Chapter 3 Introduction to Digital Image Analysis

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Chapter 3Introduction to Digital Image Analysis
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Introduction

• Image Analysis
• Manipulation of image data to determine exactly
  what information is required to develop a
  computer imaging system
• Data reduction process
• Part of a larger process
• Iterative in nature
• Answers application specific questions

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• System Model
• Image analysis can be broken into three primary
  stages as
• Preprocessing
• Data Reduction
• Feature Analysis

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• Data reduction involves reducing the data in the
  spatial domain or frequency domain

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• Application feedback loop is a key aspect which
  provides application-specific review of the
  analysis results

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Preprocessing

• To make data reduction and analysis task easier
• Consist of following operations
• Noise and artifact removal
• Extracting Region of Interest (ROI)
• Performing mathematical operations
• Enhancement of specific image features
• Data reduction in resolution and brightness

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Image with border
Image with border removed
Shape information required
Image with object shape
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• Region of Interest Image Geometry
• To investigate more closely a specific area of an
  image
• Consists of following operations
• Crop
• Zoom
• Enlarge
• Shrink
• Translate
• Rotate

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• Crop Selecting a portion of an image, a
  sub-image, and cutting it away from the rest of
  the image , for example border removal
• Zoom
• Enlarging a section of an image, to improve
  visual analysis of detailed objects
• Can be done by zero hold order (repeating
  previous pixel values) or first order hold
  (linear interpolation of adjacent pixels)

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• Zero order hold Can also be performed by
  convolution in the following way
• a. Extend the image by adding rows and columns
  of zeroes between existing rows and columns
• b. Perform convolution by using the following
  convolution mask

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• First order hold
• Can be performed in two ways
• 1. Averaging
• 2. Convolution
• 1. Averaging Allows to enlarge an NN sized
  image to a size of (2N-1) (2N-1), and can be
  repeated

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Original image array
Image with rows expanded
Image with rows and columns expanded
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• 2. Convolution Consists of 2 steps
• a. Extend the image by adding rows and columns
  of zeroes between existing rows and columns

Image extended with zeroes
Original image array
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• b. Convolution Consist of following process
• Overlay the mask on the image
• Multiply the coincident terms
• Sum all the results
• Move to the next pixel, across the entire image

Convolution mask for first order hold
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• The convolution equation is given by
• where
• M (x,y) is the convolution mask, and
• I (r,c) is the image

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• Shrink Helps to reduce the amount of data that
  needs to be processed
• Translation and Rotation
• Performed for application specific reasons like
  template matching in pattern recognition process
• Makes certain image details easier to see

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• Translation process can be done with following
  equations
• Rotation process can be done with following
  equations

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• Translation and rotation can be combined in one
  set of equations as
• where

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• Arithmetic and Logic Operations
• Performed on pixel by pixel basis
• Arithmetic operations include addition,
  subtraction, multiplication and division
• Logic operations include AND, OR, and NOT, and
  are performed in a bit-wise manner

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• Arithmetic operations are performed on a pixel by
  pixel basis

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• Addition
• Combines information in two images
• Applications include
• 1. Creating models for restoration algorithm
  development
• 2. Image sharpening algorithms
• 3. Special effects such as image morphing time
  based operation in which a proportionally
  increasing amount of second image is added to the
  first image

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Second Original
Addition of images
First Original
Original image
Gaussian noise, variance 400, mean 0
Addition of images
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• Subtraction
• Used for motion detection and background
• subtraction
• Applications include
• 1. Object tracking
• 2. Medical imaging
• 3. Law enforcement
• 4. Military applications

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b. Same scene later
a. Original scene
Subtraction of scene a from scene b
Subtracted image with threshold of 100
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• Multiplication and Division
• To adjust the brightness of an image
• Applications include
• 1. To combine two images for special
• effects
• 2. For image filtering in spectral domain
• 3. To model multiplicative noise process

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Image Multiplication
Multiplication of two images
Cameraman image
X-ray image of hand
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Image Division
Original image
Image divided by valuelt1
Image divided by valuegt1
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• Logic operations are performed on a pixel by
  pixel basis, and in a bit-wise manner

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• Logic operations
• AND, OR and NOT form a complete set of logic
  operators
• AND and OR are used
• 1. To combine information in two images
• 2. For image masking operation
• 3. For extracting Region of Interest
• NOT operation creates a negative of the original
  image

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Image Masking
a. Original image
b. Image mask (AND)
c. ANDing a and b
d. Image mask (OR)
e. ORing a and d
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NOT operation
Original image
Image after NOT operation
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• Spatial Filters
• Operate on raw image data in the (r,c)
• space, by considering small neighborhoods, 3x3,
  5x5, 7x7, and moving sequentially across and down
  the image
• Returns a result based on a linear or nonlinear
  operation
• Consists of three types of filters
• Mean filters
• Median filters
• Enhancement filters

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• Many spatial filters are linear filters
  implemented with a convolution mask
• the result is a weighted sum of a pixel and its
  neighbors
• Mask coefficients tend to effect the image in
  the following general ways
• Coefficients are positive blurs the image
• Coefficients are alternating positive and
  negative sharpens the image
• Coefficients sum to 1 brightness retained
• Coefficients sum to 0 dark image

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• Mean filters
• Averaging filters
• Tend to blur the image
• Adds a softer look to the image
• Example 3x3 convolution mask

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Mean filter
Mean filtered image
Original image
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• Median filters
• Nonlinear filter
• Sorts the pixel values in a small neighborhood
  and replaces the center pixel with the middle
  value in the sorted list
• Output image needs to be written to a separate
  image (a buffer), so that results are not
  corrupted
• Neighborhood can be of any size but 3x3, 5x5 and
  7x7 are typical

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Median filter
Original image with salt and pepper noise
Median filtered image (3x3)
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• Enhancement filters
• Implemented with convolution masks having
  alternating positive and negative coefficients
• Enhance the image by sharpening
• Two types considered here
• Laplacian-type filters
• Difference filters

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• 1. Laplacian-type filters
• Are rotationally invariant, that is they enhance
  the details in all directions equally
• Example convolution masks of Laplacian-type
  filters are

Filter 2
Filter 3
Filter 1
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Laplacian filter
Contrast enhanced version of Laplacian filtered
image
Laplacian filtered image
Original image
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• 2. Difference filters
• Also called as emboss filters
• Enhances the details in the direction specific to
  the mask selected
• Four primary difference filter convolution masks,
  corresponding to the edges in the vertical,
  horizontal, and two diagonal directions are

Diagonal 2
Horizontal
Diagonal 1
Vertical
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Difference filter
Original image
Difference filtered image
Difference filtered image added to the original
image, with contrast enhanced
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• Image Quantization
• Process of reducing the image data by removing
  some of the detail information by mapping groups
  of data points to a single point
• Performed on spatial coordinates, (r,c), for
  spatial reduction or pixel values, I(r,c,)
• for gray level reduction

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• Gray level reduction
• Reducing the number of gray levels, typically
  from 256 levels for 8-bit per pixel data to fewer
  than 8 bits
• Can be performed by
• Thresholding
• AND or OR masks

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• Thresholding
• 1. Performed by setting a threshold value
• and setting all pixels above it to 1 and
  those below it to 0
• 2. Output is a binary image
• 3. Useful in extracting object features
• such as shape, area, or perimeter

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• False Contouring
• Artificial edges or lines that appear in images
  with reduced number of gray levels
• Can be improved by using an Improved Gray Scale
  (IGS) quantization method
• IGS quantization method improves the results of
  gray level reduction by adding a random number to
  each pixel value before the quantization

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False Contouring
Original 8-bit image, 256 gray levels
Quantized to 6 bits , 64 gray levels
Quantized to 3 bits , 8 gray levels
Quantized to 1 bits , 2 gray levels
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IGS quantization
Original image
IGS quantization to 8 levels (3 bits)
Uniform quantization to 8 levels (3 bits)
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• Halftoning/Dithering
• Reduces the number of gray levels by creating dot
  patterns or dither patterns to represent various
  gray levels
• Based on the idea of diffusing the quantization
  error across edges, where changes occur in the
  image
• Reduces effective spatial resolution
• Typically used for printing purposes

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• Halftoning and Dithering

Original image
Floyd-Steinberg error diffusion, 1 bpp
Bayers ordered dither, 1 bpp
45-degree clustered-dot dither, 1 bpp
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• Uniform bin width quantization The size of the
  bins for the quantization is equal
• Variable bin width quantization Unequal bin
  size, based on an application specific basis

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Variable bin-width quantization
After variable bin-width quantization
Original image
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• Spatial Quantization
• Reducing the image size by taking groups of
  spatially adjacent pixels and mapping them to one
  pixel
• May produce simple forms of geometric distortion
• Can be performed in following ways
• Averaging
• Median
• Decimation

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Spatial Quantization Methods

• Averaging Groups of pixels are averaged and the
  group is replaced by the average
• Median Pixel gray values are sorted in small
  neighborhood and the neighborhood is replaced by
  the middle value
• Decimation Known as sub-sampling, reduces the
  image size by eliminating rows and columns

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Spatial Reduction
Averaging (64128)
Median (64128)
Original 512512 image
Decimation (64128)
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• Anti-aliasing filtering Process of improving the
  image quality when applying the decimation
  technique, by preprocessing the image with
  averaging (mean) spatial filter

Result of spatial reduction of 512x512 to
128x128 via decimation
Result of spatial reduction of 512x512 to
128x128 via decimation, preprocessed by a 5x5
averaging filter