Thinning Algorithms

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Thinning Algorithms
Thick images Thin images Color images Character
Recognition (OCR)
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Thinning from many pixels width to just one
Thinning of thick binary images

• Much work has been done on the thinning of
  thick'' binary images,
• where attempts are made to reduce shape outlines
  which are many pixels thick to outlines which are
  only one pixel thick.
• Skeletonization

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Thinning using Zhang and Suen algorithm 1984.)
(b) is slightly increased image
Point just removed
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8
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results of the first pass
results of the second pass
final results
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Example of Thinning algorithm from Zhang and Suen
1984
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Example 1 of Rules for Thinning Algorithm
Rule 1
All four rules can be illustrated like that
New and old one
Old one
Dont care
Rule 2
Rule 3
Rule 4
Rule 1
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Applying thinning to fault detection in PCB
All lines are thinned to one pixel width Now you
can check connectivity
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Thinning Algorithm
Correct background shows desired shape of letter T
image

• Thinning algorithm is sensitive to corrupted
  image segments

Noise leads to lack of connectivity. BAD
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Thinning applied after Edge Detection
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Rules of binary thinning
Thinning of thin binary images

• We will present the rules used for the binary
  thinning'' which is applied to the edge images
  (found using the edge detector).
• The rules are simple and quick to carry out,
  requiring only one pass through the image.

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The SUSAN Thinning Algorithm

• It follows a few simple rules
• remove spurious or unwanted edge points
• add in edge points where they should be reported
  but have not been.
• The rules fall into three categories
• removing spurious or unwanted edge points
• adding new edge points
• shifting edge points to new positions.
• Note that the new edge points will only be
  created if the edge response allows this.

These all can be called local improving rules
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The SUSAN Thinning Algorithm

• The rules are listed according to the number of
  edge point neighbours which an edge point has (in
  the eight pixel neighbourhood)

0 neighbors
1 neighbor
2 neighbors
2 neighbors
3 neighbors
Discuss size of window and direction of movement
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The SUSAN Thinning Algorithm

• 0 neighbors.
• Remove the edge point.
• 1 neighbor.
• Search for the neighbor with the maximum
  (non-zero) edge response, to continue the edge,
  and to fill in gaps in edges.
• The responses used are those found by the initial
  stage of the SUSAN edge detector, before
  non-maximum suppression.
• They are slightly weighted according to the
  existing edge orientation so that the edge will
  prefer to continue in a straight line.
• An edge can be extended by a maximum of three
  pixels.

Filling gaps by adding new edge points
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The SUSAN Thinning Algorithm

• 2 neighbours.
• There are three possible cases
• 1. If the point is sticking out'' of an
  otherwise straight line, then compare its edge
  response to that of the corresponding point
  within the line.
• If the potential point within the straight edge
  has an edge response greater than 0.7 of the
  current point's response, move the current point
  into line with the edge.
• 2. If the point is adjoining a diagonal edge then
  remove it.
• 3. Otherwise, the point is a valid edge point.

Edge response is a measure of neighborhood
My point has two neighbors
My point has two neighbors
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The SUSAN Thinning Algorithm

• More than 2 neighbours.
• If the point is not a link between multiple edges
  then thin the edge.
• This will involve a choice between the current
  point and one of its neighbours.
• If this choice is made in a logical consistent
  way then a clean'' looking thinned edge will
  result.

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How rules are applied?
The SUSAN Thinning Algorithm

• These rules are applied to every pixel in the
  image sequentially left to right and top to
  bottom.
• If a change is made to the edge image then the
  current search point is moved backwards up to two
  pixels leftwards and upwards.
• This means that iterative alterations to the
  image can be achieved using only one pass of the
  algorithm.

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• Thinning can remove certain types of lines from
  the image

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Correct and Incorrect Thinning Examples

• X correct
• V misread as Y
• 8 has noise added and not removed, wrong semantic
  network will be created

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Good thinning examples

• Here every symbol correctly thinned

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Thinning Rules
Another set of Rules for Thinning Algorithm

• Examples of rules for shifting up and down
  algorithm

new
Old and new
Down rules
Up rules
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Tracing direction
Tracing Direction from left to right

• Notation for points in window
• Rules based on point replacements

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Tracing Direction
This pixed changed to white
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Example of bad thinning

• We would like to have one pixel width everywhere

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Thinning algorithm for images from polygons
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Typical errors of thinning algorithms
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Gradient based thinning
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Encoding shapes after thinning
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Encoding to discrete angles

• Image after thinning

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Use of angles in encoding
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Replacement of blocks with points
Coding in 8 directions
Select the closest point
Also, coding in 4 directions or more directions
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Polygon Approximation -Encoding
We start with the set of rectangles with points
inside

• Two Methods are used
• Included objects
• Minimal objects

• Included objects

Line Segments make minimum change to the line
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• (a) original figure, (b) computation of
  distances, (c) connection of vertices, (d)
  resultant polygon

start
Draw straight angles
Method of minimal objects
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Encoding of figures

• (a) completion of a figure
• (b) partitioning to segments

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Problems

• 1. Write a program for thinning with your own set
  of rules, that transform a kernel (3 by 3 or
  larger) to a point
• 2. Write a program for thinning that replaces
  rectangle to rectangle according to one of sorted
  rules, about 10 rules.
• 3. Compare with Zhang and Suen algorithm on
  images from FAB building interiors

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More Problems to solve

• The slides describe the rules used for the
  binary thinning'' which is applied to the edge
  images (found using the SUSAN edge detector - see
  9,8) after non-maximum suppression has taken
  place. The rules are simple and quick to carry
  out, requiring only one pass through the image.
  Similar text originally appeared in Appendix B of
  7.
• Write LISP program with the code of this edge
  detector and check it on similar images.
• For examples and reviews of work on
  skeletonization'' see 6,4,1,2,5. Implement
  any of these programs in LISP. Parametrize it.

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Introduction

• Much work has been done on the thinning of
  thick'' binary images, where attempts are made
  to reduce shape outlines which are many pixels
  thick to outlines which are only one pixel thick.
  
• However, because of the non-maximum suppression
  which is applied before thinning in edge
  detectors such as SUSAN, this kind of approach is
  not necessary.

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Literature

• 1 R.M. Haralick. Performance characterization in
  image analysis Thinning, a case in point.
  Pattern Recognition Letters, 135--12, 1992.
• 2 P. Kumar, D. Bhatnagar, and P.S. Umapathi Rao.
  Pseudo one pass thinning algorithm. Pattern
  Recognition Letters, 12543--555, 1991.
• 3 O. Monga, R. Deriche, G. Malandain, and J.P.
  Cocquerez. Recursive filtering and edge tracking
  Two primary tools for 3D edge detection. Image
  and Vision Computing, 9(4)203--214, 1991.
• 4 J.A. Noble. Descriptions of Image Surfaces.
  D.Phil. thesis, Robotics Research Group,
  Department of Engineering Science, Oxford
  University, 1989.
• 5 M. Otte and H.-H. Nagel. Extraction of line
  drawings from gray value images by non-local
  analysis of edge element structures. In Proc. 2nd
  European Conf. on Computer Vision, pages
  687--695. Springer-Verlag, 1992.

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Literature

• 6 S. Pal. Some Low Level Image Segmentation
  Methods, Algorithms and their Analysis. PhD
  thesis, Indian Institute of Technology, 1991.
• 7 S.M. Smith. Feature Based Image Sequence
  Understanding. D.Phil. thesis, Robotics Research
  Group, Department of Engineering Science, Oxford
  University, 1992.
• 8 S.M. Smith. SUSAN -- a new approach to low
  level image processing. Internal Technical Report
  TR95SMS1, Defence Research Agency, Chobham Lane,
  Chertsey, Surrey, UK, 1995. Available at
  www.fmrib.ox.ac.uk/steve for downloading.
• 9 S.M. Smith and J.M. Brady. SUSAN - a new
  approach to low level image processing. Int.
  Journal of Computer Vision, 23(1)45--78, May
  1997.