Chapter 2: Image Analysis

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Chapter 2 Image Analysis

• Introduction and Preprocessing

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Overview

• Image analysis involves manipulating image data
  to provide the info necessary to solve a computer
  imaging problem.
• It is primarily a data reduction process.
• Extract only the necessary information.
• Used in both computer vision and image processing.

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Overview

• For computer vision, the end product is typically
  the extraction of high-level information.
• Shape parameters, color and texture features.
• For image processing, it is used to help
  determine the type of processing required and the
  parameters needed.
• Degradation function, enhancement algorithm, and
  determining visually important information.

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System Model
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System Model

• Preprocessing is used to remove noise and
  eliminate irrelevant, visually unnecessary
  information.
• This process may involve
• Gray-level or spatial quantization (reduction of
  number of bits per pixel or image size).
• Finding regions of interest for further
  processing.

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System Model

• Data reduction involves either reducing the data
  in spatial domain, or transforming it into
  another domain (the frequency domain).
• Then the data needed for the analysis process is
  extracted.
• Finally, the extracted features are examined and
  evaluated for their use in the application.

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System Model
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System Model
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Preprocessing

• The objective is to make the data reduction and
  analysis task easier.
• The requirements are typically obvious and
  simple. For example
• Noise removal.
• Eliminate borders from images digitized from
  film.
• Mask out rulers in skin tumor slides.
• Convert gray-level image to binary.

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Preprocessing

• Among the preprocessing operations are
• Extracting region of interest.
• Performing basic algebraic operations on images.
• Enhancing specific image features.
• Reducing data in both resolution and brightness.

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Region-of-Interest Image Geometry

• Often, for image analysis, we want to investigate
  more closely a specific area within an image.
• Region of Interest (ROI).
• This requires operations that modify the spatial
  coordinates of the image.
• Image geometry operations.

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Region-of-Interest Image Geometry

• Examples of image geometry operations
• Crop, zoom, enlarge, shrink, translate, rotate.
• Crop is the process of selecting a small portion
  of the image, and cutting it away from the rest
  of the image.
• After we have crop the image, we can zoom in on
  it by enlarging it.

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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry

• The zoom process can be done in numerous ways,
  but typically zero-order or first-order hold is
  used.
• Zero-order Repeating the previous pixel values,
  thus creating a blocky effect.
• First-order Perform linear interpolation
  (averaging) between two pixels.
• These methods allow us to enlarge an NxN size
  image to a size of (2N-1)x(2N-1).

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Example of First-order Hold
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Region-of-Interest Image Geometry

• Another method that can achieve the same result
  (first-order hold) is a mathematical process
  called convolution.
• The process has two steps
• Extend the image by adding rows and columns of
  zeros between the existing rows and columns.
• Perform convolution.

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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry

• Convolution is done using a convolution mask.

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Region-of-Interest Image Geometry

• The convolution process requires us to overlay
  the mask on the image, multiply the coincident
  values, and sum all these results.
• The result is used to substitute the pixel value
  that coincide with the center of the mask.
• The process is repeated for every pixels in the
  image (except the outer ones).

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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry

• Why use convolution instead of basic-averaging-of-
  neighbors method?
• Many computer imaging board can perform
  calculation in hardware.
• Convolution can be done very fast in hardware.
• Zero-order hold can also be performed using
  convolution. But a different mask is used.

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Region-of-Interest Image Geometry

• Since there is no center pixel, the result need
  to be put in the pixel location corresponding to
  the lower-right corner.

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Region-of-Interest Image Geometry

• To enlarge by a factor of K (rather than of
  2N-1)
• Subtract the two adjacent values.
• Divide the result by K.
• Add the result to the smaller value, and keep
  adding the result from the second step in a
  running total until all (K-1) intermediate pixel
  locations are filled.
• This is done for every pair of adjacent pixels.

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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry

• Translation is the process of moving an ROI from
  one position to another.
• Rotation is the process of rotating an ROI for a
  number of degrees.
• These two operations can be performed by applying
  equations.

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Region-of-Interest Image Geometry

• The equations for translation are given as
  follows
• r and c are the new coordinates.
• r and c are the original coordinates.
• r0 and c0 are the distances to move or translate
  the image.

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Region-of-Interest Image Geometry

• The equations for rotation are given as follows
• r and c are the new coordinates.
• r and c are the original coordinates.
• ? is the angle of rotation of the image, defined
  in a clockwise direction from the horizontal axis
  at the image origin in the upper left corner.

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Region-of-Interest Image Geometry

• The translation and rotation process can be
  combined into one set of equations.

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Region-of-Interest Image Geometry

• After translation, there might be a leftover
  space. What to do with it?
• There are two options
• Fill with constant values, either black (0) or
  white (255).
• Wrap around.

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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry

• After rotation, some part of the image might be
  rotated off the screen (the image plane).
• How can we view the full, rotated image?
  Solution
• Translate the image back to the center.
• Enlarge the image plane.

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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry
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Region-of-Interest Image Geometry
Example of enlarged image plane
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Image Algebra

• There are two categories of algebraic operations
  that can be applied to images.
• Arithmetic operations
• Addition, subtraction, division and
  multiplication.
• Logic operations
• AND, OR, NOT

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Image Algebra

• Addition is used to combine information in two
  images.
• Subtraction is used to detect motion.
• Multiplication and division are used to adjust
  brightness of an image.
• AND and OR are used to perform a masking
  operation (an easy way to extract an ROI).
• NOT creates a negative of original image.

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Image Algebra - Addition
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Image Algebra - Addition


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Image Algebra - Addition


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Image Algebra - Subtraction

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Image Algebra - Subtraction
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Image Algebra Multiplication
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Image Algebra Division
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Image Algebra - AND

• Logic operations operate in bit-wise fashion on
  pixel data.

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Image Algebra - AND
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Image Algebra - OR
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Image Algebra - NOT
Original image
Result of NOT operation
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Spatial Filters

• Done for noise removal or image enhancement.
• Three types of filters will be discussed
• Mean filters.
• Median filters.
• Enhancement filters.

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Spatial Filters

• Mean and median filters are primarily used to
  conceal or remove noise.
• They can also be used for special applications.
• For example, mean filter adds softer look to an
  image.
• The enhancement filters highlight edges and
  details within an image.

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Spatial Filters
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Spatial Filters
Enhancement Filter
Original image
Image after enhancement filter is applied
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Spatial Filters

• Many filters are implemented with convolution
  masks.
• Since the result is a weighted sum of the values
  of pixel of its neighbors, it is called a linear
  filter.
• The overall effect on the image can be predicted
  based on the general pattern of the convolution
  mask.

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Spatial Filters

• If the coefficients of the mask sum to one,
  average brightness is retained.
• If the coefficients of the mask sum to zero, the
  average brightness will be lost and will return a
  dark image.
• If the coefficients are alternating positive and
  negative, filtering will return edge information.
• If the coefficients are all positive, the image
  will be blurred.

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Spatial Filters

• Mean filters are averaging filters.
• They replace the center pixel with the average of
  neighboring pixels.
• The 3x3 mean filter convolution mask

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Spatial Filters

• The result of applying this filter can be
  guessed
• Coefficients sum to one, therefore the image
  brightness is retained.
• The coefficients are all positive, therefore it
  will blur the image.

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Spatial Filters

• Median filter replaces the center pixel value
  with the median value present among its
  neighbors.
• Median filter is a non-linear filter
• The result cannot be found by a weighted sum of
  the neighborhood pixels
• It can use a neighborhood of any size, but 3x3,
  5x5 and 7x7 are typical.

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Spatial Filters
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Spatial Filters
Median Filter
Original Image
Median-filtered Image
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Spatial Filters

• Enhancement filters will tend to bring out or
  enhance details in the image.
• We will discuss two types of enhancement filters
• Laplacian filters
• Difference filters

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Spatial Filters

• Two 3x3 convolution masks for laplacian filters
  are

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Spatial Filters

• Laplacian filters will enhance detail in all
  directions equally.
• The difference filters will enhance details in
  the direction specific to the mask selected.
• There are four difference filter convolution
  masks, corresponding to lines in the vertical,
  horizontal, and two diagonal directions.

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Spatial Filters
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Spatial Filters
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Spatial Filters
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Spatial Filters
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Spatial Filters
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Spatial Filters
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Image Quantization

• Process of reducing image data by removing some
  of the detail information by mapping groups of
  data to a single point.
• There are two types gray-level reduction and
  spatial reduction.
• Gray-level reduction
• Reduce the precision of pixel values.
• Map groups of values into one.

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Image Quantization

• Spatial reduction
• Reduce number of pixels.
• Map a group of pixels into one pixels.
• The simplest method of gray-level reduction is
  thresholding.
• Any pixel above the threshold is set to 1, and
  the rest to 0.
• This turns a gray-level image into binary image.

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Image Quantization

• A more versatile method of gray-level reduction
  is by reducing the number of bits per pixel.
• This can be done by masking the lower bits via an
  AND operation.
• The number of bits that are masked determines the
  number of gray-levels available.

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Image Quantization
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Image Quantization

• The general rule goes like this. If we want to
  reduce 256 gray levels to n gray levels
• Find k such that 256/2k n.
• Mask the lower k bits.
• We can reduce the number of gray-levels to any
  power of 2 2, 4, 8, 16, 32, 64, or 128.
• As the number of gray-level decreases, contouring
  increases.

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Image Quantization
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Image Quantization
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Image Quantization

• Contouring effect can be visually improved by
  using IGS (Improved gray-scale) quantization
  method.
• It takes advantage of human visual systems
  sensitivity to edge by adding small random number
  to each pixel before quantization.
• Results in a more visually pleasing appearance.

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Image Quantization
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Image Quantization

• The AND-based method maps the quantized
  gray-level values to the low end of each range.
• Alternatively, we can map the quantized
  gray-level values to the high end of the range
  using an OR operation.

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Image Quantization
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Image Quantization

• The quantized values can also be mapped to the
  mid-point of the range.
• This is done by an AND after an OR operation, or
  an OR after an AND operation.

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Image Quantization

• Although AND/OR method is very efficient, it is
  not very flexible since the size of the
  quantization bin is not variable.
• There are also gray-level quantization methods
  that allow for variable bin sizes.
• These methods are more complicated and the
  variable bin size is application dependent.

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Image Quantization
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Image Quantization

• Quantization in spatial coordinates results in
  reducing the size of the image.
• This is accomplished by taking groups of pixels
  that are spatially adjacent and mapping them to
  one pixel.

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Image Quantization

• This can be done in one of three ways
• Averaging Find the average of the pixels
  (highest visual quality).
• Median Sort the pixels from lowest to highest
  and find the median.
• Decimation Simply choose one of the pixel
  (lowest visual quality).

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Image Quantization

• The quality of a decimation quantization image
  can be improved by preprocessing the image with
  an averaging, or mean spatial filter.
• This type of filtering is called anti-aliasing
  filtering.