Image Segmentation Edge Detection

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Image Segmentation Edge Detection

• Dr. Jiajun Wang
• School of Electronics Information Engineering
• Soochow University

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Contents

• Edge detection
• Gradient operators
• Edge linking
• Hough transform

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Revisit - Goals of image processing

• Image improvement low level IP
• Improvement of pictorial information for human
  interpretation (Improving the visual appearance
  of images to a human viewer )
• Image analysis high level IP
• Processing of scene data for autonomous machine
  perception (Preparing images for measurement of
  the features and structures present )

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Image analysis HLIP

• Extracting information form an image
• Step 1 segment the image -gtobjects or regions
• Step 2 describe and represent the segmented
  regions in a form suitable for computer
  processing
• Step 3 image recognition and interpretation

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Image analysis HLIP (cont)
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Image segmentation

• Definition
• Subdivide an image into its constituent regions
  or objects
• Based on two properties of gray-level image
  values
• Discontinuity
• point / line / edge / corner detection
• Similarity
• thresholding
• region growing / splitting / merging

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Image Segmentation (cont)
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What Should Good Image segmentation be?

• Region interiors
• Simple
• Without many small holes
• Adjacent regions
• Should have significantly different values
• Boundaries
• Simple
• Not ragged
• Spatially accurate

Achieving all these desired properties is
difficult. There is no theory of image
segmentation. Image segmentation techniques are
basically ad hoc.
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Point detection
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Line detection
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Line detection (cont)
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Edge detection

• Definition
• An edge is a set of connected pixels that lie on
  the boundary between two regions
• The difference between edge and boundary, pp.68
• Edge detection steps
• Compute the local derivative
• Magnitude of the 1st derivative can be used to
  detect the presence of an edge
• The sign of the 2nd derivative can be used to
  determine whether an edge pixel lies on the dark
  or light side of an image
• Zero crossing of the 2nd derivative is at the
  midpoint of a transition in gray level, which
  provides a powerful approach for locating the
  edge.

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Edge detection (cont)
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Edge detection (cont)
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Edge detection (cont)
The derivatives are sensitive to noise
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Gradient operators

• Use gradient for image differentiation
• The gradient of an image f(x,y) at point (x,y) is
  defined as
• Some properties about this gradient vector
• It points in the direction of maximum rate of
  change of image at (x,y)
• Magnitude
• angle

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Edge operator
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Sobel edge operator

• Advantages providing both differencing and a
  smooth effect and slightly superior noise
  reduction characteristics.

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Edge detection example
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Edge detection example (cont)
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Edge detection example (cont)
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Laplacian edge operator

• A second order derivative
• Problems
• Very sensitive to noise
• Detect double edges
• Cant detect edge direction
• Usage
• Find the location of edge using zero-crossing
  property

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Marr and hildreths approach

• Smooth the image to reduce noise
• Then calculate the 2nd derivative
• Finally, find the zero-crossing
• LoG (Laplacian of Gaussian, Mexican hat
  function)

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LoG function
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discussion

• Edge detection by gradient operations tends to
  work well when
• Images have sharp intensity transitions
• Relative low noise
• Zero-crossing approach work well when
• Edges are blurry
• High noise content
• Provide reliable edge detection

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Gradient operators examples
Zero-Crossing Advantages noise reduction
capability edges are thinner. Drawbacks
edges form numerous closed loops (spaghetti
effect) computation complex.
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Edge linking

• How to deal with gaps in edges?
• How to deal with noise in edges?
• Linking points by determining whether they lie on
  a curve of a specific shape

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Edge linking Local Processing

• Analyze the characteristics of the edge pixels in
  a small neighborhood
• Its magnitude
• Its direction

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Edge linking - Hough transform

• Can tolerate noise and gaps in edge image
• Look for solutions in a parameter space
• Classical Hough transform
• Detect simple shape
• Line detection
• Circle detection
• Generalized Hough Transform
• Detect complicated shapes

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Edge linking - Hough transform
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Edge linking - Hough transform
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Edge linking - Hough transform
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Edge linking - Hough transform
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Edge linking - Hough transform
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• Dr. Jiajun Wang
• School of Electronics Information Engineering
• Soochow University

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Foundation of thresholding

• Idea object and background pixels have gray
  levels grouped into two dominant modes

Original image
histogram
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Foundation of thresholding

• Input f(x,y), given threshold T

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Issues of thresholding

• Selection of threshold T ?
• Complex environment illumination
• Multiple thresholds more than one object
• Global threshold
• Local threshold

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1. Automatic selection of T

• 1. Select an initial T
• Average gray level
• Mean of max. and min. gray level

G2
G1
2. Segment the image using T
T
3. Calculate mean of G1 and G2
T2
4. New threshold T2 0.5(m1 m2)
5. Repeat steps 24 until difference in
successive T is small
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Example automatically select T
Initial gray level mean 3 iterations T 125.4
fingerprint
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2. Effects of illumination

• Recall f(x,y)i(x,y) r(x,y)

illumination
reflectance
Illumination source
scene
reflection
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Example illumination
x
Original image
Illumination source
histogram
histogram
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Example bad histogram
The gray levels of the object is mixed with
background
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Why illumination is hard to handle?

• f(x,y)i(x,y) r(x,y)
• gt z(x,y) ln f(x,y) ln i(x,y) ln r(x,y)

Histogram (distribution)
Histogram (distribution)
convolution
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3. Multiple thresholds

• Multiple objects or bad illumination

Thresholds
60
70
77
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Result of thresholding
4 gray levels
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4. Motivation for adaptive thresholding
A single Global threshold
histogram
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Adaptive local thresholding
Subdivide image into blocks
Q Improperly segmented subimages !
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Iterative subdivision
histogram
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Region based segmentation

• R the entire image
• Segmentation partition R into n subregions
  R1,Rn
• Ri is a connected region
• P(Ri) true
• P( ) false

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Region growing

• Groups pixels or subregions into larger regions
  based on predefined criteria (gray tone or
  texture).
• Step 1 Assume we find a good threshold, and use
  it to partition the regions into pure black and
  white.
• Step 2 Use different labels to identify
  different objects
• Use region growing to connect parts that should
  have belong to the same region
• This is called Connected component analysis
• The region with the same label generate one
  segment

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Region growing - example
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Region Splitting and Merging
QuadTree Decomposition
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Motion as a clue to extract object
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• Spatial technique

Reference image f(x,y,1)
next image f(x,y,2)
time index
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Image difference thresholding
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Use more than one images in time eliminate noise

Reference image R(x,y)
Image f(x,y,2)
Image f(x,y,3)
d(x,y)R(x,y)-f(x,y,t)
counter
a. if d(x,y) gt T positive ADI b. if d(x,y)
lt -T negative ADI c. if d(x,y) gt T
absolute ADI
counter 1,
Accumulative difference image
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Example
Negative ADI
Positive ADI
Absolute ADI
Object shape Location in ref. image