★mean shift a_robust_approach_to_feature_space_analysis
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Mean ShiftA Robust Approach to
Feature Space Analysis
Kalyan Sunkavalli
04/29/2008
ES251R
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An Example Feature Space
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An Example Feature Space
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An Example Feature Space
Parametric Density Estimation?
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Mean Shift
• A non-parametric technique for analyzing complex multimodal feature spaces and estimating the stationary points (modes) of the underlying probability density function without explicitly estimating it.
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Outline
• Mean Shift– An intuition– Kernel Density Estimation– Derivation– Properties
• Applications of Mean Shift– Discontinuity preserving Smoothing– Image Segmentation
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Outline
• Mean Shift– An intuition– Kernel Density Estimation– Derivation– Properties
• Applications of Mean Shift– Discontinuity preserving Smoothing– Image Segmentation
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Intuitive Description
Distribution of identical billiard balls
Region ofinterest
Center ofmass
Mean Shiftvector
Objective : Find the densest regionSlide Credit: Yaron Ukrainitz & Bernard Sarel
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Intuitive Description
Distribution of identical billiard balls
Region ofinterest
Center ofmass
Mean Shiftvector
Objective : Find the densest region
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Intuitive Description
Distribution of identical billiard balls
Region ofinterest
Center ofmass
Mean Shiftvector
Objective : Find the densest region
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Intuitive Description
Distribution of identical billiard balls
Region ofinterest
Center ofmass
Mean Shiftvector
Objective : Find the densest region
![Page 12: ★Mean shift a_robust_approach_to_feature_space_analysis](https://reader036.vdocuments.site/reader036/viewer/2022062614/54639ffdaf79590c328b5620/html5/thumbnails/12.jpg)
Intuitive Description
Distribution of identical billiard balls
Region ofinterest
Center ofmass
Mean Shiftvector
Objective : Find the densest region
![Page 13: ★Mean shift a_robust_approach_to_feature_space_analysis](https://reader036.vdocuments.site/reader036/viewer/2022062614/54639ffdaf79590c328b5620/html5/thumbnails/13.jpg)
Intuitive Description
Distribution of identical billiard balls
Region ofinterest
Center ofmass
Mean Shiftvector
Objective : Find the densest region
![Page 14: ★Mean shift a_robust_approach_to_feature_space_analysis](https://reader036.vdocuments.site/reader036/viewer/2022062614/54639ffdaf79590c328b5620/html5/thumbnails/14.jpg)
Intuitive Description
Distribution of identical billiard balls
Region ofinterest
Center ofmass
Objective : Find the densest region
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Outline
• Mean Shift– An intuition– Kernel Density Estimation– Derivation– Properties
• Applications of Mean Shift– Discontinuity preserving Smoothing– Image Segmentation
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Assumed Underlying PDF
Estimate from data
Data Samples
Parametric Density Estimation
The data points are sampled from an underlying PDF
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Assumed Underlying PDF Data Samples
Data pointdensity
Non-parametric Density Estimation
PDF value
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Assumed Underlying PDF Data Samples
Non-parametric Density Estimation
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Parzen Windows
Kernel Properties
1. Bounded
2. Compact support
3. Normalized
4. Symmetric
5. Exponential decay
6.
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Kernels and Bandwidths
• Kernel Types
• Bandwidth Parameter
(product of univariate kernels) (radially symmetric kernel)
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Various KernelsEpanechnikov
Normal
Uniform
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Outline
• Mean Shift– An intuition– Kernel Density Estimation– Derivation– Properties
• Applications of Mean Shift– Discontinuity preserving Smoothing– Image Segmentation
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Density Gradient Estimation
Epanechnikov Uniform
Normal Normal
Modes of the probability density
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Mean Shift
KDE Mean Shift
Mean Shift Algorithm
• compute mean shift vector
• translate kernel (window) by mean shift vector
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Mean Shift
• Mean Shift is proportional to the normalized density gradient estimate obtained with kernel
• The normalization is by the density estimate computed with kernel
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Outline
• Mean Shift– An intuition– Kernel Density Estimation– Derivation– Properties
• Applications of Mean Shift– Discontinuity preserving Smoothing– Image Segmentation
![Page 27: ★Mean shift a_robust_approach_to_feature_space_analysis](https://reader036.vdocuments.site/reader036/viewer/2022062614/54639ffdaf79590c328b5620/html5/thumbnails/27.jpg)
Properties of Mean Shift• Guaranteed convergence
– Gradient Ascent algorithms are guaranteed to converge only for infinitesimal steps.
– The normalization of the mean shift vector ensures that it converges.
– Large magnitude in low-density regions, refined steps near local maxima Adaptive Gradient Ascent.
• Mode Detection– Let denote the sequence of kernel locations.– At convergence– Once gets sufficiently close to a mode of it will
converge to the mode.– The set of all locations that converge to the same mode define
the basin of attraction of that mode.
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Properties of Mean Shift
• Smooth Trajectory– The angle between two consecutive mean shift vectors
computed using the normal kernel is always less that 90°– In practice the convergence of mean shift using the normal
kernel is very slow and typically the uniform kernel is used.
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Mode detection using Mean Shift
• Run Mean Shift to find the stationary points– To detect multiple modes, run in parallel starting with
initializations covering the entire feature space.
• Prune the stationary points by retaining local maxima– Merge modes at a distance of less than the bandwidth.
• Clustering from the modes– The basin of attraction of each mode delineates a cluster of
arbitrary shape.
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Mode Finding on Real Data
initialization
detected mode
tracks
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Mean Shift Clustering
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Outline
• Mean Shift– Density Estimation– What is mean shift?– Derivation– Properties
• Applications of Mean Shift– Discontinuity preserving Smoothing– Image Segmentation
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Joint Spatial-Range Feature Space
• Concatenate spatial and range (gray level or color) information
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Discontinuity Preserving Smoothing
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Discontinuity Preserving Smoothing
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Discontinuity Preserving Smoothing
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Discontinuity Preserving Smoothing
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Outline
• Mean Shift– Density Estimation– What is mean shift?– Derivation– Properties
• Applications of Mean Shift– Discontinuity preserving Smoothing– Image Segmentation
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Clustering on Real Data
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Image Segmentation
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Image Segmentation
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Image Segmentation
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Image Segmentation
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Image Segmentation
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Acknowledgements
• Mean shift: A robust approach toward feature space analysis. D Comaniciu, P Meer Pattern Analysis and Machine Intelligence, IEEE Transactions on, Vol. 24, No. 5. (2002), pp. 603-619.
• http://www.caip.rutgers.edu/riul/research/papers.html
• Slide credits: Yaron Ukrainitz & Bernard Sarel
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Thank You