CS 556: Computer Vision. Lecture 21

CS 556: Computer Vision Lecture 21 Prof. Sinisa Todorovic sinisa@eecs.oregonstate.edu 1

Meanshift 2

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

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

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

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

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

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

Meanshift Clustering 8

Meanshift Clustering Region of interest 9

Meanshift Clustering Region of interest Center of mass 10

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

Meanshift Clustering Region of interest Center of mass 12

Meanshift Clustering Region of interest 12

Meanshift Clustering Region of interest 13

Meanshift Clustering Region of interest Center of mass 13

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

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

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

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

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

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

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

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

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

Results -- Meanshift Segmentation 20

Results -- Comparison Meanshift vs cuts input cuts Meanshift 21