Edge Detection using Mean Shift Smoothing

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Edge Detection using Mean Shift Smoothing
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Introduction

• Edge detection problems
• noise
• problematic images low contrast along edges
• parameter dependant (thresholds)

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Introduction Mean Shift Clustering

• The Clustering Problem
• Given a set of data points xi in a
  d-dimensional Euclidean space Rd, assign a label
  li to each point xi, based on proximity to high
  density regions in the space.

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Introduction Mean Shift ClusteringMathematical
Background
The multivariate kernel density estimate is
defined as

• Using the Epanechnikov kernel

We obtain the Mean Shift Vector
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Introduction Mean Shift ClusteringMathematical
BackgroundThe multivariate kernel density
estimate
Example Data Set xi
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Introduction Mean Shift ClusteringMathematical
Background

• The mean shift iteration, derived from the mean
  shift vector M(x)

nk number of points in a sphere of radius h
h window radius
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Mean Shift Smoothing

• Initialize data set
• For each j 1..n
• Initialize k 1 and yk xj.
• Repeat Compute yk1 using the mean shift
  iteration k?k1
• until convergence (yk1 yk lt e).
• Assign Ismoothed( xj(1), xj(2) ) yk(3).

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Mean Shift Smoothing

• The window radius h

Original Image
h 4
h 8
h 16
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Mean Shift SmoothingThe window radius h
Original Image
h 10
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Mean Shift SmoothingThe window radius h
h 15
h 20
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Mean Shift SmoothingThe window radius h
h 10
Original Image
h 15
h 20
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Edge Detection viaMean Shift Smoothing

• Gradient Amplitude Estimation

Hysteresis Procedure
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Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed - Edges
Original Image
No Smoothing
Smoothed - Edges
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Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed
Smoothed - Edges
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Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed
Smoothed - Edges
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Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed
Smoothed - Edges
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Summary

• Good performance handling Gaussian noise, while
  preserving objects edges.
• Amplification of edges in some cases.
• Possible improvement different rescaling policy
  (though more parameters needed).
• Problems
• RUNNING TIME. 300 X 300 pixels image, with h
  20 30 minutes on a household PC
• Many parameters involved h, T1, T2, e.
• Doesnt always improve edge detection. In some
  cases even produces poor results in comparison to
  edge detection without the smoothing process.

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References

• 1 D. Comaniciu, P. Meer Distribution Free
  Decomposition of Multivariate Data, (Invited),
  Pattern Analysis and Applications, Vol. 2,
  22-30, 1999
• 2 Lecture Notes from Introduction to
  Computational and Biological Vision at
• http//www.cs.bgu.ac.il/ben- Shahar/Teaching/
  Computational- Vision/LectureNotes.php.

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The End