CS 556: Computer Vision. Lecture 21

Transcription

1 CS 556: Computer Vision Lecture 21 Prof. Sinisa Todorovic 1

2 Meanshift 2

3 Meanshift Clustering Assumption: There is an underlying pdf governing data properties in R Clustering based on estimating the underling pdf Each cluster corresponds to one mode of the pdf assumed pdf real data samples 3

4 Meanshift Clustering Assumption: There is an underlying pdf governing data properties in R Clustering based on estimating the underling pdf Each cluster corresponds to one mode of the pdf assumed pdf real data samples 3

5 Meanshift Clustering Assumption: There is an underlying pdf governing data properties in R Clustering based on estimating the underling pdf Each cluster corresponds to one mode of the pdf assumed pdf real data samples 3

6 Meanshift Clustering Assumption: There is an underlying pdf governing data properties in R Clustering based on estimating the underling pdf Each cluster corresponds to one mode of the pdf assumed pdf real data samples 3

7 Assumption: Parametric Density Estimation The functional form of the pdf is known Example: Mixture of Gaussians K k=1 C k exp 1 2 (x µ k) T 1 k (x µ k) assumed pdf real data samples 4

8 Assumption: Parametric Density Estimation The functional form of the pdf is known estimate Example: Mixture of Gaussians K k=1 C k exp 1 2 (x µ k) T 1 k (x µ k) assumed pdf real data samples 4

9 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

10 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

11 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

12 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

13 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

14 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

15 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

16 onparameteric Density Estimation Given data samples Estimate the pdf, P(x), at some value x by Counting data samples, xn, around x P (x) = 1 K(x x n ) data Data kernel 5

17 Common Kernels Epanechnikov K E (x) = c(1 x 2 ), x 1 0, otherwise Gaussian K G (x) = exp 1 2 x 2 6

18 Meanshift Clustering Goal = Identify modes o need to estimate the pdf Meanshift: Estimate the gradient of the pdf Cluster data that are in the attraction basin of a mode 7

19 Meanshift Clustering 8

20 Meanshift Clustering Region of interest 9

21 Meanshift Clustering Region of interest Center of mass 10

22 Meanshift Clustering Region of interest Center of mass Mean Shift vector 11

23 Meanshift Clustering Region of interest Center of mass 12

24 Meanshift Clustering Region of interest Center of mass 12

25 Meanshift Clustering Region of interest 12

26 Meanshift Clustering Region of interest 13

27 Meanshift Clustering Region of interest Center of mass 13

28 Meanshift Clustering Region of interest Center of mass Mean Shift vector 13

29 Kernel Density Gradient Estimation P (x) = 1 K(x x n ) P (x) = 1 K(x x n ) 14

30 Kernel Density Gradient Estimation P (x) = 1 K(x x n ) P (x) = 1 K(x x n ) K(x x n )=f x x n h 2 K(x x n ) = g n (x n x) g(x) = f(x) 14

31 Kernel Density Gradient Estimation P (x) = 1 K(x x n ) P (x) = 1 K(x x n ) K(x x n )=f x x n h 2 K(x x n ) = g n (x n x) g(x) = f(x) rp (x) = 1 X g n (x n x) = 1 g n g n x n g n x 14

32 Meanshift -- Algorithm Steps meanshift vector m(x) {z } P (x) = 1 g n g n x n g n x 1. Compute the meanshift vector m(x) 2. Translate the kernel window by m(x) 3. Repeat steps 1-2 until convergence 15

33 Meanshift -- Algorithm Steps meanshift vector m(x) P (x) = 1 g n g n x n g n x 1. Compute the meanshift vector m(x) 2. Translate the kernel window by m(x) 3. Repeat steps 1-2 until convergence 16

34 Meanshift -- Algorithm Steps meanshift vector m(x) P (x) = 1 g n g n x n g n x 1. Compute the meanshift vector m(x) 2. Translate the kernel window by m(x) 3. Repeat steps 1-2 until convergence 16

35 Experimental Results -- Meanshift Clustering input data colors denote distinct clusters 17

36 Results -- Meanshift Clustering input image pixel values in LUV color space 18

37 Results -- Meanshift Clustering (continued) input only LU final result trajectories in attraction basins 19

38 Results -- Meanshift Segmentation 20

39 Results -- Comparison Meanshift vs cuts input cuts Meanshift 21