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The Discrete Circular Active Contour

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Circles occur naturally in many images. Finding the edges of these circles is ... pushing it inwards with a magnitude based on differences in pixel brightness. ... – PowerPoint PPT presentation

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Title: The Discrete Circular Active Contour


1
The Discrete Circular Active Contour
  • Nicola Ritter
  • Murdoch University
  • James Cooper
  • Curtin University of Technology

2
The Problem
  • Circles occur naturally in many images
  • Finding the edges of these circles is trivial
    for humans
  • Getting a computer to find the edges is very
    difficult

Test Image 1
Test Image 2
Image of an Eye
Erythrocytes
3
Past Attempts
  • Edge detectors often find too manyor too
    fewedges
  • The Hough Transform is computationally expensive
  • Random polling is cheaper but still expensive
  • Other active contours get confused by
    intersections or bright patches or else require
    prior knowledge of the outer bounds of the object.

4
The DCAC
  • The Discrete Circular Active Contour is a set of
    nodes, intialised as a circle.
  • Each node is then subject to an internal force
    pushing it outwards towards a larger circle.
  • And an external force pushing it inwards with
    a magnitude based on differences in pixel
    brightness.
  • The nodes of the contour are then moved
    iteratively under the combined forces.

5
Internal Force Magnitude
  • If the force pushing the contour outwards is too
    large, the edge of the image is reached, rather
    than the circle edge.
  • However, if the magnitude of this force is
    steadily dropped, it is obvious when it becomes
    just right.

6
Oscillation
  • When the circle edge has been found, the contour
    oscillates.

189
190
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199
7
Identifying Oscillation
  • Identification of the oscillation allows
    recognition that an object has been found.
  • This is done by considering the moving average of
    the radius.

8
The Best Contour
  • Once oscillation has been reached, the root mean
    square deviation (RMSD) from a perfect circle can
    be used to choose the best contour.

150
346
748
1558
2536
rmsd 0.157
rmsd 0.130
rmsd 0.128
rmsd 0.127
rmsd 0.153
9
RMSD
  • The minimum RMSD reduces with the number of
    iterations
  • The more time available, the more accurate the
    contour gets

10
Results
  • The average circle based on the final contour.

11
Robustness
  • Positions from which a contour can be found.

12
Conclusion
  • Advantages
  • Very fast
  • Reasonably robust
  • Almost parameterless
  • Disadvantages
  • Still needs an initial point interior to the
    circular object

13
Questions?
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