《图像处理与计算机视觉 Image Processing and Computer Vision》课程教学资源（PPT课件讲稿）Chapter 07 Mean-shift and Cam-shift

Image processing and computer vision Chapter 7 Mean-shift and cam-shift Ref o[1] Dorin Comaniciu, Peter Meer, "Mean Shift: A Robust Approach Toward Feature Space Analysis"Volume 24, Issue 5(May 2002),IEEE Transactions on Pattern Analysis and Machine Intelligence e[2]web. missouri. edu/hantx/ECE8001/notes/Lect7 mean shift. pdf Camshift vod

Image processing and computer vision Chapter 7: Mean-shift and Cam-shift Ref ⚫[1] Dorin Comaniciu, Peter Meer,"Mean Shift: A Robust Approach Toward Feature Space Analysis"Volume 24 , Issue 5 (May 2002),IEEE Transactions on Pattern Analysis and Machine Intelligence ⚫[2] web.missouri.edu/~hantx/ECE8001/notes/Lect7_mean_shift.pdf Camshift v9d 1

INtroduction Kernel density I Kernel choices I Peak finding I Mean-shift 1 Cam-shift What is Mean-shift? Find the peak of a probability function by the change of the mean of the data Applications Non-rigid object tracking Segmentation Camshift vod

Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift What is Mean-shift? • Find the peak of a probability function by the change of the mean of the data • Applications: – Non-rigid object tracking – Segmentation Camshift v9d 2

INtroduction Kernel density I Kernel choices I Peak finding I Mean-shift 1 Cam-shift Applications: segmentation of regions of images in a movie Use color to segment the image into logical regions for analysIS. If the regions are moving, mean-shift is useful Camshift vod .https://www.youtube.com/watch?v=rdtun7a6h08

Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift Applications: segmentation of regions of images in a movie • Use color to segment the image into logical regions for analysis. • If the regions are moving , mean-shift is useful. Camshift v9d 3 •https://www.youtube.com/watch?v=rDTun7A6HO8

INtroduction Kernel density I Kernel choices I Peak finding I Mean-shift 1 Cam-shift Application: tracking non-rigid object Human tracking http.://ww.youtube.com/watch?v=zltjpfpp9hy Camshift vod

Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift Application: tracking non-rigid object • Human tracking Camshift v9d 4 http://www.youtube.com/watch?v=zLtjPfPP9HY

INtroduction Kernel density I Kernel choices I Peak finding I Mean-shift 1 Cam-shift Intuition: find the mode by mean shift Target: Find the modes (peaks) in a set of sample data The mode of a continuous probability distribution is the peak. There may be multiple peaks The method used is called mean -shift MIX By finding the shift of the mean, we can find the tp mode (peak) It can be used to segment an image into logical regions.e.g. within each region, the color is the same) Camshift vod 5

Introduction | Kernel density | Kernel choices | Peak finding | Mean-shift | Cam-shift Intuition: find the mode by mean-shift • Target : Find the modes (peaks) in a set of sample data. – The mode of a continuous probability distribution is the peak. – There may be multiple peaks. • The method used is called mean-shift. – By finding the shift of the mean, we can find the mode (peak) • It can be used to segment an image into logical regions. (e.g. within each region, the color is the same.) Camshift v9d 5

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)