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Mean Shift A Robust Approach to Feature Space Analysis

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Mean Shift A Robust Approach to Feature Space Analysis Kalyan Sunkavalli 04/29/2008 ES251R An Example Feature Space An Example Feature Space An Example Feature Space ... – PowerPoint PPT presentation

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Title: Mean Shift A Robust Approach to Feature Space Analysis


1
Mean ShiftA Robust Approach toFeature Space
Analysis
  • Kalyan Sunkavalli
  • 04/29/2008
  • ES251R

2
An Example Feature Space
3
An Example Feature Space
4
An Example Feature Space
Parametric Density Estimation?
5
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.

6
Outline
  • Mean Shift
  • An intuition
  • Kernel Density Estimation
  • Derivation
  • Properties
  • Applications of Mean Shift
  • Discontinuity preserving Smoothing
  • Image Segmentation

7
Outline
  • Mean Shift
  • An intuition
  • Kernel Density Estimation
  • Derivation
  • Properties
  • Applications of Mean Shift
  • Discontinuity preserving Smoothing
  • Image Segmentation

8
Intuitive Description
Region of interest
Center of mass
Mean Shift vector
Slide Credit Yaron Ukrainitz Bernard Sarel
Objective Find the densest region
Distribution of identical billiard balls
9
Intuitive Description
Region of interest
Center of mass
Mean Shift vector
Objective Find the densest region
Distribution of identical billiard balls
10
Intuitive Description
Region of interest
Center of mass
Mean Shift vector
Objective Find the densest region
Distribution of identical billiard balls
11
Intuitive Description
Region of interest
Center of mass
Mean Shift vector
Objective Find the densest region
Distribution of identical billiard balls
12
Intuitive Description
Region of interest
Center of mass
Mean Shift vector
Objective Find the densest region
Distribution of identical billiard balls
13
Intuitive Description
Region of interest
Center of mass
Mean Shift vector
Objective Find the densest region
Distribution of identical billiard balls
14
Intuitive Description
Region of interest
Center of mass
Objective Find the densest region
Distribution of identical billiard balls
15
Outline
  • Mean Shift
  • An intuition
  • Kernel Density Estimation
  • Derivation
  • Properties
  • Applications of Mean Shift
  • Discontinuity preserving Smoothing
  • Image Segmentation

16
Parametric Density Estimation
The data points are sampled from an underlying PDF
Estimate from data
Assumed Underlying PDF
Data Samples
17
Non-parametric Density Estimation
PDF value
Data point density
Assumed Underlying PDF
Data Samples
18
Non-parametric Density Estimation
Assumed Underlying PDF
Data Samples
19
Parzen Windows
  • Kernel Properties
  • Bounded
  • Compact support
  • Normalized
  • Symmetric
  • Exponential decay

20
Kernels and Bandwidths
  • Kernel Types
  • Bandwidth Parameter

(product of univariate kernels)
(radially symmetric kernel)
21
Various Kernels
Epanechnikov
Normal
Uniform
22
Outline
  • Mean Shift
  • An intuition
  • Kernel Density Estimation
  • Derivation
  • Properties
  • Applications of Mean Shift
  • Discontinuity preserving Smoothing
  • Image Segmentation

23
Density Gradient Estimation
24
Mean Shift
25
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

26
Outline
  • Mean Shift
  • An intuition
  • Kernel Density Estimation
  • Derivation
  • Properties
  • Applications of Mean Shift
  • Discontinuity preserving Smoothing
  • Image Segmentation

27
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.

28
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.

29
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.

30
Mode Finding on Real Data
initialization
tracks
detected mode
31
Mean Shift Clustering
32
Outline
  • Mean Shift
  • Density Estimation
  • What is mean shift?
  • Derivation
  • Properties
  • Applications of Mean Shift
  • Discontinuity preserving Smoothing
  • Image Segmentation

33
Joint Spatial-Range Feature Space
  • Concatenate spatial and range (gray level or
    color) information

34
Discontinuity Preserving Smoothing
35
Discontinuity Preserving Smoothing
36
Discontinuity Preserving Smoothing
37
Discontinuity Preserving Smoothing
38
Outline
  • Mean Shift
  • Density Estimation
  • What is mean shift?
  • Derivation
  • Properties
  • Applications of Mean Shift
  • Discontinuity preserving Smoothing
  • Image Segmentation

39
Clustering on Real Data
40
Image Segmentation
41
Image Segmentation
42
Image Segmentation
43
Image Segmentation
44
Image Segmentation
45
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.h
    tml
  • Slide credits Yaron Ukrainitz Bernard Sarel

46
Thank You
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