1. Edge Detection using Mean Shift Smoothing

2. Introduction Edge detection problems: noise
problematic images: low contrast along edges
parameter dependant (thresholds…)

3. 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.

4. Introduction – Mean Shift Clustering Mathematical Background
The multivariate kernel density estimate is defined as:
Using the Epanechnikov kernel:
We obtain the Mean Shift Vector:

5. Introduction – Mean Shift Clustering Mathematical Background The multivariate kernel density estimate:
Example Data Set {xi}

6. Introduction – Mean Shift Clustering Mathematical 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

7. Mean Shift Smoothing Initialize data set: For each j = 1..n
Initialize k = 1 and yk = xj.
Repeat: Compute yk+1 using the mean shift iteration; k←k+1;
until convergence (yk+1 – yk < ε).
Assign Ismoothed( xj(1), xj(2) ) = yk(3).

8. Mean Shift Smoothing The window radius h: Original Image h = 4 h = 8

9. Mean Shift Smoothing The window radius h:
Original Image
h = 10

10. Mean Shift Smoothing The window radius h:

11. Mean Shift Smoothing The window radius h:
Original Image
h = 10
h = 15
h = 20

12. Edge Detection via Mean Shift Smoothing
Gradient Amplitude Estimation:
Hysteresis Procedure:

13. Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed - Edges
Original Image
No Smoothing
Smoothed - Edges

14. Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed
Smoothed - Edges

15. Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed
Smoothed - Edges

16. Edge Detection via Mean Shift Smoothing
Original Image
No Smoothing
Smoothed
Smoothed - Edges

17. Summary Amplification of edges in some cases.
Good performance handling Gaussian noise, while preserving object’s 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, ε.
Doesn’t always improve edge detection. In some cases even produces poor results in comparison to edge detection without the smoothing process.

18. 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:
Shahar/Teaching/Computational- Vision/LectureNotes.php.

19. The End