CV2005_3Lec02.ppt

Introduction to Computer
Vision
Lecture 2
Dr. Roger S. Gaborski

RS Gaborski 2
Vector Indexing
 Row vector dimension is 1 x N
 Elements accessed using 1 dimension index,
if vector is v, access first element by v(1), etc.
 Create row vector by: v = [ 1 3 5 7 9]
or v = [ 1,3,5,7,9]
>>v(3)
>> ans = 5

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Transpose Operator
 >> w = v’
w = 1
3
5
7
9
Convert row vector
to column vector

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Access Blocks of Elements
 Colon notation
>> v(1:3)
>> ans = 1 3 5
>> v(4:5)
>> ans 7 9
>> v(3:end) Don’t need to know size of v
>> ans 5 7 9
>> v(end:-2:1)
>> ans 9 5 1

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linspace
 Generate a row vector x of n elements
equally spaced between and including a
and b
X = linspace( a, b, n)

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>> k=linspace(1, 5, 3)
k =
1 3 5

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k =
1 3 5
k =
1.0000 2.3333 3.6667 5.0000
>> k=linspace(-12, 5, 4)
k =
-12.0000 -6.3333 -0.6667 5.0000

RS Gaborski 8
Matrix Indexing
 A = [ 1 2 3; 4 5 6; 7 8 9]
A = 1 2 3
4 5 6
7 8 9
Note semicolon
>>A(3,2)
>> ans = 8

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Matrix Indexing
 >> C3 = A(: , 3)
>> C3 = 3
6
9
>>R1 = A(1 , :)
>>R1 = 1 2 3

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Matrix Indexing
>> A(1:2,2:3)
ans =
2 3
5 6
>> A(end,end-1)
ans =
8

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Matrix Indexing
A( [ a b] , [c d] ) (rows,columns)
Recall [ ] is a vector
Picks out elements in A with coordinates
(row a, column c)
(row a, column d)
(row b, column c)
(row b, column d)

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Matrix Indexing
>> A
A =
1 2 3
4 5 6
7 8 9
>> E = A([1 3], [2 3]) ????

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Matrix Indexing
>> A
A =
1 2 3
4 5 6
7 8 9
>> E = A([1 3], [2 3])
E =
2 3
8 9

RS Gaborski 14
Matrix Storage
 MATLAB stores matrices as a column of
values (columns of original matrix appended
end to end. For matrix A:
1
4
7
2
5
8
3
6
9
Accessing A with a single subscript indexes
Directly into the column, so A(3) accesses the 3rd value
In the column, A(8) accesses the 8th value
>> A(8)
ans =
6

RS Gaborski 15
Matrix Operations
 True Matrix Multiply
1 2
3 4
5 6
7 8
*
=1*5+2*7 = 19
=1*6+2*8 = 22
Etc
19 22
43 50
=

RS Gaborski 16
Matrix Operations
 Point by Point Matrix Multiply
1 2
3 4
5 6
7 8
.*
=1*5 = 5
=2 * 6 = 12
Etc.
5 12
21 32
=

RS Gaborski 17
Another Example
f * g vs f .* g
>> f=[1 2;3 4]; g=[1 2; 2 1];
>> f .* g
ans =
1 4
6 4
>> f=[1 2;3 4]; g=[1 2; 2 1];
>> f * g
ans =
5 4
11 10
Element by Element True Matrix Multiply

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Additional Matrix Operations

RS Gaborski 20
Chapter 2 – Fundamentals
www.prenhall.com/gonzalezwoodseddins

RS Gaborski 21
Max Operation
A =
1 2
4 5
>> max(A)
ans =
4 5
>> max(A(:))
ans =
5

RS Gaborski 22
Simple Image Operations
f is a 1024 x 1024 intensity image
Flip the image: fp = f( end : -1 : 1, : )
Take a section out of the image: fc = f( 257:768, 257:768 )
Subsample an image: fs = f( 1:2:end, 1:2:end)
Plot the values of a horizontal line through the image:
plot( f( 512, :) )

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Data Classes
 Eight numeric data classes
 One character class
 One logical class
 All numeric operations in MATLAB are
done using double quantities
 Class uint8 are common in reading data
from devices

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Converting Between Data
Classes
 B = data_class_name(A) where
data_class_name is from first column of
Table 2.2
 If A is an array of class uint8. Can generate
a double precision array B by command:
B = double(A);

RS Gaborski 27
Converting Between Data Classes
 B = data_class_name(A)
 data_class_name is from first column of
Table 2.2
 If A is an array of class double can
generate a logical array B by command:
B = logical(A);

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Recall MATLAB expects operands in numeric
expressions to be double precision, floating
point numbers
 B = data_class_name(A) where
data_class_name is from first column of
Table 2.2
 If A is an array of class uint8 can generate
a double precision array B by command:
B = double(A);

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Logical Conversion
>> a = [ 0 1; 1 0];
whos a
Name Size Bytes Class
a 2x2 32 double array
Grand total is 4 elements using 32 bytes
>> b = logical (a)
b =
0 1
1 0
>> whos b
b 2x2 4 logical array

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Logical Conversion
>> c= [ -17.5 21.5; 13.95 311.05]
c =
-17.5000 21.5000
13.9500 311.0500
>> E = logical (c)
????????????????????

RS Gaborski 31
Logical Conversion
>> c= [ -17.5 21.5; 13.95 311.05]
c =
-17.5000 21.5000
13.9500 311.0500
>> E = logical (c)
Warning: Values other than 0 or 1 converted to logical 1
E =
1 1
1 1
Even though E(1,1) less than zero

RS Gaborski 32
>> whos
E 2x2 4 logical array
c 2x2 32 double array
>> G = c>0
G =
0 1
1 1
>> whos
E 2x2 4 logical array
G 2x2 4 logical array

RS Gaborski 33
 If C is an array of class double in which
all values in the range [0, 255] can be
converted to uint8 with the following
command:
D = uint8(C)

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c =
17.5000 21.5000
13.9500 11.0500
>> D= uint8(c)
D =
18 22
14 11
c =
-17.5000 21.5000
13.9500 311.0500
>> D= uint8(c)
What is D in this case?

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c =
17.5000 21.5000
13.9500 11.0500
>> D= uint8(c)
D =
18 22
14 11
c =
-17.5000 21.5000
13.9500 311.0500
>> D= uint8(c)
D =
0 22
14 255

RS Gaborski 36

mat2gray
 Converts arbitrary array of class double to
array of class double scaled to the range
[0,1]
g = mat2gray(A, [Amin, Amax])
range of g: [0,1]
values less than Amin become 0
values greater than Amax become 1
g = mat2gray(A) set Amin and Amax to the
actual minimum and maximum values

RS Gaborski 38
im2double
 Converts input to class double
 If input is of class uint8, uint16 or
logical, convert to class double in the
range [0,1]
 If input is already double there is no
change

RS Gaborski 39
im2double
d =
0 22
14 255
>> whos d
d 2x2 4 uint8 array
>> im2double(d)
ans =
0 0.0863
0.0549 1.0000

RS Gaborski 40
im2double
c =
-17.5000 21.5000
13.9500 311.0500
>> whos c
>> im2double(c)

RS Gaborski 41
im2double
c =
-17.5000 21.5000
13.9500 311.0500
>> whos c
>> im2double(c)
ans =
-17.5000 21.5000
13.9500 311.0500

RS Gaborski 42
Displaying Images [0, 255]
 Consider we would like to display a gray level
image that has a possible range of values 0-
255
 When we display the image we can arrange
for each gray level value to be displayed as a
different light level on the display
 Black would map to the gray level 0, white
would map to the gray level 255.
 Gray level values between 0 and 255 would
map to shades of gray.

RS Gaborski 43
Displaying Images [0,1]
 The gray level of images can also be
represented by real value numbers
between 0 and 1.
 0 represents pixels that are black, 1
represents pixels that are white.
 Values between 0 and 1 represent gray
level values.

RS Gaborski 44
Range of Gray Level Values
 The maximum range of values is [0,1] or
[0,255] (for 8 bit images)
 It is possible for images to use the maximum
range of gray level values, or some subset
 An image may only contain values between 0 and
.6, or .3 and .9
 In general, gray_min and gray_max, where
gray_min and gray_max may not be 0 and 1

RS Gaborski 45
Displaying Images
 imshow( f, G )
 f is image array
 G is number of intensity levels used to display. If G is
omitted, 256 is the default
 imshow( f, [ low high ] )
 Displays as black values less than low
 Displays as white all values equal or greater than high
 imshow( f, [ ] )
 Sets variable low to lowest value in f
 Sets variable high to highest value in f

RS Gaborski 46
Intensity Image Display Demo
%imshowDemo
%Create intensity image - values between 0 and 1
%f= (rand([30 30])/5);
f= (rand([30 30]));
%Display image
figure, subplot(1,3,1), imshow(f), title('imshow(f)')
subplot(1,3,2),
imshow(f, [.25 .75]), title('imshow(f, [.25 .75]')
subplot(1,3,3),
imshow(f, [ ] ), title('imshow(f, [ ] )')

RS Gaborski 48
Results - 2
Low contrast image

RS Gaborski 49

RS Gaborski 50
IMPORTANT POINT
 In the previous slides the data values
for each image didn’t change, but how
they were displayed did change.

RS Gaborski 51
Writing Images to Disk-
Syntax
 Syntax:
 imwrite( f, ‘filename’ ) string filename
must contain file format extension
imwrite( f, ‘xray1.tif’)
OR, third input argument can specify format
 imwrite( f, ‘xray1’, ‘tif’)

RS Gaborski 52
Writing Images to Disk-
Parameters
 imwrite(f, ‘filename.jpg’, ‘quality’, q)
 jpg (jpeg) are compressed images
 There is a trade off between file size
(degree of compression) and image quality
 Highly compressed images have small file
sizes, but poorer image quality
 q is an integer between 0 and 100
 Smaller numbers result in more compression

RS Gaborski 53

RS Gaborski 54
Image Types
 Intensity images
 When elements are class uint8 or uint16 they have
integer values in the range [0 255] or [0 65535]
 When elements are class double values are
floating point numbers. Valued are scaled in the
range [0 1] by convention
 Binary images
 RGB images
 Indexed images

RS Gaborski 55
Image Types
 Binary images
 A logical array of 0s and 1s
 An array of 0s and 1s that are of type uint8 is NOT
a binary image
 If A is a numeric array of 0s and 1s can create a
logical array B using statement:
B = logical(A) (all non zero values converted to
logical 1s, entries with value 0 converted to
logical 0s
 RGB images
 Indexed images

RS Gaborski 56
Image Types
 Binary images
 RGB images
 RGB color image is an MxNx3 array of color pixels
 Each pixel is a triplet corresponds to the red,
green and blue components at a specific spatial
location
 Can be interpreted as 3 planes of gray scale
images fed into red, green and blue inputs of a
color monitor
 Class double, range of values [0,1]
 Class uint8 or uint16 ranges are [0 255], [0
65535]
 Indexed images

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RS Gaborski 58
Image Types
 Binary images
 RGB images
 Indexed images
 Two components: data matrix of integers, X, and
a color map matrix, map
 Matrix map is an mx3 array of class double
floating point numbers in the range [0,1]
 m is the number of colors defined for the image
 Each row of m specifies the r,g and b components
of a single color

RS Gaborski 59

RS Gaborski 60
Functions
 M files
 Scripts : series of statements
 Functions : can accept arguments and
can have one or more outputs
function [ outputs ] = name( inputs )

RS Gaborski 61
Functions
 Find the element by element product of two
matrices and find the max and min of the
product
function [p, pmax, pmin]=improd( f, g )
%input images can be uint8, unit16 or double
fd=double(f);
gd=double(g);
p=fd .* gd;
pmax=max(p(:));
pmin = min(p(:));

RS Gaborski 62
Function
>> f=[1 2;3 4]; g=[1 2; 2 1];
>>[p, pmax, pmin] = improd(f, g)
p =
1 4
6 4
pmax = 6
pmin = 1

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>> I = imread('boxster5.jpg');
>> figure, imshow(I)

RS Gaborski 69
>> subplot(3,1,1), imshow(I(:,:,1)), title('Red Plane')
>> subplot(3,1,2), imshow(I(:,:,2)), title('Green Plane')
>> subplot(3,1,3), imshow(I(:,:,3)), title('Blue Plane')
Notice bright grass region
Blue highlight
White (contains r,g,b)

RS Gaborski 70
>> Region = I(120:170,30:80,1:3);
>> figure, imshow(Region)
>> size(Region)
ans =
51 51 3
Copy and Paste

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imwrite(Region, 'Region.jpg');

RS Gaborski 72
>> R=rand([100,100]);
>> figure, imshow(R)

RS Gaborski 73
>> r=rand([100,100]);
>> g=rand([100,100]);
>> b=rand([100,100]);
>> image(:,:,1)=r;
>> image(:,:,2)=g;
>> image(:,:,3)=b;
>> figure, imshow(image)
Synthetic Color Image

RS Gaborski 74
>> S = R>.75;
>> figure, imshow(S)

CV2005_3Lec02.ppt

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