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Thinning: from many pixels width to Thinning: from many pixels width to just onejust one
• 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
Thinning of thick binary imagesThinning of thick binary images
Thinning using Thinning using Zhang and Suen algorithm [1984].)
results of the first pass results of the second pass final results
Point just removed 8 7
2625
(b) is slightly increased image
Example of Thinning algorithm from Example of Thinning algorithm from Zhang and Suen 1984Zhang and Suen 1984
Example 1 of Rules for Thinning Example 1 of Rules for Thinning AlgorithmAlgorithm
Don’t care
Old one New and old one
Rule 1 Rule 2 Rule 3 Rule 4
Rule 1 All four rules can be illustrated like that
Applying thinning to fault Applying thinning to fault detection in PCBdetection in PCB
All lines are thinned to one pixel width
Now you can check connectivity
Thinning AlgorithmThinning Algorithm
• Thinning algorithm is sensitive to corrupted image segments
imageCorrect background shows desired shape of letter T
Noise leads to lack of connectivity. BAD
Rules of binary thinningRules of binary thinning• 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.
Thinning of thin binary imagesThinning of thin binary images
The SUSAN Thinning AlgorithmThe 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
• The rules are listed according to the number of edge point neighbours which an edge point has (in the eight pixel neighbourhood)
Discuss size of window and direction of movement
The SUSAN Thinning AlgorithmThe SUSAN Thinning Algorithm0 neighbors
1 neighbor
2 neighbors
2 neighbors
3 neighbors
• 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.
The SUSAN Thinning AlgorithmThe SUSAN Thinning Algorithm
Filling gaps by adding new edge points
• 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.
The SUSAN Thinning AlgorithmThe SUSAN Thinning Algorithm
My point has two neighbors
My point has two neighbors
“Edge response” is a measure of neighborhood
• 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.
The SUSAN Thinning AlgorithmThe SUSAN Thinning Algorithm
How rules are applied?How rules are applied?• 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.
The SUSAN Thinning AlgorithmThe SUSAN Thinning Algorithm
Thinning can remove certain types of Thinning can remove certain types of lines from the imagelines from the image
Correct and Incorrect Thinning ExamplesCorrect and Incorrect Thinning Examples• X correct
• V misread as Y
• 8 has noise added and not removed, wrong semantic network will be created
Thinning Rules• Examples of rules
for shifting up and down algorithm Down rules
Up rules
Another set of Rules for Thinning AlgorithmAnother set of Rules for Thinning Algorithm
newOld and new
Tracing direction
• Notation for points in window• Rules based on point replacements
Tracing Direction from left to rightTracing Direction from left to right
Replacement of blocks with
points
Coding in 8 directions
Also, coding in 4 directions or more directions
Select the closest point
Polygon Approximation -EncodingPolygon Approximation -Encoding
• Included objects
• Two Methods are used:– Included objects
– Minimal objects
We start with the set of rectangles with points inside
Line Segments make minimum change to the line
• (a) original figure, (b) computation of distances, (c) connection of vertices, (d) resultant polygon
start
Draw straight angles
Method of minimal objects
ProblemsProblems
• 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
More Problems to solveMore 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.
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.
LiteratureLiterature• 1 R.M. Haralick. Performance characterization in image analysis:
Thinning, a case in point. Pattern Recognition Letters, 13:5--12, 1992.
• 2 P. Kumar, D. Bhatnagar, and P.S. Umapathi Rao. Pseudo one pass thinning algorithm. Pattern Recognition Letters, 12:543--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.
LiteratureLiterature• 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.