Image Visualization

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Image Visualization
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Image Visualization
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Outline

• 9.1. Image Data Representation
• 9.2. Image Processing and Visualization
• 9.3. Basic Imaging Algorithms
• Contrast Enhancement
• Histogram Equalization
• Gaussian Smoothing
• Edge Detection
• 9.4. Shape Representation and Analysis
• Segmentation
• Connected Components
• Morphological Operations
• Distance Transforms
• Skeletonization

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Image Data Representation
What is an image?

• An image is a well-behaved uniform dataset.
• An image is a two-dimensional array, or matrix of
  pixels, e.g., bitmaps, pixmaps, RGB images
• A pixel is square-shaped
• A pixel has a constant value over the entire
  pixel surface
• The value is typically encoded in 8 bits integer

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Image Processing and Visualization

• Image processing follows the visualization
  pipeline, e.g., image contrast enhancement
  following the rendering operation
• Image processing may also follow every step of
  the visualization pipeline

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Image Processing and Visualization
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Image Processing and Visualization
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Basic Image Processing

• Image enhancement operation is to apply a
  transfer function on the pixel luminance values
• Transfer function is usually based on image
  histogram analysis
• High-slope function enhance image contrast
• Low-slope function attenuate the contrast.

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(Continued) Image Visualization Chap.
9 November 12, 2009
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Basic Image Processing

• The basic image processing is the contrast
  enhancement through applying a transfer function

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Image Enhancement
Linear Transfer
Non-linear Transfer
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Histogram Equalization

• All luminance values covers the same number of
  pixels
• Histogram equalization method is to compute a
  transfer function such as the resulted image has
  a near-constant histogram

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Histogram Equalization

• Histogram equalization is a technique for
  adjusting image intensities to enhance contrast.
• In general, a histogram is the estimation of the
  probability distribution of a particular type of
  data.
• An image histogram is a type of histogram which
  offers a graphical representation of the tonal
  distribution of the gray values in a digital
  image.
• By viewing the images histogram, we can analyze
  the frequency of appearance of the different gray
  levels contained in the image.

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Histogram Equalization
Original Image
After equalization
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Smoothing
How to remove noise?

• Fact Images are noisy
• Noise is anything in the image that we are not
  interested in
• Noise can be described as rapid variation of high
  amplitude
• Or regions where high-order derivatives of f have
  large values
• Smoothing is often used to reduce noise within an
  image

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Smoothing
Noise image
After filtering
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Fourier Transform

• The Fourier Transform is an important image
  processing tool which is used to decompose an
  image into its sine and cosine components.
• The output of the transformation represents the
  image in the Fourier or frequency domain, while
  the input image is the spatial domain equivalent.
• In the Fourier domain image, each point
  represents a particular frequency contained in
  the spatial domain image.

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Spatial Domain Vs Frequency Domain

• Spatial Domain (Image Enhancement)
• is manipulating or changing an image representing
  an object in space to enhance the image for a
  given application.
• Techniques are based on direct manipulation of
  pixels in an image
• Used for filtering basics, smoothing filters,
  sharpening filters, unsharp masking and laplacian
• 2. Frequency DomainTechniques are based on
  modifying the spectral transform of an image
• Transform the image to its frequency
  representation
• Perform image processing
• Compute inverse transform back to the spatial
  domain

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Frequency Filtering

1. Computer the Fourier transform F(wx,wy) of f(x,y)
2. Multiple F by the transfer function F to obtain a
   new function G, e.g., high frequency components
   are removed or attenuated.
3. Compute the inverse Fourier transform G-1 to get
   the filtered version of f

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Frequency Filtering

• Frequency filter function F can be classified
  into three different types
• Low-pass filter A low-pass filter is a filter
  that passes signals with a frequency lower than a
  certain cutoff frequency and attenuates signals
  with frequencies higher than the cutoff
  frequency.
• High-pass filter A high-pass filter is an
  electronic filter that passes signals with a
  frequency higher than a certain cutoff frequency
  and attenuates signals with frequencies lower
  than the cutoff frequency.
• Band-pass filter A band-pass filter is a device
  that passes frequencies within a certain range
  and rejects (attenuates) frequencies outside that
  range.

To remove noise, low-pass filter is used
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Gaussian Filter

• In image processing, a Gaussian blur (also known
  as Gaussian smoothing) is the result of blurring
  an image by a Gaussian function.
• It is a widely used effect in graphics software,
  typically to reduce image noise and reduce
  detail.
• Gaussian smoothing is also used as a
  pre-processing stage in computer vision
  algorithms in order to enhance image structures
  at different scales.
• The Gaussian outputs a weighted average' of each
  pixel's neighborhood, with the average weighted
  more towards the value of the central pixels.
• This is in contrast to the mean filter's
  uniformly weighted average. Because of this, a
  Gaussian provides gentler smoothing and preserves
  edges better than a similarly sized mean filter.

To remove noise, low-pass filter is used
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Edge Detection

• Edge detection is an image processing technique
  for finding the boundaries of objects within
  images.
• It works by detecting discontinuities in
  brightness. Edge detection is used for image
  segmentation and data extraction in areas such as
  image processing, computer vision, and machine
  vision.
• Edges are curves that separate image regions of
  different luminance
• The points at which image brightness changes
  sharply are typically organized into a set of
  curved line segments termed edges.

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Origin of Edges
surface normal discontinuity
depth discontinuity
surface color discontinuity
illumination discontinuity

• Edges are caused by a variety of factors

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Edge Detection
Original Image
Edge Detection
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First Order Derivative Edge Detection
Generally, the first order derivative
operators are very sensitive to noise and produce
thicker edges.  a.1)  Roberts filtering diagonal
edge gradients, susceptible to fluctations. Gives
no information about edge orientation and works
best with binary images. a.2)  Prewitt
filter The Prewitt operator is a discrete
differentiation operator which functions similar
to the Sobel operator, by computing the gradient
for the image intensity function. Makes use of
the maximum directional gradient. As compared
to Sobel, the Prewitt masks are simpler to
implement but are very sensitive to
noise.  a.3)  Sobel filter Detects edges are
where the gradient magnitude is high.This makes
the Sobel edge detector more sensitive
to diagonal edge than horizontal and vertical
edges. 
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2nd Order Derivative Edge Detection

• If there is a significant spatial change in the
  second derivative, an edge is detected.
• Good on producing thinner edges.
• 2nd Order Derivative operators are more
  sophisticated methods towards automatized edge
  detection, however, still very noise-sensitive. 
• As differentiation amplifies noise, smoothing is
  suggested prior to applying the Laplacians. In
  that context, typical examples of 2nd order
  derivative edge detection are the Difference of
  Gaussian (DOG) and the Laplacian of Gaussian

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(Continued) Image Visualization Chap.
9 November 19, 2009
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Shape Representation and Analysis
Shape Analysis Pipeline
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Shape Representation and Analysis

• Filtering high-volume, low level datasets into
  low volume dataset containing high amounts of
  information
• Shape is defined as a compact subset of a given
  image
• Shape is characterized by a boundary and an
  interior
• Shape properties include
• geometry (form, aspect ratio, roundness, or
  squareness)
• Topology (type, kind, number)
• Texture (luminance, shading)

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Segmentation

• Segment or classify the image pixels into those
  belonging to the shape of interest, called
  foreground pixels, and the remainder, also called
  background pixels.
• Segmentation results in a binary image
• Segmentation is related to the operation of
  selection, i.e., thresholding

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Segmentation
Find soft tissue
Find hard tissue
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Connected Components
Find non-local properties Algorithm start from
a given foreground pixels, find all foreground
pixels that are directly or indirectly neighbored
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Morphological Operations
To close holes and remove islands in segmented
images a original image b segmentation c
close holes d remove island
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Introduction

• Morphology a branch of image processing that
  deals with the form and structure of an object.
• Morphological image processing is used to extract
  image components for representation and
  description of region shape, such as boundaries,
  skeletons, and shape of the image.

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Structuring Element (Kernel)

• Structuring Elements can have varying sizes
• Usually, element values are 0,1 and none(!)
• Structural Elements have an origin
• For thinning, other values are possible
• Empty spots in the Structuring Elements are dont
  cares!

Box Disc
Examples of stucturing elements
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Dilation Erosion

• Basic operations
• Are dual to each other
• Erosion shrinks foreground, enlarges Background
• Dilation enlarges foreground, shrinks background

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Erosion

• Erosion is the set of all points in the image,
  where the structuring element fits into.
• Consider each foreground pixel in the input image
• If the structuring element fits in, write a 1
  at the origin of the structuring element!
• Simple application of pattern matching
• Input
• Binary Image (Gray value)
• Structuring Element, containing only 1s!

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Erosion Operations (cont.)
Structuring Element (B)
Original image (A)
Intersect pixel
Center pixel
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Erosion Operations (cont.)
Result of Erosion
Boundary of the center pixels where B is inside
A
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Dilation

• Dilation is the set of all points in the image,
  where the structuring element touches the
  foreground.
• Consider each pixel in the input image
• If the structuring element touches the foreground
  image, write a 1 at the origin of the
  structuring element!
• Input
• Binary Image
• Structuring Element, containing only 1s!!

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Dilation Operations (cont.)
Reflection
Structuring Element (B)
Intersect pixel
Center pixel
Original image (A)
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Dilation Operations (cont.)
Result of Dilation
Boundary of the center pixels where
intersects A
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Opening Closing

• Important operations
• Derived from the fundamental operations
• Dilatation
• Erosion
• Usually applied to binary images, but gray value
  images are also possible
• Opening and closing are dual operations

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Morphological Operations

• Morphological closing dilation followed by an
  erosion
• Morphological opening erosion followed by a
  dilation operation

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Opening

• Similar to Erosion
• Spot and noise removal
• Less destructive
• Erosion next dilation
• the same structuring element for both operations.
• Input
• Binary Image
• Structuring Element, containing only 1s!

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Opening

• erosion followed by a dilation operation
• Take the structuring element (SE) and slide it
  around inside each foreground region.
• All pixels which can be covered by the SE with
  the SE being entirely within the foreground
  region will be preserved.
• All foreground pixels which can not be reached by
  the structuring element without lapping over the
  edge of the foreground object will be eroded away!

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Opening

• Structuring element 3x3 square

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Opening Example

• Opening with a 11 pixel diameter disc

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Closing

• Similar to Dilation
• Removal of holes
• Tends to enlarge regions, shrink background
• Closing is defined as a Dilatation, followed by
  an Erosion using the same structuring element for
  both operations.
• Dilation next erosion!
• Input
• Binary Image
• Structuring Element, containing only 1s!

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Closing

• dilation followed by an erosion
• Take the structuring element (SE) and slide it
  around outside each foreground region.
• All background pixels which can be covered by the
  SE with the SE being entirely within the
  background region will be preserved.
• All background pixels which can not be reached by
  the structuring element without lapping over the
  edge of the foreground object will be turned into
  a foreground.

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Closing

• Structuring element 3x3 square

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Closing Example

• Closing operation with a 22 pixel disc
• Closes small holes in the foreground

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Closing Example 1

1. Threshold
2. Closing with disc of size 20

Thresholded closed
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Opening

• Erosion and dilation are not inverse transforms.
  An erosion followed by a dilation leads to an
  interesting morphological operation

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Opening

• Erosion and dilation are not inverse transforms.
  An erosion followed by a dilation leads to an
  interesting morphological operation

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Opening

• Erosion and dilation are not inverse transforms.
  An erosion followed by a dilation leads to an
  interesting morphological operation

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Closing

• Closing is a dilation followed by an erosion
  followed

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Closing

• Closing is a dilation followed by an erosion
  followed

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Closing

• Closing is a dilation followed by an erosion
  followed

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Closing

• Closing is a dilation followed by an erosion
  followed

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Distance Transform
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Distance Transform

• The distance transform DT of a binary image I is
  a scalar field that contains, at every pixel of
  I, the minimal distance to the boundary ? O of
  the foreground of I

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Distance Transform

• Distance transform can be used for morphological
  operation
• Consider a contour line C(d) of DT

• d 0
• d gt 0
• d lt 0

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Distance Transform

• The contour lines of DT are also called level sets

Shape
Level Sets
Elevation plot
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Feature Transform

• Find the closest boundary points, so called
  feature points

Given a Feature point is b
Given p Feature points are q1 and q2
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Skeletonization
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Skeletonization the Goals

• Geometric analysis aspect ratio, eccentricity,
  curvature and elongation
• Topological analysis genus
• Retrieval find the shape matching a source shape
• Classification partition the shape into classes
• Matching find the similarity between two shapes

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Skeletonization

• Skeletons are the medial axes
• Or skeleton S( O) was the set of points that are
  centers of maximally inscribed disks in O
• Or skeletons are the set of points situated at
  equal distance from at least two boundary feature
  points of the given shape

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Skeletonization
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Skeleton Computation
Feature Transform Method Select those points
whose feature transform contains more than two
boundary points.
Fails on discreate data
Works well on continuous data
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Skeleton Computation
Using distance field singularities Skeleton
points are local maxima of distance transform
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Endof Chap. 9
Note covered all sections except 9.4.7 (skeleton
in 3D)