Post on 02-May-2017
Roger S. Gaborski 1
Introduction to Computer Vision
Lecture 4Dr. Roger S. Gaborski
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HW#2 Due 02/13
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In Class Exercise Review1. Given the following MATLAB code:>> image1 = rand([3])image1 = 0.9500 0.6555 0.0318 0.7431 0.1712 0.2769 0.3922 0.7060 0.0462 >> image2 = imadjust(image1, [ .1,.75],[.2, .6]) Carefully draw the transformation map specified by the imadjust statement. Label the x and y axis.
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Brighter Output (gamma<1) Darker Output (gamma>1)
Gamma specifies the shape of the curve
Characteristics:• gamma >1 : all pixels become darker• gamma <1 : all pixels become brighter• gamma =1 : linear transform
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image1 =
0.9500 0.6555 0.0318 0.7431 0.1712 0.2769 0.3922 0.7060 0.0462 >> image2 = imadjust(image1, [ .1,.75],[.2, .6])
image2 =
0.6000 0.5418 0.2000 0.5958 0.2438 0.3089 0.3798 0.5729 0.2000
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Example0
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0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0INPUT
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image2 = imadjust(image1, [ .1,.75],[.2, .6],1)0
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image2 = imadjust(image1, [ .1,.75],[.2, .6],1)0
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Gray Scale Ramp Image
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Minimum gray value = .01Maximum gray value = 1.0
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Ramp Image
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image_ramp = zeros(100); for i = 1:100 image_ramp(:,i) = i*.01;end fprintf('minimum gray value = %d, \n', min(image_ramp(:)));fprintf('maximun gray value = %d, \n', max(image_ramp(:)));figure, plot(image_ramp(50,:)), xlabel('pixel position'), ylabel('pixel value') title('values')pause
figure, imshow(image_ramp),title('ramp intensity image')pause
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Map .01 to .5 and 1.0 to .75
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disp('Use imadjust to map to .50 to .75');
image1 = imadjust(image_ramp,[.01, 1.0],[.5, 0.75]); %map to .5 to .75
fprintf('minimum gray value = %d, \n', min(image1(:)));fprintf('maximun gray value = %d, \n', max(image1(:)));
figure, plot(image1(50,:)), xlabel('pixel position'), ylabel('pixel value') title('values')axis([0,100,0,1])Grid
pause figure, imshow(image1, [0,1]);
pause
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Map .01 to .5 and 1.0 to .75
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Map values in range <=.25 to .35 and >=.50 to .65');
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Map values in range <=.25 to .35 and >=.50 to .65');
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disp('Use imadjust to map values in range <=.25 to .35 and >=.50 to .65');image2 = imadjust(image_ramp,[.25, .50],[.35, 0.65]);fprintf('minimum gray value = %d, \n', min(image2(:)));fprintf('maximun gray value = %d, \n', max(image2(:)));figure, plot(image2(50,:)), xlabel('pixel position'), ylabel('pixel value') title('values')axis([0,100,0,1])grid pause figure, imshow(image2, [0,1]);
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Map values in range <=.25 to .35 and >=.50 to .65');
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Contrast Stretching Transformation• Creates an image with higher contrast than the input
image:
– r: intensities of input; – s: intensities of output;– m: threshold point (see graph) ; – E: controls slope.
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1( )1 ( )E
s T r mr
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E controls the slope of the function
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1( )1 ( )E
s T r mr
Input(r)
Output(s)
Introduction to Computer Vision
Lecture 4Dr. Roger S. Gaborski
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An image shows the spatialdistribution of gray level values
We can summary this informationby only retaining the distributionif gray level values:
value count
1 0
40 8
…
…
104 32
181 45
255 0
PARTIAL IMAGE INFO:
Intensity image is simplya matrix of numbers
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Image Histogram
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Plot of Pixel Count as a Function of Gray Level Value
20 40 60 80 100 120 140 160 180 200 2200
0.5
1
1.5
2
2.5
3
Gray Level Value
Pixel Count
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Histogram
• Histogram consists of– Peaks: high concentration of gray level values– Valleys: low concentration– Flat regions
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Formally, Image Histograms
Histogram:• Digital image• L possible intensity levels in range [0,G]• Defined: h(rk) = nk
– Where rk is the kth intensity level in the interval [0,G] and nk is the number of pixels in the image whose level is rk .
– G: uint8 255 uint16 65535
double 1.0
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Notation
• L levels in range [0, G]• For example:• 0, 1, 2, 3, 4, in this case G = 4, L = 5
– Since we cannot have an index of zero,• In this example, index of:
Index 1 maps to gray level 02 maps to 13 maps to 24 maps to 35 maps to 4
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Normalized Histogram
• Normalized histogram is obtained by dividing elements of h(rk) by the total number of pixels in the image (n):
for k = 1, 2,…, L
p(rk) is an estimate of the probability of occurrence of intensity level rk
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( )( ) ,k kk
h r np rn n
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MATLAB Histogram
• h = imhist( f, b )– h is the histogram, h(rk) – f is the input image– b is the number of bins (default is 256)
• Normalized histogram
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( , )( )
imhist f bpnumel f
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Color and Gray Scale Images
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Background: Gray Image
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>> 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 resultsin a slightly different image
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Gray Scale Histogram
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Plots
• bar(horz, v, width)– v is row vector
• points to be plotted– horz is a vector same dimension as v
• increments of horizontal scale• omitted axis divided in units 0 to length(v)
– width number in [0 1]• 1 bars touch• 0 vertical lines• 0.8 default
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p= imhist(Igray)/numel(Igray);>> h1 = p(1:10:256);>> horz = (1:10:256);>> figure, bar(horz,h1)
Review other examplesin text and in MATLABdocumentation
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Color and Gray Scale ImagesRecall from Previous Slide
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Gray Scale Histogram
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Normalized Gray Scale Histogram
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>> p= imhist(Igray)/numel(Igray);>> figure, plot(p)
Normalized Gray Scale Histogram
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imhist(Igray)/numel(Igray); imhist(Igray,32)/numel(Igray)
256 bins 32 bins
Normalized Gray Scale Histogram
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>> p= imhist(Igray)/numel(Igray);>> figure, plot(p)
Gray level values
prob
abili
ty
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0 50 100 150 200 250 3000
0.005
0.01
0.015
0.02
0.025
0.03
0 50 100 150 200 250 3000
0.01
0.02
0.03
0.04
0.05
0.06
0 50 100 150 200 250 3000
0.01
0.02
0.03
0.04
0.05
0.06
Original Dark Light
Contract enhancement
• How could we transform the pixel values of an image so that they occupy the whole range of values between 0 and 255?
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Gray Scale Transformation
• How could we transform the pixel values of an image so that they occupy the whole range of values between 0 and 255?
• If they were uniformly distributed between 0 and x we could multiply all the gray level values by 255/x
• BUT – what if they are not uniformly distributed??
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Cumulative Distribution Function
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Histogram CDF
Histogram Equalization(HE)
• HE generates an image with equally likely intensity values• Transformation function: Cumulative Distribution
Function (CDF)• The intensity values in the output image cover the full
range, [0 1]• The resulting image has higher dynamic range• The values in the normalized histogram are approximately
the probability of occurrence of those values
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Histogram Equalization• Let pr(rj), j = 1, 2, … , L denote the histogram associated with
intensity levels of a given image
• Values in normalized histogram are approximately equal to the probability of occurrence of each intensity level in image
• Equalization transformation is:
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k = 1,2,…,Lsk is intensity valueof output rk is input value
Sum of probability up to k value
1 1
( ) ( )k k
jk k r j
j j
ns T r p r
n
Histogram Equalization Example
• g = histeq(f, nlev) where f is the original image and nlev number of intensity levels in output image
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Original ImageINPUT
Transformation
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Input Gray Level Value
x255
Out
put G
ray
Leve
l Val
ue
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OUTPUT
Equalization of Original Image
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histogram Equalization of Light Image
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histogram Equalization of Dark Image
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Simple Histogram Equalization Example
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Histogram Equalization
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Input Image Output Image
Adaptive Equalization
• g = adapthisteq(f, parameters..)• Contrast-limited adaptive histogram equalization• Process small regions of the image (tiles) individually• Can limit contrast in uniform areas to avoid noise
amplification
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>> help adapthisteq adapthisteq Contrast-limited Adaptive Histogram Equalization (CLAHE). adapthisteq enhances the contrast of images by transforming the values in the intensity image I. Unlike HISTEQ, it operates on small data regions (tiles), rather than the entire image. Each tile's contrast is enhanced, so that the histogram of the output region approximately matches the specified histogram. The neighboring tiles are then combined using bilinear interpolation in order to eliminate artificially induced boundaries. The contrast, especially in homogeneous areas, can be limited in order to avoid amplifying the noise which might be present in the image.
J = adapthisteq(I) Performs CLAHE on the intensity image I. J = adapthisteq(I,PARAM1,VAL1,PARAM2,VAL2...) sets various parameters. Parameter names can be abbreviated, and case does not matter. Each string parameter is followed by a value as indicated below: 'NumTiles' Two-element vector of positive integers: [M N]. [M N] specifies the number of tile rows and columns. Both M and N must be at least 2. The total number of image tiles is equal to M*N. Default: [8 8].
Adaptive Histogram Equalization
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Grayscale Adaptive Histogram EqualizedGrayscale Histogram Equalized
Default, 8x8 tiles
Adaptive Equalization
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Grayscale Adaptive Histogram Equalized
Number of Tiles: 24x24
Grayscale Adaptive Histogram Equalized
Number of Tiles: 24x24, ClipLimit = .05
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Create a ‘color image’
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>> red = rand(5)
red =
0.0294 0.0193 0.3662 0.7202 0.0302 0.7845 0.3955 0.2206 0.4711 0.2949 0.7529 0.1159 0.6078 0.9778 0.5959 0.1586 0.1674 0.5524 0.9295 0.1066 0.7643 0.6908 0.3261 0.5889 0.1359
>> green = rand(5)
green =
0.2269 0.5605 0.6191 0.0493 0.1666 0.0706 0.4051 0.3297 0.7513 0.6484 0.9421 0.0034 0.8243 0.7023 0.8097 0.8079 0.5757 0.6696 0.9658 0.8976 0.0143 0.3176 0.6564 0.1361 0.0754
>> blue = rand(5)
blue =
0.6518 0.0803 0.8697 0.6260 0.9642 0.5554 0.2037 0.8774 0.5705 0.6043 0.8113 0.8481 0.5199 0.0962 0.8689 0.5952 0.2817 0.6278 0.7716 0.8588 0.5810 0.9290 0.2000 0.1248 0.7606
First create three color planes of data
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>> colorIm(:,:,1)=red;>> colorIm(:,:,2)=green;>> colorIm(:,:,3)=blue;>> colorIm
figure imshow(colorIm, 'InitialMagnification', 'fit')
colorIm(:,:,1) =
0.0294 0.0193 0.3662 0.7202 0.0302 0.7845 0.3955 0.2206 0.4711 0.2949 0.7529 0.1159 0.6078 0.9778 0.5959 0.1586 0.1674 0.5524 0.9295 0.1066 0.7643 0.6908 0.3261 0.5889 0.1359
colorIm(:,:,2) =
0.2269 0.5605 0.6191 0.0493 0.1666 0.0706 0.4051 0.3297 0.7513 0.6484 0.9421 0.0034 0.8243 0.7023 0.8097 0.8079 0.5757 0.6696 0.9658 0.8976 0.0143 0.3176 0.6564 0.1361 0.0754
colorIm(:,:,3) =
0.6518 0.0803 0.8697 0.6260 0.9642 0.5554 0.2037 0.8774 0.5705 0.6043 0.8113 0.8481 0.5199 0.0962 0.8689 0.5952 0.2817 0.6278 0.7716 0.8588 0.5810 0.9290 0.2000 0.1248 0.7606
colorIm
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colorIm(1,1,: )
colorIm(4,4,: )
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colorIm(:,:,1) =
0.0294 0.0193 0.3662 0.7202 0.0302 0.7845 0.3955 0.2206 0.4711 0.2949 0.7529 0.1159 0.6078 0.9778 0.5959 0.1586 0.1674 0.5524 0.9295 0.1066 0.7643 0.6908 0.3261 0.5889 0.1359
colorIm(:,:,2) =
0.2269 0.5605 0.6191 0.0493 0.1666 0.0706 0.4051 0.3297 0.7513 0.6484 0.9421 0.0034 0.8243 0.7023 0.8097 0.8079 0.5757 0.6696 0.9658 0.8976 0.0143 0.3176 0.6564 0.1361 0.0754
colorIm(:,:,3) =
0.6518 0.0803 0.8697 0.6260 0.9642 0.5554 0.2037 0.8774 0.5705 0.6043 0.8113 0.8481 0.5199 0.0962 0.8689 0.5952 0.2817 0.6278 0.7716 0.8588 0.5810 0.9290 0.2000 0.1248 0.7606
• What are two methods to convert from a color image to a gray scale image?
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RECALL
• What are two methods to convert from a color image to a gray scale image?– Average red, green and blue pixels
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Average
• For example:
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>> colorImAverage = ( colorIm(:,:,1) + colorIm(:,:,2) + colorIm(:,:,3) )/3
colorImAverage =
0.3027 0.2200 0.6183 0.4651 0.3870 0.4701 0.3348 0.4759 0.5976 0.5159 0.8354 0.3224 0.6507 0.5921 0.7582 0.5206 0.3416 0.6166 0.8890 0.6210 0.4532 0.6458 0.3942 0.2833 0.3240
>> figure, imshow(colorImAverage, 'InitialMagnification', 'fit')
Gray scale version of color image
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.5976
.5921
Color and Gray scale Images
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Color and Gray scale Images
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Conversion to gray scale results in a loss of information
• What are two methods to convert from a color image to a gray scale image?– Average red, green and blue pixels– Matlab’s rgb2gray function
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MATLAB’s rgb2gray Function
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>> colorIm_rgb2gray = rgb2gray(colorIm)
colorIm_rgb2gray =
0.2163 0.3439 0.5721 0.3156 0.2168 0.3393 0.3792 0.3596 0.6469 0.5377 0.8706 0.1333 0.7249 0.7155 0.7525 0.5895 0.4202 0.6298 0.9328 0.6567 0.3031 0.4989 0.5056 0.2702 0.1716
colorIm and rgb2gray(colorIm)
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How does rgb2gray work?
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rgb2gray converts RGB values to grayscale values by forming a weighted sum of the R, G, and B components:
Gray = 0.2989 * R + 0.5870 * G + 0.1140 * B
Color and Gray Scale Images
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