Edge Detection using Mean Shift Smoothing

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

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.

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

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

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

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).

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

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

Mean Shift Smoothing The window radius h:

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

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

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

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

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

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

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.

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.

The End