Introduction to Computer Vision Lecture 16 Dr. Roger S. Gaborski.

Introduction to Computer Vision

Lecture 16

Dr. Roger S. Gaborski

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Binary Morphological Processing

• Non-linear image processing technique– Order of sequence of operations is important

• Linear: (3+2)*3 = (5)*3=153*3+2*3=9+6=15

• Non-linear: (3+2)2 + (5)2 =25 [sum, then square] (3)2 + (2)2 =9+4=13 [square, then sum]

• Based on geometric structure• Used for edge detection, noise removal and

feature extraction Used to ‘understand’ the shape/form of a

binary image

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Image – Set of Pixels

• Basic idea is to treat an object within an image as a set of pixels (or coordinates of pixels)

• In binary images, pixels that are ‘off’, set to 0, are background and appear black. Foreground pixels (objects) are 1 and appear white

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Neighborhood

• Set of pixels defined by their location relation to the pixel of interest– Defined by structuring element– Specified by connectivity

• Connectivity- – ‘4-connected’ – ‘8-connected’

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Chapter 9Morphological Image Processing


From: Digital Image Processing, Gonzalez,Woods And Eddins

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Translation of Object A by vector b

• Define Translation ob object A by vector b:At = { t I2 : t = a+b, a A }

Where I2 is the two dimensional image space that contains the image

• Definition of DILATION is the UNION of all the translations:

A B = { t I2 : t = a+b, a A } for all b’s in B

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DILATION

Object B is one point located at (a,0) A1: Object A is translated by object BSince dilation is the union of all the translations, A B = At where the set union is for all the b’s in B, the dilation of rectangle A in the positive x direction by a results in rectangle A1 (same size as A, just translated to the right)

A1A

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DILATION – B has 2 Elements

Object B is 2 points, (a,0), (-a,0) There are two translations of A as result of two elements in BDilation is defined as the UNION of the objectsA1 and A2. NOT THE INTERSECTION

A2 A1(part of A1 is under A2)

A

-a a -a a

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DILATIONRounded corners

Round Structuring Element (SE) can be interpretedas rolling the SE around the contour of the object.New object has rounded corners and is larger by½ width of the SE

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DILATIONRounded corners

Square Structuring Element (SE) can be interpretedas moving the SE around the contour of the object.New object has square corners and is larger by½ width of the SE


DILATION

• The shape of B determines the final shape of the dilated object. B acts as a geometric filter that changes the geometric structure of A


imdilate

IM2 = IMDILATE(IM,NHOOD) dilates the image IM, where NHOOD is a matrix of 0s and 1s that specifies the structuring element neighborhood. This is equivalent to the syntax IIMDILATE(IM, STREL(NHOOD)). IMDILATE determines the center element of the neighborhood by FLOOR((SIZE(NHOOD) + 1)/2).

>> se = imrotate(eye(3),90)se =

0 0 1 0 1 0 1 0 0

>> ctr=floor(size(se)+1)/2ctr = 2 2


>> I = zeros([13 19]);>> I(6,6:8)=1;>> I2 = imdilate(I,se);

0.5 1 1.5 2 2.5 3 3.5

0.5

1

1.5

2

2.5

3

3.5

2 4 6 8 10 12 14 16 18

2

4

6

8

10

12

2 4 6 8 10 12 14 16 18

2

4

6

8

10

12


MATLAB Dilation Example

>> I = zeros([13 19]);>> I(6, 6:12)=1;>> SE = imrotate(eye(5),90);>> I2=imdilate(I,SE);>> figure, imagesc(I)>> figure, imagesc(SE)>> figure, imagesc(I2)


SE

DILATED IMAGEINPUT IMAGE


>> I(6:9,6:13)=1;>> figure, imagesc(I)>> I2=imdilate(I,SE);>> figure, imagesc(I2)

I I2

SE


SE =

1 1 1 1 1 1 1 1 1

I I2


Dilation and Erosion

• DILATION: Adds pixels to the boundary of an object

• EROSIN: Removes pixels from the boundary of an object

• Number of pixels added or removed depends on size and shape of structuring element


MATLAB Erosion Example

I3=imerode(I2,SE);

2 pixelwide

SE = 3x3


Combinations

• In most morphological applications dilation and erosion are used in combination

• May use same or different structuring elements


Morphological Opening and Closing

• Opening of A by B A BErosion of A by B, followed bythe dilation of the result by B

Closing of A by B A B Dilation of A by B, followed bythe erosion of the result by B

MATLAB: imopen(A, B) imclose(A,B)


MATLAB Function strel

• strel constructs structuring elements with various shapes and sizes

• Syntax: se = strel(shape, parameters)

• Example:– se = strel(‘octagon’, R);– R is the dimension – see help function


• Opening of A by B A BErosion of A by B, followed by the dilation of the result by B

Erosion- if any element of structuring element overlaps with background output is zero

FIRST - EROSION

>> se = strel('square', 20);fe = imerode(f,se);figure, imagesc(fe),title('fe')


Dilation of Previous ResultOutputs 1 at center of SE when at least one element of SE overlaps object

SECOND - DILATION

>> se = strel('square', 20);fd = imdilate(fe,se);figure, imagesc(fd),title('fd')


FO=imopen(f,se); figure, imagesc(FO),title('FO')


What if we increased size of SE for DILATION operation??

se = strel('square', 25);fd = imdilate(fe,se);figure, imagesc(fd),title('fd')se = strel('square', 30);fd = imdilate(fe,se);figure, imagesc(fd),title('fd')

se = 25 se = 30


Closing of A by B A B Dilation of A by B

se = strel('square', 20);fd = imdilate(f,se);figure, imagesc(fd),title('fd')

Outputs 1 at center of SE when at least one element of SE overlaps object


Erosion of the result by B

Erosion- if any element of structuring element overlaps with background output is zero


ORIGINAL

OPENING CLOSING


Hit or Miss Transformation

• Useful to identify specified configuration of pixels, such as, isolated foreground pixels or pixels at end of lines (end points)

• A B = (A B1) (Ac B2)• A eroded by B1, intersection A

complement eroded by B2 (two different structuring elements)


Hit or Miss Example

• Find cross shape pixel configuration:

0 1 0

1 1 1

0 1 0

MATLAB Function: C = bwhitmiss(A, B1, B2)


Original Image A and B1

A eroded by B1

Complement of OriginalImage and B2

Erosion of A complementAnd B2

Intersection of eroded images



Hit or Miss

• Have all the pixels in B1, but none of the pixels in B2


Hit or Miss Example #2

• Locate upper left hand corner pixels of objects in an image

• Pixels that have east and south neighbors (Hits) and no NE, N, NW, W, SW Pixels (Misses)

B1 = B2 = 0 0 0

0 1 1

0 1 0

1 1 1

1 0 0

1 0 0

Don’tCare aboutSE




G = bwhitmiss(f, B1, B2);Figure, imshow(g)



bwmorph(f, operation, n)

• Implements various morphological operations based on combinations of dilations, erosions and look up table operations.

• Example: Thinning>> f = imread(‘fingerprint_cleaned.tif’);

>> g = bwmorph(f, ‘thin’, 1);

>> g2 = bwmorph(f, ‘thin’, 2);

>> g3 = bwmorph(f, ‘thin’, Inf);




Input



Labeling Connected Components

• Label objects in an image

• 4-Neighbors

• 8-Neighbors

p p


4 and 8 Connect

Input Image 8 – Connect 4 - Connect


Reflection

• Dilation definition:

“Dilation of A by B is the set consisting of all structuring element origin locations where the reflected and translated B overlaps at least some portion of A”

• If structuring element is symmetric with respect to origin, reflection of B has no effect

Introduction to Computer Vision Lecture 16 Dr. Roger S. Gaborski.

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Transcript of Introduction to Computer Vision Lecture 16 Dr. Roger S. Gaborski.