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.
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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
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
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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
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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From: Digital Image Processing, Gonzalez,Woods And Eddins
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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
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>> 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
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2 4 6 8 10 12 14 16 18
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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)
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SE
DILATED IMAGEINPUT IMAGE
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>> I(6:9,6:13)=1;>> figure, imagesc(I)>> I2=imdilate(I,SE);>> figure, imagesc(I2)
I I2
SE
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SE =
1 1 1 1 1 1 1 1 1
I I2
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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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
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From: Digital Image Processing, Gonzalez,Woods And Eddins
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MATLAB Erosion Example
I3=imerode(I2,SE);
2 pixelwide
SE = 3x3
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Combinations
• In most morphological applications dilation and erosion are used in combination
• May use same or different structuring elements
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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)
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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
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• 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')
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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')
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FO=imopen(f,se); figure, imagesc(FO),title('FO')
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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
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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
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Erosion of the result by B
Erosion- if any element of structuring element overlaps with background output is zero
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ORIGINAL
OPENING CLOSING
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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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)
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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)
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Original Image A and B1
A eroded by B1
Complement of OriginalImage and B2
Erosion of A complementAnd B2
Intersection of eroded images
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Hit or Miss
• Have all the pixels in B1, but none of the pixels in B2
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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
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
G = bwhitmiss(f, B1, B2);Figure, imshow(g)
From: Digital Image Processing, Gonzalez,Woods And Eddins
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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);
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
Input
From: Digital Image Processing, Gonzalez,Woods And Eddins
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From: Digital Image Processing, Gonzalez,Woods And Eddins
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Labeling Connected Components
• Label objects in an image
• 4-Neighbors
• 8-Neighbors
p p
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4 and 8 Connect
Input Image 8 – Connect 4 - Connect
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins
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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
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Chapter 9Morphological Image Processing
Chapter 9Morphological Image Processing
From: Digital Image Processing, Gonzalez,Woods And Eddins