Lecture 9 (4.2.07) Image Segmentation. Shahram Ebadollahi 4/4/ DIP ELEN E4830

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1 Lecture Image Segmentation Shahram Ebadollahi 4/4/007 1 DIP ELEN E4830

2 Lecture Outline Skeletonizaiton GSAT Watershed Algorithm Image Segmentation Introduction Edge detection and linking Thresholding Region-based Approach Motion Segmention 4/4/007

3 Skeletonization Medial Ais Transorm B is a Maimal Disc in set X i there are no other discs included in X and containing B Notion o Maimal Disc Skeleton is the loci o the centers o all maimal discs S X k 0 { ε X \ γ [ ε X ]} kb B kb 4/4/007 3

4 Skeletonization K S X S k k 0 S k X X ε X γ ε X kb B kb Notion o Maimal Disc ε kb K X ε ε ε X B B { k ε X φ} ma kb B Reconstruction X δ kb K δ k 0 kb S k X X δ δ δ S X B B B k Skeleton is the loci o the centers o all maimal discs 4/4/007 4

5 Gra-level SAT Skeletonization or Gra-level Images 4/4/007 5

6 GSAT GSAT is the etension o skeletonization to gra-level images GSAT is the locus o the centers o maimal discs whose plane is perpendicular to the gra-level ais and which it in the region above or below the topographic map o image Smmetr surace or gra-level skeleton or bi-level Represent the collection o smmetr suraces as a graph GSAT graph nodes: g_min: gra-level at bottom o surace path delta_g: dierence in gra-level between top and bottom p_avg: average location o maimal discs on the path n_avg: average size o maimal discs on the path 4/4/007 6

7 GSAT - Implementation 4/4/007 7

8 D n S n 4/4/007 8

9 Image Segmentation b Region Growing on GSAT graph 4/4/007 9

10 Image Segmentation - Intro Goal decompose image into regions R k such that: R i H R H R K k 1 R k i j R k φ i j true k R There are various approaches: edge-based vs. region-based global vs. local eature teture motion color j { 1 K} alse i j 4/4/007 10

11 Watershed image topographic map Watershed line watershed Goal: Find watershed lines 4/4/007 11

12 Watershed: Intuition 4/4/007 1

13 Recursion relation T h+1 X h X h+1 4/4/007 13

14 Boundaries between looded catchment basins 4/4/007 14

15 4/4/ Edge Detection G G gradient Laplacian +

16 Gradient Operation on Images Isotropic condition is lost [ G + G ] 1/ G G mag + ang tan 1 G / G Vertical & Horizontal Edges Diagonal Edges 4/4/007 16

17 Edge Detection - Eample Diagonal Sobel Mask 4/4/007 17

18 Laplacian Operation on Images 4z5 z + z4 + z6 + z8 8z5 z1 + z + z3 + z4 + z6 + z7 + z8 + z9 Problems: Too sensitive to noise double edges edge direction not detectable User or: Detecting edge location dark or light side o edge 4/4/007 18

19 LoG h r e r σ h r r [ σ 4 σ ] e r σ LoG Gaussian Smooth Laplacian 4/4/007 19

20 Original Image Sobel Gradient Gaussian Function Laplacian Operator LoG LoG Thresholded Zero Crossings 4/4/007 0

21 Hough Method or Curve Detection Hough Transorm: Intuition i j a i a + b j + b b a + b a + i j i j Accumulator matri A p q A p q M M points in image with slope a p and intercept b q a b Algorithm: 1. For each point in image determine a p and b q that satis the line equation. Increment Apq b 1 4/4/007 1

22 Hough Method: Normal line representation cosθ + sinθ ρ image accumulator hough 4/4/007 houghpeaks houghlines

23 4/4/007 3

24 Edge-based segmentation: Problems Spurious edges due to noise and low qualit image. Diicult to identi spurious edges. Dependent on local neighborhood inormation No notion o higher order organization o the image Gaps and discontinuities in the linked edges 4/4/007 4

25 4/4/007 5 Thresholding ] [ p T T > T i T i g 0 1 local vs. global static vs. dnamic

26 Global Thresholding 1. TT 0. Segment using T 3. Get average gra-level or region G 1 > T and region G < T 4. T_new average o average o gra-levels 5. Repeat until convergence histogram Input image T80.8 segmented T30 T4.5 T46.7 T5.1 4/4/007 6

27 Adaptive Thresholding 4/4/007 7

28 4/4/007 8 Optimal Threshold Pr FG z Pr BG z ] [ ] Pr[ Pr FG z BG z z + Pr Pr Pr FG z FG z Pr Pr BG z BG Pr 1 z p P z p P z BG FG BG P FG P where

29 Optimal Threshold cont. T 1 T p E z dz Probabilit o classiing a BG piel as FG b mistake T p1 T E z dz Probabilit o classiing a FG piel as BG b mistake Overall probabilit o error: E T P E T P E BG 1 + FG T Gaussian densities case: T arg min E T P opt FG p Optimal threshold minimizes the probabilit o misclassiication T T P p T T 1 BG opt p z µ FG z µ BG P FG P σ FG BG σ e + e µ FG + µ BG σ PFG T ln πσ FG πσ opt + BG µ FG µ BG PBG σ FG σ BG σ 4/4/007 9 BG z

30 Split & Merge Method 1. Pick a grid structure and homogeneit propert H. I or an region R HRalse split region into 4 3. I or an neighboring regions HR 1 UR true merge regions into single region 4. Stop when no more split or merge H R true cnt z m σ k j k k 4/4/

31 Segmentation as Clustering in Feature Space Feature Space Color Teture B R G Clustering algorithms: K-means Gaussian Miture Model Neural Network Issues/Choices: Feature Distance Method 4/4/007 31

32 K-means Clustering Algorithm Select K initial cluster centers: C C 1 C K Assign each piel representation i to nearest cluster C k Recomputer cluster centroids or all clusters Iterate until convergence 1 3 Change in clusters and migration o centroids in consecutive steps 4/4/007 3

33 Accumulative Dierence 4/4/007 33

Chapter 10 Image Segmentation. Yinghua He

Chapter 10 Image Segmentation. Yinghua He Chapter 10 Image Segmentation Yinghua He The whole is equal to the sum of its parts. -Euclid The whole is greater than the sum of its parts. -Max Wertheimer The Whole is Not Equal to the Sum of Its Parts: