Fundamentals of Computer Vision
Lecture 4
Dr. Roger S. Gaborski
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QUIZ 1
Closed book except one page of
handwritten notes
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Intensity Transformation and
Spatial Transformation
• Intensity – modify each pixel in the image
independent of its neighbors
• Spatial – modify a pixel as a function of its
neighbors (spatial convolution)
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If you look at a pixel of an intensity
(gray level image- Next Slide) in
isolation what can you tell me about
the image?
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If you look at a pixel of an intensity
(gray level image- Next Slide) in
isolation what can you tell me about
the image?
The brightness or intensity value at that spatial location
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What if you inspect a neighborhood
of pixel values?
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Depends on the neighborhood
Sky Region
Flag Region (2 rows, 3 columns)
The ‘flag region’ contains more information about the image
– There is a horizontal line in this region
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Can we modify the intensity values to
change the image (improve in some
way) or extract information from the
image (edges, shapes, etc.)?
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Spatial Transformation
• The general spatial domain processing equation:
g(x, y) = T [ f (x, y)]
– f (x, y) is the input image
– g(x, y) is the output image
– T is an operator on f defined over a specific neighborhood
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Chapter 3
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- Define spatial neighborhood about a point,
(x, y)
- Neighborhood is typically a square or
rectangle, but could be other shapes
- Center of neighborhood is moved from pixel
to pixel starting at the upper left hand corner
of the Image
- Operator T is applied at each location (x, y)
to yield g(x, y) at that location
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Intensity Transformations
• Let the neighborhood be reduced to a size of 1 x 1
pixel
• Now the transformation is only a function of the
pixel itself.
• This is commonly called an intensity transformation
or gray level transformation function:
s = T(r)
where r is the intensity of f at (x, y) and s is the resulting
intensity of g at (x, y)
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Intensity Transformations
• Assume the range of pixel intensity values is [0,1]
• What can be accomplished with transformation T ?
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Intensity Transformations
>> R = rand([1 4])
R=
0.0272 0.7937 0.9992 0.1102
>> R2 = R .* R ( note .* and not simply * )
R2 =
0.0007 0.6299 0.9985 0.0122
(small numbers are much smaller)
>> RSR = sqrt(R)
RSR =
0.1649 0.8909 0.9996 0.3320
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R = rand(1, 4)
R2 = R .* R
RSR = sqrt(R)
In this case the data is actually changed
Not the only display as in previous lecture
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Characteristics:
• y = x2 : all pixels become darker
• y = sqrt(x): all pixels become
brighter
• y = x: all pixels remain the same
value
Output (y)
Input (x)
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Intensity Transformations
• Function imadjust
– intensity transformation of gray scale images
• g = imadjust( f, [low_in high_in], [low_out,
high_out], gamma)
– Input - output defined in [0,1] range:
• [low_in high_in]  [0 1] (min max)
• [low_out high_out]  [0 1] (min max)
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Characteristics:
• gamma >1 : all pixels become darker
• gamma <1 : all pixels become brighter
• gamma =1 : linear transform
Gamma specifies the shape of the curve
Brighter Output (gamma<1)
Darker Output (gamma>1)
Chapter 3
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>> I = imread('mammogram.tif');
>> figure, imshow(I)
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>> I2 = imadjust(I, [.5 .75], [0 1]);
>> figure, imshow(I2)
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Reduce the amount of tissue Mapped to black:
>> I3 = imadjust(I, [.25 .75], [0 1]);
>> figure, imshow(I3)
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.75
1.0
Output
.50
I3
.25
I2
.25
.50
.75
1.0
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Input
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I4 = imadjust(I, [0, 1], [0, 1], 2)
Gamma=2
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Negative of image:
>> I4 = imadjust(I,[0 1], [1 0]);
>> figure, imshow(I4)
Or
I4 = imcomplement(I);
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Example, continued
H = [.5 .5 .6 .7 .8 .2; .6 .3 .8 .9 .2 .4 ]
H=
0.5000 0.5000 0.6000 0.7000 0.8000 0.2000
0.6000 0.3000 0.8000 0.9000 0.2000 0.4000
b = imadjust(H, [.3 .7],[.1 .9],1)
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1.0 OUTPUT
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Example
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INPUT
1.0 OUTPUT
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Example:b=imadjust(H, [.3 .7],[.1 .9],1)
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INPUT
1.0 OUTPUT
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Example:b=imadjust(H, [.3 .7],[.1 .9],1)
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INPUT
Example, continued
H = [.5 .5 .6 .7 .8 .2; .6 .3 .8 .9 .2 .4 ]
H=
0.5000 0.5000 0.6000 0.7000 0.8000 0.2000
0.6000 0.3000 0.8000 0.9000 0.2000 0.4000
b=imadjust(H, [.3 .7],[.1 .9],1)
b=
0.5000 0.5000 0.7000 0.9000 0.9000 0.1000
0.7000 0.1000 0.9000 0.9000 0.1000 0.3000
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Logarithmic Transformation
• g = log(f ), where f is the input image
– Issue: log(0) = -Inf
– Any zeros in the input will be mapped to -Inf
– Note: log(1) = 0
• g = log(1+f )
– This ensures that log(f ) is never mapped to -Inf
– Similar to gamma transformation
– Commonly used for dynamic range compression
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Contrast Stretching Transformation
• Creates an image with higher contrast than the input
image:
1
s  T (r ) 
m
1  ( )E
r
– r: intensities of input;
– s: intensities of output;
– m: threshold point (see graph) ;
– E: controls slope.
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Chapter 3
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E controls the slope of the function
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>> I = imread('mammogram.tif');
>> figure, subplot(2,2,1), imshow(I), title('I')
>> E= 1;
>> g = 1./(1+(m./(double(I)+eps)).^E);
>> subplot(2,2,2), imshow(g),title('E=1')
>> E= 3;
>> g = 1./(1+(m./(double(I)+eps)).^E);
>> subplot(2,2,3), imshow(g),title('E=3')
>> E= 5;
>> g = 1./(1+(m./(double(I)+eps)).^E);
>> subplot(2,2,4), imshow(g),title('E=5')
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1
s  T (r ) 
m E
1 ( )
r
Output(s)
Input(r)
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Chapter 3
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Input
Output
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Gray Image
>> I = imread('Flags.jpg');
>> figure, imshow(I) % uint8
>> Im = im2double(I); % convert to double
>> Igray = (Im(:,:,1)+Im(:,:,2)+Im(:,:,3))/3;
>> figure, imshow(Igray)
There is also the rgb2gray function that results
in a slightly different image
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rgb2gray
help rgb2gray
rgb2gray Convert RGB image or colormap to grayscale.
rgb2gray converts RGB images to grayscale by eliminating the
hue and saturation information while retaining the
luminance.
I = rgb2gray(RGB) converts the truecolor image RGB to the
grayscale intensity image I.
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