INtroduction Kernel density I Kernel choices I Peak finding I Mean-shift 1 Cam-shift First we need to understand the Probability density Function PDF We use Kernel density estimation to find PDF Obtain the probability function from samples Camshift vod 6
Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift First we need to understand the Probability Density Function PDF We use Kernel density estimation to find PDF Obtain the probability function from samples Camshift v9d 6
Introduction KKernel density Kernel choices I Peak finding I Mean-shift I Cam-shift Motivation for Kernel density estimation to find pdf The formula(parametric form) of the PDf (probability density function)is difficult to find Use sampling method to estimate the p.D.f That means: Gaussian(a parametric form with mean, standard deviation etc. is easy to use) but it is too simple to model real life problems. PDF(X) K/ Too simple to model o onaL HR real life problems X KN(x=ce An irregular shape pd, the distribution Gaussian distribution Is difficult to model using parameters Camshift vod use non-parametric methods instead
Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift Motivation for Kernel density estimation to find PDF • The formula (parametric form) of the PDF (probability density function) is difficult to find. • Use sampling method to estimate the P.D.F. • That means: Gaussian ( a parametric form with mean , standard deviation etc., is easy to use), but it is too simple to model real life problems. 2 || || 2 1 ( ) x N K x c e − = Camshift v9d 7 Gaussian distribution An irregular shape PDF, the distribution Is difficult to model using parameters --use non-parametric methods instead PDF(x) 0 x Too simple to model real life problems
IntroductionKKernel density Kernel choices |Peak finding/Mean-shiftICam-shift Example Outbreak of flu in a year How do you model this Pdf? CUHK Clinic Patients Number 100+ Per day 3 9 12 month Camshift vod 8
Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift Example • Outbreak of flu in a year • How do you model this PDF? Camshift v9d 8 month CUHK Clinic Patients Number Per day 3 6 9 12 100
IntroductionKKernel density Kernel choices |Peak finding/Mean-shiftICam-shift Kernel density estimation KDE Demo mei Density Estm Dataset 0waBa们a钟(动 https://courses.cs.ut.ee/demos/kernel-density-estimation/ https:/en.wikipedia.org/wiki/kerneldensityestimation Camshift vod 9
Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift Kernel density estimation KDE Demo • Camshift v9d 9 https://courses.cs.ut.ee/demos/kernel-density-estimation/ https://en.wikipedia.org/wiki/Kernel_density_estimation
Introduction KKernel density Kernel choices I Peak finding I Mean-shift I Cam-shift kernel density distribution function K is a function o be explained (see slide 19) The general form of a kernel x-xi x)三 density distribution function ∑k The Kernel (k) has many n= number of samples choices h window radius Epanechnikov d=dimension Uniform x=target position Normal (Gaussian i- Samples C= normalization constant Camshift vod
Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift kernel density distribution function • The general form of a kernel density distribution function • The Kernel (K) has many choices – Epanechnikov – Uniform – Normal (Gaussian) C normalization constant samples target position dimension window radius number of samples ( ) ˆ 1 = = = = = = − = = i n i i h d x xd h n h x x K nhC f x Camshift v9d 10 K is a function: To be explained (see slide19)