meanshift算法详解 PPT

Region of interest
Center of mass
Objective : Find the densest region Distribution of identical billiard balls
What is Mean Shift ?
A tool for: Finding modes in a set of data samples, manifesting an underlying probability density function (PDF) in RN
K(x - xi )
A function of some finite number of data points x1…xn
In practice one uses the forms:
Data
d
K (x) c k(xi ) or K(x) ck x i 1
Same function on each dimension
Non-parametric Density GRADIENT Estimation
(Mean Shift)
PDF Analysis
ቤተ መጻሕፍቲ ባይዱ
Non-Parametric Density Estimation
Assumption : The data points are sampled from an underlying PDF
Data point density implies PDF value !
Assumed Underlying PDF
Real Data Samples
Non-Parametric Density Estimation
Assumed Underlying PDF
Real Data Samples
Mean Shift
Theory and Applications
Yaron Ukrainitz & Bernard Sarel
Agenda
• Mean Shift Theory
• What is Mean Shift ? • Density Estimation Methods • Deriving the Mean Shift • Mean shift properties
Non-Pa?rametric Density Estimation
Assumed Underlying PDF
Real Data Samples
Parametric Density Estimation
Assumption : The data points are sampled from an underlying PDF
PDF(x) =
c e
(
x-μi )2
2
2 i
i
i
Estimate
Assumed Underlying PDF
Real Data Samples
Kernel Density Estimation
Parzen Windows - Function Forms
P(x)

1 n
n i 1
Center of mass
Objective : Find the densest region Distribution of identical billiard balls
Mean Shift vector
Intuitive Description
Region of interest
Center of mass
Intuitive Description
Region of interest
Center of mass
Objective : Find the densest region Distribution of identical billiard balls
Mean Shift vector
Intuitive Description
Objective : Find the densest region Distribution of identical billiard balls
Mean Shift vector
Intuitive Description
Region of interest
Center of mass
Objective : Find the densest region Distribution of identical billiard balls
• Applications
• Clustering • Discontinuity Preserving Smoothing • Object Contour Detection • Segmentation • Object Tracking
Mean Shift Theory
Intuitive Description
PDF in feature space
• •
Color Scale
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• Actually any feature space you can conceive
•…
Discrete PDF Representation
Data
Mean Shift vector
Intuitive Description
Region of interest
Center of mass
Objective : Find the densest region Distribution of identical billiard balls
Mean Shift vector
Function of vector length only
Kernel Density Estimation
Various Kernels
Region of interest
Center of mass
Objective : Find the densest region Distribution of identical billiard balls
Mean Shift vector
Intuitive Description
Region of interest