Chapter 2: Digital Image Fundamentals

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Images and MATLAB
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Matlab Advantages

• Every variable in Matlab is a multidimensional
  matrix.
• Highly modular.
• No memory allocation is necessary.
• Matlab enables its own garbage collection.
• Simple interface for complex mathematical
  concepts.

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Image Types

• Intensity imagesscaled to represent intensities
  (uint8 0,255, double 0,1)
• Binary imageslogical array of 0s and 1s
• Indexed imagesLook up table x, map
• RGB imagestruecolor, array of (mn3)

Checking the image type isind, isbw, isgray,
isrgbConverting image types rgb2ind, rgb2gray,
gray2ind, ind2gray,.
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Data Classes
Converting between types B data_class_name(A)
for example B double(A)
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Conversions

• When converting between data classes and types it
  is important to keep the value range for each
  data class
• gtgt img double(img)/255
• gtgt img im2double(img)

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MATLAB supported image formats

• JPEG Joint Photographics Experts Group
• TIFF Tagged Image File Format
• GIF Graphics Interchange Format
• BMP Microsoft Bitmap Format
• PNG Portable Network Graphics

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Displaying an image(cont.)

• Spatial domain

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Matlab Basics

• Digital image representation 2D function
  f(x,y) -gt finite discrete quantities
• Coordinate Conventions
• img(r,c)r rows (height)c cols (width)
• The first pixelimg(1,1)

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Matlab ????

• C\MATLAB7\toolbox\images\imdemos
• ??Matlab Help?????????
• ???????????????,?????
• ???????????

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Different Image Types

• Indexed images
• Intensity (grayscale) images
• Binary images
• RGB (true-color) images

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Reading an image

• imread()
• ??????????array????
• ??I,map imread(filename)
• I imread(filename)
• ex I imread('pout.tif')
• I????????
• ?????,??ans

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Displaying an image

• imshow()
• ????????????
• ?? imshow(I)
• imshow(I,map)
• Figure, imshow()
• ?????????????
• ?? figure,imshow(I)

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Displaying an image(cont.)

• imshow(I, low, high)
• imshow(I, )
• ??displays I as a grayscale intensity image,
  specifying the data range for I. The minimum
  value in I is displayed as black, and the maximum
  value is displayed as white.
• pixval
• ??cursor on image to show pixel values
• ?? imshow(I),pixval

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Displaying an image(cont.)

• colorbar
• ??To display an image with a colorbar that
  indicates the range of intensity values.
• ?? imshow(I), colorbar
• ex
• I imread('pout.tif')
• imshow(I) , colorbar

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Writing an image

• imwrite()
• ??????????
• ?? imwrite(I,filename,format)
• ex
• imwrite(I,'pout.jpg','JPEG')

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Image information

• Image size size()
• ex
• I imread('saturn.png')
• size(I)
• M,N size(I)
• M??I??
• N??I??

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Image information

• whos
• ??display information about an image .
• ex whos I
• Imfinfo( filename )
• ?? display information about image file .
• ex info imfinfo('saturn.png')

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Digital Image processing

• ?????
• g im2bw(I, T)
• ??Convert intensity image I to binary image g
  using threshold T, where T must be in range 0,
  1.
• ex
• I imread('pout.tif')
• g im2bw(I, 0.4)
• imshow(g) colorbar

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Digital Image processing(cont.)

• ?????
• Rgb2gray()
• ???RBG???????gray-level???ex
• I2 imread ('onion.png')
• figure,imshow(I2) colorbar
• g2 rgb2gray(I2)
• figure,imshow(g2) colorbar

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Digital Image processing(cont.)

• ??
• imcomplement( )
• ??The negative of an image.
• ex
• I2 imread ('onion.png')
• figure,imshow(I2) colorbar
• J2 imcomplement(g2)
• figure, imshow(J2) colorbar

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Grayscale images ????

• Matlab example
• wimread('pout.tif')
• figure, imshow(w), pixval on
• figure create a window to place graphic object
• imshow display matrix
• Data type of w?
• 291x240 uint8 (unsigned integer 8 bits

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Binary image ????

• Matlab example
• w2imread('circles.png')
• figure, imshow(w2), pixval on
• Data type of w?
• 256x256 logical
• Pixel value is 0 or 1

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RGB (true color) images ????

• Matlab example
• w3imread('peppers.png')
• figure, imshow(w3), pixval on
• size(w3)
• w3(100,200,2)
• w3(100,200,13)
• w3(100,200,)

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RGB color model
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Pixel depth

• Pixel depth the number of bits used to represent
  each pixel in RGB space
• Full-color image 24-bit RGB color image
• (R, G, B) (8 bits, 8 bits, 8 bits)

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Indexed color image ??????

• Matlab example
• wIimread('trees.tif')
• figure, imshow(w), pixval on
• Whats wrong?

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Indices
Color Map
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Indexed color image

• Matlab example
• wI,wmapimread('trees.tif')
• figure, imshow(wI, wmap)
• How do we know its an indexed image?

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Indexed color image ??????

• Matlab example
• wimread(emu.tif)
• figure, imshow(w), pixval on
• Whats wrong?

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Indexed color image
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Indexed color image

• Matlab example
• w,wmapimread(emu.tif)
• imshow(w, wmap)
• How do we know its an indexed image?

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Get information about image

• imfinfo('emu.tif')

Filename 'emu.tif'
FileModDate '12-Jul-2004 114000'
FileSize 119804
Format 'tif'
FormatVersion Width
331 Height 384
BitDepth 8
ColorType 'indexed' ByteOrder
'little-endian' NewSubfileType 0
BitsPerSample 8
Colormap 256x3 double
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Get information about image

• imfinfo(emu.tif)

Filename 'emu.tif'
FileModDate '12-Jul-2004 114000'
FileSize 119804
Format 'tif'
FormatVersion Width
331 Height 384
BitDepth 8
ColorType 'indexed' ByteOrder
'little-endian' NewSubfileType 0
BitsPerSample 8
Colormap 256x3 double
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Data types and conversion

• uint8 image must be converted to double before
  any arithmetic operation
• wimread('pout.tif')
• ww1 fail
• wdouble(w) data type is also conversion
  func.
• ww1 ok

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Write image matrix to file

• Matlab code
• wimread('pout.tif')
• imwrite(w, 'pout.jpg','jpg')
• General form
• imwrite(X, map, filename, format)

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Zooming and Shrinking Digital Images

• Zooming
• Create a new pixel location.
• Assign a gray-level to those new locations
• Nearest neighbor interpolation
• Pixel replication a checkboard effect
• Bilinear interpolation using four nearest
  neighbors
• v(x, y)axbycxyd
• where a, b, c, and d are determined from the
  gray-level of the four neighbors.
• Shrinking
• Direct shrinking causes aliasing
• Expansion then Shrinking blurring the image
  before shrinking it and reduce aliasing.

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Sampling Methods of Inverse Mapping

• If transformed pixel X locates among
• P1, P2, P3 and P4
• Nearest neighbor method
• I(X) I(P3 )
• where I(p) is the intensity value of pixel p
• Bi-linear interpolation
• I(X) (1-a)(1-b)I( P1 ) a(1-b)I(P2 )
• (1-a)bI(P3 ) abI(P4 )
• where a, b are the fractional parts of X
• Bi-cubic interpolation
• based on cubic splines

P2
P1
P3
P4
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Nearest neighbor interpolation

• The closest neighbor is chosen , by rounding the
  new indexes to original images coordinates .

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Digital Image processing(cont.)

• ??????
• imresize(I,scale,method)
• ??To change the size of an image.
• interpolation Method
• -'nearest Nearest-neighbor interpolation
• -'bilinear Bilinear (the default)
• -'bicubic Bicubic interpolation

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Digital Image processing(cont.)

• ??????
• imresize(I,scale,method)
• ??To change the size of an image.
• interpolation Method
• -'nearest Nearest-neighbor interpolation
• -'bilinear Bilinear (the default)
• -'bicubic Bicubic interpolation

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Digital Image processing(cont.)

• ex
• I3 imread('circuit.tif')
• J3 imresize(I3,1.25)
• figure, imshow(I3)
• figure, imshow(J3)
• ex
• I3 imread('circuit.tif')
• J4 imresize(I3,100 150, 'bilinear')
• figure, imshow(I3)
• figure, imshow(J4)

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Digital Image processing(cont.)

• ????
• imrotate(I, angle)
• ??To rotate an image.
• ex
• I imread('pout.tif')
• J5 imrotate(I,35)
• figure, imshow(J5)

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Contents

• Histogram
• Histogram transformation
• Histogram equalization
• Contrast streching
• Applications

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Histogram
The (intensity or brightness) histogram shows how
many times a particular grey level (intensity)
appears in an image. For example, 0 - black,
255 white
0 1 1 2 4
2 1 0 0 2
5 2 0 0 4
1 1 2 4 1
histogram
image
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Histogram equalization (HE)
                               

transforms the intensity values so that the
histogram of the output image approximately
matches the flat (uniform) histogram
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Histogram equalization II.
                               
As for the discrete case the following formula
applies k 0,1,2,...,L-1 L number of grey
levels in image (e.g., 255) nj number of times
j-th grey level appears in image n total number
of pixels in the image

(L-1)
?
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Histogram equalization III
                               

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histogram

• pimread('pout.tif')
• imshow(p), figure, imhist(p), axis tight

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Histogram equalization

• phhisteq(p)
• imshow(ph), figure, imhist(ph), axis tight

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Histogram equalization (cont.)

• ph, thisteq(p)
• plot(t), title('transform function')

Exercise1. Apply histogram equalization to tire
image