Module 2JH

8/18/2019 Module 2JH

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Binary Image Processing

• Binary Image Generation•

• Blob Coloring• nary orp o ogy

• Binary Template Matching

• Binary Image Compression

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Binary Images

sampled image intensities: A 10 x 10 image

rows

columns • Each gray level is

quantized: assignedone of a finite set of

numbers [0,…, K -1].

• K = 2 B possible gray

levels: each pixel• Binary images

=

2represented by B bits.


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• For printed page (notes, homework, and tests):

‒

Unless otherwise stated, BLACK = 1 = TRUE andWHITE = 0 = FALSE

“ ” ‒ y y

background and this creates a “cleaner” look in print.

Think of a page in a book: the text is printed in blackon a white background.

• For the computer monitor:

– Unless otherwise stated, WHITE = 1 = TRUE = 255dand BLACK = 0 = FALSE = 0d.

– “ ”

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.


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Binary Image Generation

• nary mages can come rom s mp e

sensors with binary output, e.g., tablet,

res s ve pa , or g pen.

• Quite useful for engineering drawing,

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entering handprinted characters, etc.


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-

• en, a nary mage s o a ne y

thresholding a gray-level image.

• Why do this?

- B-fold reduction in required storage- Simple abstraction of information

- - - Good binary compression algorithms

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Simple Thresholding

• The simplest image processing operation.• .

• Requires the definition of a thresholdT - .

• Every pixel intensity is compared to T , and a

nary ec s on ren ere .• Ex: binary pixel = TRUE if gray-level pixel > T

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Simple Thresholding

-

K gray-levels: 0, 1,...., K -1

• Select a threshold 0


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Binary Image Information

• Artists have long understood that binaryima es contain much information: form

structure, shape, etc.

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“Don Quixote” by Pablo Picasso


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original image, B=8 T =32

T =128 T =192

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original image, B=8 T =64

T =128 T =160

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original T =32 T =64 T =96

T =128 T =160 T =192 T =224

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Threshold Selection

• The usefulness of the binary image J fromthresholding I depends heavily on the threshold T .

• Different thresholds may give different valuable

abstractions of the image (preceding examples).• Some images do not produce any interesting results

when thresholded by any T .

• So: How does one decide if thresholding ispossible? How does one select the threshold T ?

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-

•

the frequency of occurrence of each gray.

• H I

is a one-dimensional function (array)

, ... , - .

• H I(k ) = n if I contains exactly n pixels with

gray eve ; = , ... - .

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Histogram Appearance

• The appearance of a histogram can tell youa lot about the ima e:

I (k ) I (k)

0 -1 gray level k 0 -1 gray level k

Predominantly dark image Predominantly light image

• Could be histo rams of underex osed and

16overexposed images, respectively.


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• The histogram contains first-order information only. It can tell you:

– e average, m n, an max p xe va ues, as we as t e stan ar

deviation. – The probability that a pixel picked at random from the image has

va ue 32.

• But it does not contain any 2nd or higher-order information ( i.e., how

the pixel values occur together in groups of two or more). – It can tell you variance, but it cannot tell you covariance.

– It can’t tell you the probability that a pixel with value 32 occurs

next to a pixel with value 40.

– If you take an image and scramble it up by moving all the pixelsaround to make a mess, the histogram remains unchanged.

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Histogram Appearance

• Here is a well-distributed histogram:

I(k )

0 -1 gray level k

too bright nor too dark.

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•

there are dark objects on a brightback round.

• Or when there are bright objects on a dark

back round.• Images of this type tend to have histograms

with distinct eaks or modes.

• Threshold selection is easier when theeaks are well se arated.

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I (k ) bimodal histogram

poorly separated;threshold selection

-

I (k) bimodal histogram

well separated peaks;

threshold selection

0 -1 gray level k eas er.

• Often, the peaks (modes) correspond to the

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o ec s an o e ac groun .


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• Suppose the histogram is bimodal and well separated.

• ac ng t e t res o etween t e mo es can o ten

yield a binary image that is TRUE on the object and FALSEon the background (or vice-versa).

• The exact optimal threshold placement is usually difficult

to determine. threshold

T

I (k )

hresholdselection

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0 -1 gray level k


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-• The histogram may have multiple modes. Different values for T

will give very different results.

• In some cases, the multiple modes may be from multiple objects.

–

out the objects in some cases.

– This is called “multi-thresholdin .”

T ? T ?

I (k ) multi-modal

histogram

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0 -1

gray level k


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• The histogram may be "flat," making

I (k) flat histogram

0 -1 gray level k

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• We'll use the histo ram extensivel for ra -level

processing later.• Some general observations for now:

– Bimodal histograms often imply objects and background

of different average brightness. – Bimodal histograms are easiest to threshold.

– The ideal result is a simple binary image showing

– Ex: printed text characters, blood cells in solution,

machine parts on an assembly line.

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Discussion of Histogram Types

• Multi-modal histograms often occur in images ofmultiple objects with different average.

• “Flat” or level histograms usually imply more

- background, etc.

• Thresholding rarely gives perfect results. Usually,

some kind of region correction must be applied.• We will study a region correction technique later

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.


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• Matlab provides a built-in function “hist” to compute

.

• But to use a Matlab built-in function correctly, you MUSTread the documentation!

Incorrect!! Correct:

h = hist(Lena); h = sum(hist(Lena,0:255)’);

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// the ima e is in unsi ned char arra x

// the total number of pixels is n

// the histogram will go into int array hist

since K=256 hist has 256 bins

for (i=0; i


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In C: In Matlab:

// x is the input image

// y is the output image

// n is the number of pixels

// T is the threshold

% x is the input image

% y is the output image

y = 255 * (x >= T);

for (i=0; i


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• Suppose we have obtained some binary

images:

• nce e p xe s ave og ca va ues(TRUE/FALSE), we can perform logical

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opera ons e , , an on em.


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Logical Operations - Notation

• Suppose X1,..., Xn are binary variables. Forexam le binar ixel values.

• Here is the notation we will use:

1 1

AND(X1, X2) = X1 ∧ X2

OR(X1, X2) = X1 ∨ X2

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More Notation

• Multivariate logical operations:= · · ·, ..., n n

OR(X1

, ..., Xn

) = X1

∨ · · · ∨ Xn

• nary a or ty:

MAJ(X1, ..., Xn) = ‘1’ if more 1’s than 0’s.

Else MAJ(X1, ..., Xn) = ‘0’.

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Binary Majority

• Defined for an odd number of binary variablesonly. X X X MAJ X , X , X

0 0 0

0 0 1

0

0 Three-Variable

0 1 1

1

1 0 0 0

Truth Table

for MAJ

1 1 01 1 1

1 1

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• We will define some very useful binary image

filters using MAJ later on.


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Image Complement

• We will now define several point-wiselo ical ima e o erations.

• Image complement:

, , ,

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Image AND

• Image AND:= =,

if J (m, n) = AND[I1(m, n), I2(m, n)] ∀ (m, n)

• ows over ap etween o ects n 1 an 2:

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I 1 I 2 J

= I1I

2


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• Image OR :

J = OR(I , I ) = I ∨ I

if J (m, n) = OR[I1(m, n), I2(m, n)] ∀ (m, n)

1 2

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I 1 J

= 1


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Comments on AND, OR, MAJ

• As we will see later, AND, OR, and MAJare ver useful when a lied to local ima e

regions rather than the whole image.

• - ,and MAJ is quite limited.

...

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Assembly Line Example

• An assembly line image inspection system.

I

computer

stored model image

I model conveyer

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• Objective: Meaningfully compare the acquired

mage o e s ore mage model

Note that I is

shifted slightly

measure of

overlap (match)

I model I ∧ Imodel I

• goo measuremen o m sma c : .

XOR(I, Imodel) = OR{AND[Imodel, NOT(I)], AND[NOT(Imodel), I]}

XOR(I, Imodel)

38• Not done yet…


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• XOR gives an image of mismatch.

• To decide if there is a problem or flaw, the

' 'mo e

model# of '1' pixels in

=I

• This may be compared to a pre-determined

tolerance percentage Q.

• If PERCENT > Q, then the part may beflaw or inc rr ctl lac .

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“ ” • In a binary image, a blob or connected component is a group of “1”

“ ” .

• This means that there is a connected path of “1” pixels between anytwo pixels in the blob.

“ ”

by the toplogy that we impose on the image.

• The topology specifies which neighbor pixels are connected to each

’ .

• There are two common topologies:

4-connected 8-connected

ne g or oo s ne g or oo s

Unless otherwise specified,assume the 4-connected

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Blob Coloring with Minor Region

Removal• In our resent context, the assum tion is that we have a ra scale

image with one main object against a background.

• Our goal is to use thresholding to produce a binary image that is ‘1’

on the ob ect and ‘0’ on the back round.

• The thresholding result will generally be imperfect:

– Some object pixels will be misclassified as background

– Some background pixels will be misclassified as object

• Blob coloring with minor region removal is a simple technique to

accomplish region classification and correction after thresholding.

Initial

thresholdingFinal

with minorregion removal

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result


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Blob Coloring with Minor Region

Removal• Wh mi ht we want to do this?

– It is often used as a “low level” image processing step that is performed prior to

some “higher level” computer vision process. – The “higher level” process could be, e.g., target tracking, biometric person

, , .

– The higher level process will generally take both the binary image and the original

grayscale image as input.

– The binary image is used as a map that tells the higher level process where theobject of interest is located in the grayscale image.

• How it works:

1. Perform blob coloring to label the blobs.

2. Perform blob counting to compute the size of each blob.

3. Delete all but the largest blob (minor region removal).

4. There will still be extraneous holes. So, invert and repeat steps 1-3.

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. .

• This will make more sense after we go through the details!


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• For binary image I, define a "region color" array R .

R m, n) = region number o p xe I m, n)

• Set R = 0 (all zeros) and k = 1 (k = counter for “next available region number”)• While scanning the image left-to-right and top-to-bottom do

if I(m, n) = 1 and I(m, n-1) = 0 and I(m-1, n) = 0 then // new blob found!

set R(m, n) = k and k = k + 1; // use new color!

if I(m, n) = 1 and I(m, n-1) = 0 and I(m-1, n) = 1 then // part of an old blobset R(m, n) = R(m-1, n); // use old color

if I(m, n) = 1 and I(m, n-1) = 1 and I(m-1, n) = 0 then // part of old blob

set R(m, n) = R(m, n-1);

if I(m, n) = 1 and I(m, n-1) = 1 and I(m-1, n) = 1 then

set R(m, n) = R(m-1, n); // all 3 are in the same blob!

if R(m, n-1) ≠ R(m-1, n) then // oops! 2 old blobs are really the same!

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Record that R(m, n-1) and R(m-1, n) are equivalent;


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• " "

each blob. Counting the pixels in each blob.

blob coloring

1

2 blob counting

793 11346

esu t3

4

5

resu t 1327 171

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• “Color” of largest blob: 2

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Colored blob display


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Minor Region Removal

• Let q = "color" of largest region (blob)• - -

top-to-bottom do

, ,

set I(m, n) = 0 ;

minor regionremoval

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• Not finished! To remove the holes, we must

repeat the procedure on the WHITE pixels:

complement

126471 673

blob coloring/counting 821

complement

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removal


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•

binary image operators we will consider.•

mathematical morphology

=• Morphological operations affect the shapes

.

• All processing done on a local basis - region

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manner.


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• Mor holo ical o erators:

- Expand (dilate) objects

-

- Smooth object boundaries and

eliminate small regions or holes

- Fill a s and eliminate ' eninsulas'• All is accomplished using local logical

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• Also known as ‘Windows”

• Some examples:

• A structuring element has a reference point (usually in the

cen er – s own n green a ove

• When the reference point is placed over a pixel in an

ima e a set of ixels are selected the ones that are

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covered by the structuring element)


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• To implement a morphological filter, the structuring

element is passed over the image pixels, row-by row,

column-by-column (moving window concept).

• Along the way, the structuring element is referenced

to each pixel in the image, selecting a set of input

.

• A logical operation is performed on the selected set

.

• Usually, the structuring element is approximately

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commutes with object/image rotation.


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.

.

.

.A structuring

element moving

. . over an mage.

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• The terms ‘window’ and ‘structuring element’ are

.

• In morphology, the term ‘structuring element’ is usuallyused.

• Some typical windows with a 1-D structure:

ROW(3) ROW(5)

OL(5) COL(3)

i.e. ROW 2 +1 and COL 2 P +1

• The window usually covers an odd number of pixels (2 P +1)

so that it is s mmetric about the reference oint and there

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is no phase shift between the input and output images.


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• Some windows with a 2-D structure:

SQUARE(9) CROSS(5)

SQUARE(25) CROSS(9) CIRC(13)

SQUARE(2 P +1), CROSS(2 P +1), CIRC(2 P +1)

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“ ” • Consider a 1-D LTI system H 1 with impulse response

• The output is

1[ ] [ 1] [ ] [ 1].

4 2 4

h n n n nδ δ δ = + + + −

1 1

1

[ ] [ ] [ ]

[ ] [ ]

y n x n h n

h k x n k

∞

= ∗

= −1 1 1

[ 1] [ ] [ 1]4 2 4

k

x n x n x n

=−∞

= + + + −

• Thus, at each point n, the number y1[n] is a weightedaverage of three surrounding inputs that is centered .

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• o e a 1 s no causa , s nce e curren ou pu y1 n

depends on the future input x[n+1].

Y thi k f th filt H h i 3 i t i d th t lid


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• You can think of the filter H 1 as having a 3-point window that slides

• Because the window is centered, there is no shift in the output signal

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relative to the input signal; i.e., the filter introduces no delay .

• Because h [ ] is real and even the frequency response H ( jω) is also


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• Because h1[n] is real and even, the frequency response H 1(e jω ) is also

.

• The frequency response is given by

j j n H e h n eω ω ∞

−=

1 1 14 2 4

n

j je eω ω

=−∞

−= + +

•

1 1cos .

2 2ω = +

1 .

• This again shows that, because the window is centered, there is no

shift (delay) between the input signal and the output signal.

.

• To implement the filter in real-time, you would have to shift h1[n] to

the right by one sample to make it causal.

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• So now consider a 2nd 1 D LTI system H with impulse response


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• So, now consider a 2nd 1-D LTI system H 2 with impulse response

• Notice that H 2 is causal, because h2[n] = 0 ∀ n < 0.

2 11 1 1[ ] [ 1] [ ] [ 1] [ 2].4 2 4

h n h n n n nδ δ δ = − = + − + −

• The output of H 2 is given by

2 2[ ] [ ] [ ] y n x n h n

∞

= ∗

2[ ] [ ]

1 1 1

k

h k x n k =−∞

= −

= − −

• The output signal is still a weighted average of the input signal, but it

is no longer centered.

4 2 4

• T e output signa is s i te to t e rig t y one samp e re ative to t e

input signal.

• In other words, the filter H 2 introduces delay – a phase shift .

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• “Sliding window” picture for H :


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• Sliding window picture for H 2:

• The current output is a weighted average of the current input and the

two previous inputs; the output signal is delayed or shifted by one

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sample relative to the input signal.

• Because h [n] does not have symmetry the frequency response


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• Because h2[n] does not have symmetry, the frequency responseω

2 .

• It is given by

2 2( ) [ ] j j n

n

H e h n eω ω ∞

−

=−∞

=

21 1 1

4 2 4

j j

e e

ω ω − −= + +

1

4 2 4

( )

j j j

j j

e e e

H e e

ω ω ω

ω ω

− −

−

= + +

=

• The phase response is arg H 2(e jω ) = -ω .

• The filter H 2 is causal and it could be implemented in real-time.

• But ecause t e win ow is not centere , t e output signa is s i te

to the right by one sample relative to the input signal.

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• In image processing, such shifting is usually undesirable.


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•

image – we usually want them to be “lined up.”

• Moreover, in image processing we usually receive the whole image at once;

– So there is no reason to restrict ourselves to causal processing!

– Mathematically, for the output pixel J(m, n), the input pixels I(m-1, n) and

“ ”, - , ,

I(m, n+1) are non-causal or “future” inputs.

– A filter that uses I(m+1, n) and I(m, n+1) to compute J(m, n) is non-

.

– But that’s usually not a problem in image processing – because we

usually get all the pixels at the same time.

• or ese reasons, n mage process ng e w n ow or s ruc ur ng e emen

is usually symmetric, usually covers an odd number of pixels, and thereference point is usually in the center.

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• s ensures a e ou pu mage s no s e re a ve o e npu mage.

If the filter is linear, then it has a zero phase response.


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•

coordinates (or “offsets”) Bi = ( p

i, q

i) of the covered

pixels relative to the reference pixel (0, 0):

B = {B1, ..., B2 P +1} = {( p1, q1), ..., ( p2 P +1, q2 P +1)}

Windows with a 1-D structure:

B = ROW(2 P +1) = {(0, - P ), ..., (0, P )}

= + = - , , ..., ,

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or examp e, = = , - , , , ,


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= = , , , , , ,

(0, -1) , (0, 0), (0, 1),

(1, -1) , (1, 0), (1, 1)}

For exam le B = R 5 = -1 0

(0, -1), (0, 0), (0, 1),

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,


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• ,

windowed set at (m, n) by:BI m n = I m- n- ∈ B

• It is the set of input pixels from the image that

located at pixel (m, n).

• -

simple concept will enable us to write simpleand flexible definitions for binary filters.

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• B = ROW(3):


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m, n = m, n- , m, n , m, n• B = COL(3):

m, n = m- , n , m, n , m+ , n

• B = SQUARE(9):

BI(m, n) = {I(m-1, n-1) , I(m-1, n), I(m-1, n+1),

I(m, n-1) , I(m, n), I(m, n+1),

I(m+1, n-1) , I(m+1, n), I(m+1, n+1)}

• B = CROSS(5):

B

I(m, n) = { I(m-1, n),I(m, n-1), I(m, n), I(m, n+1),

65I(m+1, n) }


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General Binary Filter

• Denote a logical operation G on thewindowed set BI(m, n) by

J(m, n) = G{BI(m, n)} = G{I(m- p, n-q); ( p, q) ∈ B}

• By performing this at every pixel in the image,

J = G[I, B] = [J(m, n); 0 ≤ m ≤ M -1, 0


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• What happens near the edges of the image

when the window "hangs over" ?

,

“empty space” by

making extra copies of

the image pixels on the

outside rows & columns

• This is called “handlin

the edge effects byreplication”

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,

define the morphological filter= ,

by

J(m, n) = OR{BI(m, n)}

= - -, ,

• Often written as J = I ⊕ B

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Dilation Filter-

size of logical ‘1’ objects.

Example of a local

OR

computation.

I J

= og ca

= logical ‘0’

= logical ‘1’

chan ed b

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= DILATION


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Dilation Filter

• Global effect of DILATION:

It is useful to think of thestructuring element asrolling along all of the

boundaries of all BLACK

The center point of thestructuring elementtraces out a set of paths.

That form the boundariesof the dilated image.

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.


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Qualitative Properties of Dilation

• Dilation also removes gaps or bays that are

too narrow:

DILATE

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• For a window B and a binary image I, we

define the morphological filter

= ,

by

, = ,

= AND{I(m- p, n-q); ( p, q) ∈ B}

• Often written as J = I B

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Erosion Filter

• Global effect of EROSION:

It is useful to think of the

structuring element asrolling inside of the

boundaries of all BLACKobjects in the image.

The center point of the

structuring elementtraces out a set of paths.

That form the boundaries

of the eroded image.

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Qualitative Properties of Erosion

• ros on removes o ects t at are too sma :

ERODE

• Erosion also removes peninsulas that are

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Erosion of the BLACK

same as dilation of the

WHITE part!

OT

OT

DILATE RODE

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• NOT(I ⊕ B) = NOT(I) B (dual operations)

• However, erosion and dilation are only

approximate inverses of one another.• Di ation en arges t e o jects.

– An erosion will return the objects to their original size

–• Erosion shrinks the objects

– A dilation will return the objects to their original size

– but it cannot restore the objects/peninsulas that wereremoved by erosion

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• For a window B and a binar ima e I we

define the morphological filter

= ,

or

J = MAJORITY(I, B)

by

J(m, n) = MAJ{BI(m, n)}= - -

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, ,


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• Removes both objects and holes of

insufficient size, as well as both gaps (bays)

and eninsulas of insufficient width.

• But generally does not change the overall

them).

-

complementation:

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=


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Median Filter

MAJ

A

C

B

I JB =

The median removed the small object A and the small holehole B, but did not change the boundary (size)

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.


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•

that are too small, as well as both gaps

MEDIAN

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3-D Median Filter Example

• The following example is a 3-D Laser

Scannin Confocal Microsco e LSCM

image (binarized) of a pollen grain.

Ma nification » 200x

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Examples of 3-D windows: CUBE(125) and CROSS3-D(13)


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LSCM image of pollen grain


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median filter


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• Define new morphological operations by

performing the basic ones in sequence.

• Given an ima e I and window B define

OPEN(I, B) = DILATE [ERODE(I, B), B]

or I ο B = (I B) ⊕ B

CLOSE I B = ERODE DILATE I B B

or I ● B = (I ⊕ B) B

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• In other words,

OPEN = erosion (by B) followed by dilation (by B)

CLOSE = dilation (by B) followed by erosion (by B) ,

holes that are too small, OPEN and CLOSE are“asymetric” smoothers that remove either objects or holes:

– OPEN removes small objects fingers better thanMEDIAN), but not holes, gaps, or bays.

– CLOSE removes small holes/gaps (better thanMEDIAN) but not objects or peninsulas.

• OPEN and CLOSE generally do not affect object size.

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.

d d


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OPEN and CLOSE vs. Median

OPEN

CLOSE

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C i OPEN CLOSE d CLOSE OPEN


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Comparing OPEN-CLOSE and CLOSE-OPEN

CLOSE-OPEN

CLOSE-OPEN

OPEN-CLOSE

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PEN-CLOSE


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• Often, it is of interest to find instances of a certain object

n a nary mage.

• This can be accomplished with simple logical operationsand a tem late.

• The template is similar to a structuring element, but the

pixels of the template have logical values (‘1’ or ‘0’).

a tem late for the letter “P”

the template is like a “mini image”

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• For two binary variables A and B, define MATCH(A,B) by

A B MATCH(A,B)

0 0 1

0 1 0

1 0 0

1 1 1

.

• Define the MATCH between two images I and J by

= =

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, , , , , ,


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• Let K = MATCH(I, J).

• Define:

M1(I, J) = AND[ K (m,n) ∀ (m,n) ]revea s per ec ma c es on y

M2(I, J) = SUM[ K (m,n) ∀ (m,n) ]

(measures how good the match is)

1 , =

M2(I, J) = 29

94I J K =MATCH(I, J)


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• When the template T is centered at pixel (m,n), we define

, ; m, n

to be the MATCH of T and that part of I that is covered by T. It is a

“mini-image” of the same size and shape as T.

• The binary template matching operation can then apply either match

measure M1 or M2 to this “mini-image.”

• By doing this at every pixel (m, n), we obtain a full-size match measure

image M1(I, T; m, n) or M2(I, T; m, n).

• M1(I, T; m, n) is ‘1’ where the neighborhood about pixel (m,n) matches

the template exactly and is ‘0’ elsewhere.

• Each pixel of M2(I, T; m, n) is an integer that gives the count of how

many pixels in the neighborhood about (m,n) match the template. Thiscount quantifies how well the neighborhood “matches” the template.

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• Because it is a filtering operation that is based on matching, template

.

• It is used often in target detection applications.

• The goal is to find instances of the template T in the image I; i.e. topro uce a nary map mage a s a p xe s w ere con a ns an

instance of T and is ‘0’ elsewhere.

• If we are only interested in detecting exact matches, then the binary

mage 1 , ; m, n can e a en as e na resu .• Except in controlled environments, this is usually impractical because

of noise and variations in the actual target appearance relative to the

, , , .

• Thus, we often threshold the integer image M2(I, T; m, n) instead toobtain a binary “map” image that is ‘1’ where the match is “close

”

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.


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• As usual, choosing the best value for the threshold can be difficult.

•

target in I, then it suffices to set the binary “map” image to ‘1’ at the

pixel where M2(I, T; m, n) is maximized (and to ‘0’ elsewhere).•

I, one common approach is to convert the integer match image

M2(I, T; m, n) to a floating point “percentage match” image.

– , , – The “percentage match” image can then be threhsolded with a threshold

that is between zero and one.

• There are two advanta es to this a roach:

1. It tends to make the task of choosing the threshold conceptually easier;

for example: “declare a detection if the match is 95% or better.”

2. It saves us from having to continually adjust the threshold in applications

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where the size of the target (and the template) may be changing over

time ̶ as in a video sequence where the target is moving.

Binary Image Compression


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Binary Image Compression

• In later Modules we will discuss gray-level

and color ima e and video com ression at

length.

•images.

.

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-


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• The number of bits required to store an M × N nary mage s .

• This can usually be significantly reduced by.

– This kind of coding is called source coding; theoal is to achieve com ression.

– It is different from channel coding, where thegoal is to add bits in order to achieve errorres ency.

• Run-length coding works well if the image‘ ’ ‘ ’

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.

How Run-Length Coding Works


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How Run-Length Coding Works

• Algorithm: For image row m:

(1) Store the first pixel value ('0' or '1') in row m as a

(2) Set run counter c = 1

3 For each pixel in the row:

- Examine the next pixel to the right

- If same as current pixel, set c = c + 1

- eren rom curren p xe , s ore c an se c =

-

Continue until end of row is reached• Each run-length is stored using b bits.

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Run-Length Code


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Run-Length Code

Example

'

row m

stored: '1' 7 5 8 3 1

Comments on Run-Length Coding

.

• If the image contains many runs of 1's and 0's.

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• ase ne uses o co e e coe c en s.

Run-Length Code


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Run-Length Code

• If the image contains only short runs, run-length coding can

increase the required storage.

row m

what'sstored: '1'1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

• Each count is stored with b bits!

• Worst-case exam le: stora e increased b-fold!

• Rule of thumb: average run-length L

>b.

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T f bi i i i d t i


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• Two types of binary images: region images and contour images.

region image contour image

-and/or curved) and single points.

• Each ‘1’ pixel in a contour image can have at most two 8-neighborsthat are also ‘1’.

Example of a neighborhood

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rom a con our mage


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• A binar re ion ima e can be converted into an a roximate contour ima e

by the following procedure.

• Let I be a region image. Define a new binary image J according to:

J(m, n) = ‘1’ if I(m, n) = ‘0’ and I(m, n) has one or more 4-neighbors that are ‘1’

• A ‘0’ ixel and it’s 4-nei hbors: one of them is ‘1’

• Intuitively, this algorithm traces out a contour of ‘1’ pixels around any region(object) of ‘1’ pixels in the input image.

• A ‘1’ pixel is output any time the window is on a ‘0’ pixel in the input image

but touches a ‘1’ pixel.

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pprox ma e on our enera on


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pprox ma e on our enera on• xamp e:

region image contour image

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•

• The output image is not guaranteed to be a true contour image.

• There may be some ‘1’ pixels in the output image that have more thantwo 8-nei hbors which are also ‘1’.

• Example:

• When this occurs, post processing such as edge thinning mustenerall be a lied to make corrections.

• For this course, we won’t be too concerned about it.

• Later, we will study more complicated edge detection algorithms thatcan be guaranteed to produce a true contour image as output.

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• The chain code is a highly efficient method

for coding binary contour images.

• -

contour is specified, then the rest of the

sequence of direction codes for how to

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contour initial pointand directions

• We use the following 8 neighbor direction codes:


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• We use the following 8-neighbor direction codes:

0

1 2

3

5 6 7

• Since the numbers 0, 1, 2, 3, 4, 5, 6, 7 can be coded bytheir 3-bit binary equivalents:

000 001 010 011 100 101 110 111

the location of each point on the contour after the initialpoint can be coded by 3 bits.

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• The end of the code is marked b a “fla ”. One o tion ̶

give the direction that “goes back” on itself: e.g., a ‘4’ and

then a ‘0’.• e compress on can e qu e s gn can : co ng y -

coordinates (B = 9 for 512 x 512 images) requires 6x as

much storage.

• Chain codes are effective for many computer vision and

pattern recognition applications, e.g. character recognition.

• omment: or c ose contours, t e n t a coor nate can e

chosen arbitrarily. If the contour is open, then it should bean end point.

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Module 2 Comments


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Module 2 Comments• any ngs can e accomp s e w

binary images – since shape is often well-preserve w en a graysca e mage s

thresholded.

• However, grayscale images are alsoimportant. We will deal with gray scales

next, but not shape – onward to Module 3.

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