

J2=2*log(1+I2);

J3=5*log(1+I2);

figure, imshow(J) figure, imshow(J2) figure, imshow(J3)


INVERSE LOG TRANSFORMATIONS

Do opposite to the Log Transformations

Used to expand the values of high pixels in an image while compressing the darker-level values.


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LOG TRANSFORMATIONS

65

InvLog Log


POWER-LAW TRANSFORMATIONS

Power-law transformations have the basic form of:

s = c.rᵞ

Where c and ᵞ are positive constants

Map a narrow range of dark input values into a wider range of output values or vice versa.


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POWER-LAW(GAMMA)TRANSFORMATIONS

Varying γ gives a whole family of curves

Different transformation curves are obtained by varying ᵞ (gamma)

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Plots of the gamma equation γs = cr for various values of g (c = 1 in all

cases). Each curve was scaled independently so that all curves would fit in the same graph. Our interest here is on the shapes of the curves, not on their relative values. G3C-P.66

WHAT GAMMA TO USE?

>1

<1?


POWER-LAW (GAMMA) TRANSFORMATIONS

For γ < 1: Expands values of dark pixels, compress values of brighter pixels

For γ > 1: Compresses values of dark pixels,expand values of brighter pixels

If γ=1 & c=1: Identity transformation (s = r)

A variety of devices (image capture, printing, display) respond according to power law and need to be corrected

Gamma (γ) correction

The process used to correct the power-law response phenomena


POWER-LAW TRANSFORMATION

power-law response functions in practice

CRT Intensity-to-voltage function has

¼ 1.8~2.5

Camera capturing distortion with c = 1.0-1.7

Similar device curves in scanners, printers, …

power-law transformations are also useful for general purpose contrast manipulation


POWER-LAW TRANSFORMATION


GAMMA CORRECTION

Many of you might be familiar with gamma correction of computer monitors

Problem is thatdisplay devices do not respond linearly to different intensities

Can be corrected using a log transform

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4.0


Monitor5.2

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Variety of devices used for image capture, printing and display respond according to apower law. The process used to correct this power-law response phenomena is calledgamma correction.

For example, cathode ray tube (CRT) devices have an intensity-to-voltage response thatis a power function, with exponents varying from approximately 1.8 to 2.5. Withreference to the curve for g=2.5 in Fig. 3.6, we see that such display systems wouldtend to produce images that are darker than intended. This effect is illustrated in Fig.3.7. Figure 3.7(a) shows a simple gray-scale linear wedge input into a CRT monitor. Asexpected, the output of the monitor appears darker than the input, as shown in Fig.3.7(b).

Is important if displaying an image accurately on a computer screen

in this case is straightforward. All we need to do is preprocess the input image beforeinputting it into the monitor by performing the transformation. The result is shown in Fig.3.7(c).When input into the same monitor, this gamma-corrected input produces an outputthat is close in appearance to the original image, as shown in Fig. 3.7(d).


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make linear input appear linear on displays

method: calibration pattern + interactive adjustment


s = r2.5

r = [1 10 20 30 40 210 220 230 240 250 255]

s( = 2.5) = [0 0 0 1 2 157 176 197 219 243 255]

s( =.4) = [28 70 92 108 122 236 240 245 249 253 255]

example calibration chart

• Cathode ray tube (CRT) devices have an intensity-to-voltage response that is a power function, with varying from 1.8 to 2.5

• The picture will become darker.

• Gamma correction is done by preprocessing the image before inputting it to the monitor with s = cr1/

Monitor

Monitor

Gammacorrection

= 2.5

=1/2.5 = 0.4


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(a) Image of a human retina. (b) Image as it appears on a monitor with a gamma setting of 2.5 (note the darkness). (c) Gamma-corrected image. (d) Corrected image, as it appears on the same monitor (compare with the original image). (Image (a) courtesy of the National Eye Institute, NIH)

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Automatic Selection

EXAMPLE: GAMMA TRANSFORMATIONS

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c=1

= 0.4 c=1

= 0.3

c=1

= 0.6

4.0 3.0

6.01


The images to the right show a magnetic resonance (MR) image of a fractured human spine

Different curves highlight different detail

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s = r 0.6

s = r 0

.4

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POWER LAW EXAMPLE


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In addition to gamma correction, power-law transformations re useful for general-purposecontrast manipulation.

See figure 3.8

Low r: wash-out in the background (Fig. 3.8r=0.3)High r: enhance a wash-out appearance (Fig. 3.9 r=0.5 areas are too dark)

(a) Magnetic resonance image (MRI) of a fractured human spine (the region of the fracture is enclosed by the circle). (b)–(d) Results of applying the transformation in Eq. (3-5) with c = 1and γ = 0.6, 0.4,

and 0.3, respectively. (Original image courtesy of Dr. David R. Pickens, Department of Radiology and Radiological Sciences, Vanderbilt University Medical Center.)

POWER LAW EXAMPLE (CONT…)γ = 0.6

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Old Intensities

Tra

nsfo

rmed

In

ten

sit

ies



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1

Original Intensities

Tra

nsfo

rmed

In

ten

sit

ies



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1


Tra

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In

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ies


EXAMPLE: GAMMA TRANSFORMATIONS

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c=1

= 3

c=1

= 5

c=1

= 4

0.3

0.50.4

1


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An aerial photo of a runway is shown

This time power law transforms are used to darken the image

Different curves highlight different detail

s = r 3.0

s = r 4

.0

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POWER LAW EXAMPLE


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Another illustration of Power-law transformation

(a) Aerial image. (b)–(d) Results of applying the transformation in Eq. (3-5) with γ = 3.0, 4.0, and 5.0, respectively. (c=1 in all cases.)

(Original image courtesy of NASA.)G3C-P.68

POWER LAW EXAMPLE (CONT…)

γ = 5.0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.2 0.4 0.6 0.8 1


Tra

nsfo

rmed

In

ten

sit

ies


EFFECT OF GAMMA ON CONSUMER PHOTOSL0

2.2L0

1/2.2L0


POINT PROCESSING

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>>imadjdemo

>>imadjust


FUNCTION IMADJUST

Function imadjust is the basic IPT tool for intensity transformations of gray scale images, it has the following syntax:

g= imadjust(f, [low_in high_in, low_out high_out], gamma)

This function maps the intensity values in image f to new values in g, such that values between low_in and high_in map to values between low_out and high_out.


GME-P.66-67

The parameter gamma specifies the shape of the curve that maps the intensity values in f to create g. If gamma is less than 1, the mapping is weighted towards higher (brighter) output values. If gamma greater than 1, the mapping is weighted towards lower (darker) output values. If it is omitted from the function argument, gamma defaults to 1.


GME-P.67

Negative image, obtained using the command

>>g1=imadjust(f,[0,1],[1,0]);

This process, which is the digital equivalent of obtaining a photographic negative, is

particularly useful for enhancing white or gray detail embedded in a large, predominantly

dark region.


GME-P.67

The negative of an image can be obtained also with IPT function imcomplement

>> g=imcomplement(f)

Expanding the gray scale region between 0.5 and 0.75 to the full [0,1] range:

>> g2=imadjust(f,[0.5 0.75], [0 1]);

This type of processing is useful for highlighting an intensity band of interest.

>> g3=imadjust(f,[ ],[ ],2);

produces a similar result by compressing the low end and expanding the high end of the gray scale.


GME-P.67-68

PIECEWISE LINEAR TRANSFORMATION FUNCTIONS

log, gamma … closed-form functions on [0,L] can be more flexible

Rather than using a well defined mathematical function we can use arbitrary user-defined transforms

The images below show a contrast stretching linear transform to add contrast to a poor quality image

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G3E-P.138G3C-P.68-69

PIECEWISE-LINEAR TRANSFORMATION FUNCTIONS

Principle Advantage: Some important transformations can be formulated only as a piecewise function.

Principle Disadvantage: Their specification requires more user input that previous transformations

•Advantage The form of piecewise functions can be arbitrary complex over the previous

functions

•Disadvantage• Require considerably more user input


PIECEWISE-LINEAR TRANSFORMATIONS

•Type of Transformations•Contrast stretching

• Expands the range of intensity levels in an image so that it spans the full intensity range of the recording medium or display device.

• Intensity-level slicing

• Highlighting a specific range of intensities in an image often is of interest.

•Bit-plane slicing

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G3E-P.137-139DIGITAL IMAGE PROCESSING

One of the simplest piecewise linear functions is a contrast-stretching transformation, which is used to enhance the low contrast images.

Goal: Increase the dynamic range of the gray levels for low contrast images

Low-contrast images can result from–poor illumination

–lack of dynamic range in the imaging sensor

–wrong setting of a lens aperture during image acquisition

–wrong shutter speed


G3E-P.137

CONTRAST STRETCHING

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CONTRAST STRETCHING

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Contrast stretching is a process that

expands the range of intensity levels in

an image

so that it spans the full intensity range of

the recording medium or display

device.

Contrast-stretching transformations

increase the contrast between the

darks and the lights

Stretch the over-concentrated gray-levels

Piece-wise linear function, where the slope

in the stretching region is greater than 1.


G3E-P.137G3C-P.69

CONTRAST STRETCHING

Figure shows a typical transformation used for contrast stretching.

The locations of (r1,s1) and (r2,s2) control the shape of the transformation function. If r1= s1 and r2= s2 the transformation is a linear function and produces no changes in gray levels.

If r1=r2, s1=0 and s2=L-1, the transformation becomes a thresholding function that creates a binary image.

Intermediate values of (r1,s1) and (r2,s2) produce various degrees of spread in the gray levels of the output image, thus affecting its contrast.In general, r1≤r2 and s1≤s2 is assumed, so the function is always increasing.


G3E-P.137

G3C-P.69

CONTRAST STRETCHING

Figure 3.10(b) shows an 8-bit image with low contrast.

Fig. 3.10(c) shows the result of contrast stretching, obtained by setting (r1, s1) = (rmin, 0) and (r2, s2) = (rmax,L-1) where rmin and rmax denote the minimum and maximum gray levels in the image, respectively. Thus, the transformation function stretched the levels linearly from their original range to the full range [0, L-1].

Finally, Fig. 3.10(d) shows the result of using the thresholding function defined previously, with r1=r2=m, the mean gray level in the image.


G3E-P.138DIGITAL IMAGE PROCESSING

G3C-P.69

CONTRAST STRETCHING EXAMPLE


G3E-P.138

Contrast stretching. (a) Piecewise linear transformation function. (b) A low-contrast electron microscope image of pollen, magnified 700 times. (c) Result of contrast stretching. (d) Result of thresholding. (Original image courtesy of Dr.Roger Heady, Research School of Biological Sciences, Australian National University, Canberra, Australia.)

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100G3C-P.69

CONTRAST STRETCHING

Example 1

For image with intensity range [50 - 150]

What should (r1,s1) and (r2,s2) be to increase the dynamic range of the image to [0 - 255]?


r

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INTENSITY-LEVEL SLICING

Purpose: To highlight a specific range of intensities in an image (e.g. to enhance certain features).

Display a high value of all gray levels in the range of interest and a low value for all other gray levels : produce a binary image

Two approaches:

Display high value for range of interest, low value else(binary image) (‘discard background’)

Display high value for range of interest(brighten the desired range of gray levels), original value else (‘preserve background’)

Applications:

Enhancing specific features, s.t. masses of water in satellite images

Enhancing flows in X-ray images


G3E-P.137-138


This technique is used to highlight a specific range of gray levels in a givenimage. It can be implemented in several ways, but the two basic themes are:

One approach is to display a high value for all gray levels in the range ofinterest and a low value for all other gray levels. This transformation, shown inFig 3.11 (a), produces a binary image.

The second approach, based on the transformation shown in Fig 3.11 (b),brightens the desired range of gray levels but preserves gray levelsunchanged.

Fig 3.11 (c) shows a gray scale image, and fig 3.11 (d) shows the result ofusing the transformation in Fig 3.11 (a).


Brighten the desired range of gray levels, but preserves the background and gray level tonalities (Fig. 3.11)

The higher order bits (especially the top four) contain the majority of the visually significant data

(a) This transformation function highlights range [A,B] and reduces all other intensities to a lower level. (b) This function highlights range [A,B] and leaves other intensities unchanged.Im

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G3E-P.138


3/13/2019 DIGITAL IMAGE PROCESSINGG3C-P.69

3/13/2019

Highlight the major blood

vessels and study the

shape of the flow of the

contrast medium (to detect

blockages, etc.)

Measuring the actual flow

of the contrast medium as

a function of time in a

series of images

G3E-P.138-139DIGITAL IMAGE PROCESSING

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(a) Aortic angiogram. (b) Result of using a slicing transformation of the type illustrated in Fig. 3.11(a), with the range of intensities of interest selected in the upper end of the gray scale. (c) Result of using the transformation in Fig. 3.11(b), with the selected range set near black, so that the grays in the area of the blood vessels and kidneys were preserved. (Original image courtesy of Dr. Thomas R. Gest, University of Michigan Medical School.)

G3C-P.70

• (a) transformation highlights range [A,B] of gray level and reduces all others to a constant level

• (b) transformation highlights range [A,B] but preserves all other levels


g2=imadjust(f,[0.5 0.75], [0.8 0.8]);

An image Result of using the

transformation in (a)



Figure Intensity mappings.

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N3E-P.87


Figure Applying the sawtooth operator.

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Figure An original image with a full range of

brightness values and several examples of arbitrary

display transfer functions which expand or alter the

contrast in various parts of the range. The plot with

each image shows the stored pixel brightness values

on the horizontal axis and the displayed brightness on

the vertical axis. The histogram of each resulting

image is also shown. (a) The original image has a

transfer function that is the identity function, so that

actual stored brightnesses are displayed; (b) inverted

(negative) image; (c) increasing gamma brightens

middle grays, shows increased detail in shadows; (d)

reducing gamma darkens middle grays, shows

increased detail in bright areas; (e) increased contrast;

(f) decreased contrast; (g) banded or wrap-around;

(h) solarization.

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BIT-PLANE SLICING


Bit-plane slicing : Pixels are digital numbers composed of bits. For

example, the intensity of each pixel in an 256-level gray-scale image is

composed of 8 bits (i.e., one byte).

Instead of highlighting intensity-level ranges, we could highlight the

contribution made to total image appearance by specific bits.

This method is useful and used in image compression.

Bit-plane 7(most significant)

Bit-plane 0(least significant)

One 8-bit byte

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G3C-P.70

BIT PLANE SLICING

Highlighting the contribution made to total image appearance by specific bits Assuming that each pixel is represented by 8 bits, the image is composed of 8 1-bit

planes.

Image is composed of eight 1-bit planes, ranging from bit-plane 0 for the least significant bit to bit plane 7 for the most significant bit.

Bit-plane 0 is the least significant bit, containing all the lowest order bits.

Bit-plane 7 is the most significant bit, containing all the highest order bits.

Plane 7 corresponds exactly with an image thresholded at gray level 128.

Each bit-plane is a binary image

Higher-order bits bits (top four) contain the majority of the visually significant data

Useful for analyzing the relative importance played by each bit of the image


BIT PLANE SLICING

Often by isolating particular bits of the pixel values in an image we can highlight interesting aspects of that image

Higher-order bits usually contain most of the significant visual information

Lower-order bits containsubtle details

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G3E-P.140

Extracts the information of a single bitplane

BIT-PLANE SLICING


255

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1 1 1 1 1 1 1 1

0 1 0 1 0 0 0 1

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1 0 0 0 0 0 1 0

0 0 1 1 0 0 0 0

1 0 0 1 0 0 1 1

1 1 1 0 1 1 0 1

1 1 1 1 0 1 1 0

1 0 1 0 1 0 1 0

MSBLSB


Bit-plane Slicing

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DEMO: A FRACTAL IMAGEIm

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BIT PLANE SLICING (CONT…)

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[10000000] [01000000]

[00100000] [00001000]

[00000100] [00000001]

2

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45 3

1 0


EIGHT BIT PLANES OF THE IMAGE

EXAMPLE

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G3C-P.71


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G3E-P.140G3C-P.71



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G3C-P.71

(a) An 8-bit grayscale image of size 837? 88 pixels. (b) through (i) Bit

planes 8 through 1, respectively, where plane 1 contains the least significant bit. Each bit plane is a binary image. Figure (a) is an SEM image of a trophozoite that causes a disease called giardiasis. (Courtesy of Dr. Stan Erlandsen, U.S. Center for Disease Control and Prevention.)

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127

Image reconstructed from bit planes: (a) 8 and 7; (b) 8, 7, and 6; (c) 8, 7, 6, and 5.

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Decomposing an image into its bits

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N3E-P.39

BP 7

BP 5

BP 0


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SLICING BITPLANES

Depend on relative importance of bits

How much to slice depend on image content

Useful in image compression, e.g. JPEG2000


G3E-P.141

EXAMPLE

3/13/2019

G3E-P.141

Useful for compression.

Reconstruction is obtained by:

1

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( , ) 2 ( , )N

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I i j I i j


PROGRAMMING HW#3(DDL APRIL 30)

Slice a gray image into 8 bit-plane?


THE END OF LECTURE 3


digital image processing - scut.edu.cn · there are two broad categories of image enhancement...

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