Region Segmentation Region Segmentation

Transcription

1 /7/ egion Segentation Lecture-7 Chapter 3, Fundaentals of Coputer Vision Alper Yilaz,, Mubarak Shah, Fall UCF egion Segentation Alper Yilaz,, Mubarak Shah, Fall UCF

2 /7/ Laer epresentation Applications of Segentation Foreground/background separation Object recognition Video copression Tracking Alper Yilaz,, Mubarak Shah, Fall UCF

3 /7/ Object ecognition Using egion Properties Training For all training saples of each odel object Segent the iage Copute region properties features ecognition Given an iage of unknown object, Segent the iage Copute its feature vector Copare with the training set Alper Yilaz,, Mubarak Shah, Fall UCF Object Based Copression Advantages of OBC High copression ratio Allows insertion deletion of objects How does it work? Find objects Object Segentation Code objects and their locations Build osaics of globall static objects ender scene at receiver Alper Yilaz,, Mubarak Shah, Fall UCF 3

4 /7/ Clustering/Segentation Alper Yilaz,, Mubarak Shah, Fall UCF Segentation-Clustering Alper Yilaz,, Mubarak Shah, Fall UCF 4

5 /7/ Segentation Find set of regions,,., n such that n i i I All piels in region i satisf soe siilarit constraint i j, i j Alper Yilaz,, Mubarak Shah, Fall UCF Siilarit Constraints All piels in an region sub-iage usts have the sae gra levels. All piels in an region sub-iage ust not differ ore than soe threshold All piels in an region sub-iage a not differ ore than soe threshold fro the ean of the gra of the region The standard deviation of gra levels in an region sub-iage ust be sall. Alper Yilaz,, Mubarak Shah, Fall UCF 5

6 /7/ Siple Segentation: Binar Iage B, B, B, if I, T Otherwise if T I, T Otherwise if I, Z Otherwise Alper Yilaz,, Mubarak Shah, Fall UCF Iage Histogra Histogra graphs the nuber of piels with a particular gra level as a function of the iage of gra levels. nuber of piels gra level Alper Yilaz,, Mubarak Shah, Fall UCF 6

7 /7/ 7 Segentation Using Histogra: Siple Case For i=; i<m; i++ For j=; j<n; j++ histogra[ii,j]++; Alper Yilaz,, Mubarak Shah, Fall UCF Segentation Using Histogra: Siple Case Otherwise, if, T f B Otherwise, if, T f T B Otherwise, if, 3 3 T f T B Alper Yilaz,, Mubarak Shah, Fall UCF

8 /7/ ealistic Histogras Not realistic eal noise Alper Yilaz,, Mubarak Shah, Fall UCF ealistic Histogras Sooth out noise Convolve hist. b averaging or D Gaussian filter peak peak valle peak valle valle Alper Yilaz,, Mubarak Shah, Fall UCF 8

9 /7/ Segentation Using Histogra eal iage histogras. Copute the histogra of a given iage.. Sooth the histogra b averaging peaks and valles in the histogra. 3. Detect good peaks b appling thresholds at the valles. 4. Segent the iage into several binar iages using thresholds at the valles. 5. Appl connected coponent algorith to each binar iage find connected regions. Alper Yilaz,, Mubarak Shah, Fall UCF Good Peaks Peakiness Test Va Vb Peakiness. P. N W P Alper Yilaz,, Mubarak Shah, Fall UCF 9

10 /7/ Segentation Using Histogras Select the valles as thresholds Appl threshold to histogra Label the piels within the range of a threshold with the sae label, i.e., a, b, c or,, 3 Alper Yilaz,, Mubarak Shah, Fall UCF Connected Coponents Disjoint segents with sae labels need to be split c d c c a a b b a a be added to segent c Alper Yilaz,, Mubarak Shah, Fall UCF

11 /7/ ecursive Connected Coponent Algorith Alper Yilaz,, Mubarak Shah, Fall UCF Sequential Connected Coponent Algorith Alper Yilaz,, Mubarak Shah, Fall UCF

12 /7/ Sequential Connected Coponent Algorith c c d c c a a b b a d=c Equivalence class Alper Yilaz,, Mubarak Shah, Fall UCF Eaple Detecting Finger Tips arked white Alper Yilaz,, Mubarak Shah, Fall UCF

13 /7/ Eaple Segenting a bottle iage 93 peaks Alper Yilaz,, Mubarak Shah, Fall UCF Eaple Segenting a bottle iage Soothed histogra averaging using ask Of size 5 54 peaks once After peakiness 8 Soothed histogra peaks twice After peakiness 7 Soothed histogra peaks three ties After peakiness 4 Alper Yilaz,, Mubarak Shah, Fall UCF 3

14 /7/ Eaple Segenting a bottle iage,4 4, 6 6,43 43,55 Alper Yilaz,, Mubarak Shah, Fall UCF Suggested eading Chapter 3, Mubarak Shah, Fundaentals of Coputer Vision Alper Yilaz,, Mubarak Shah, Fall UCF 4

15 /7/ Steps in Seed Segentation. Copute the histogra.. Sooth the histogra 3. Detect good peaks 4. Segent iage into binar iages using thresholds at the valles. 5. Appl connected coponent algorith. Alper Yilaz,, Mubarak Shah, Fall UCF Iproving Seed Segentation Merge sall neighboring regions egion growing step Split large regions egion splitting eove weak boundaries between adjacent regions Alper Yilaz,, Mubarak Shah, Fall UCF 5

16 /7/ egion Growing Seed segentation histogra based seg. egion splitting and erging Phagocte algorith Likelihood ratio test Alper Yilaz,, Mubarak Shah, Fall UCF egion Split and Merge Splitting: split non unifor region into 4 adjacent regions Merging: erge siilar regions Stop when no splitting erging are possible Uniforit/siilarit function: P Alper Yilaz,, Mubarak Shah, Fall UCF 6

17 /7/ Eaple P 3 4 P Alper Yilaz,, Mubarak Shah, Fall UCF Eaple Alper Yilaz,, Mubarak Shah, Fall UCF 7

18 /7/ Clustering / Segentation Slide credits go to David Lowe Segentation b Clustering Data reduction - obtain a copact representation for interesting iage data in ters of a set of coponents Find coponents that belong together for clusters 8

19 /7/ Clustering Alper Yilaz,, Mubarak Shah, Fall UCF Segentation b Clustering 9

20 /7/ Segentation b Clustering Segentation b Clustering

21 /7/ K-Means Clustering Choose a fied nuber of clusters Choose cluster centers and point-cluster allocations to iniize error can t do this b search, because there are too an possible allocations. iclusters jeleents of i'th cluster Algorith fi cluster centers; allocate points to closest cluster fi allocation; copute best cluster centers could be an set of features for which we can copute a distance careful about scaling j i K-Means

22 /7/ Iage Segentation b K-Means Select a value of K Select a feature vector for ever piel color, teture, position, or cobination of these etc. Define a siilarit easure between feature vectors Usuall Euclidean Distance. Appl K-Means Algorith. Appl Connected Coponents Algorith. Merge an coponents of size less than soe threshold to an adjacent coponent that is ost siilar to it. Eaple: 3-eans Clustering Convergence in 3 steps fro Duda et al.

23 /7/ Iage Clusters on intensit Clusters on color K-eans clustering using intensit alone and color alone Iage Clusters on color K-eans using color alone, segents 3

24 /7/ K-eans using color alone, segents. K-eans using colour and position, segents 4

25 /7/ Geoetric Properties of egions Alper Yilaz,, Mubarak Shah, Fall UCF egion Properties Area Centroid Moents Perieter Copactness Orientation Alper Yilaz,, Mubarak Shah, Fall UCF 5

26 /7/ Area Nuber of piels inside a region A n B, Alper Yilaz,, Mubarak Shah, Fall UCF Centroid Center of ass n n B, A B, A Alper Yilaz,, Mubarak Shah, Fall UCF 6

27 /7/ Moents Continuous i p q M pq B, dd i th oent Discrete M M n n B,, B,, M M n B, n n B,, M B, Alper Yilaz,, Mubarak Shah, Fall UCF Central Moents Translation invariant If sae region appears in different places in the iage its central oents are sae pq p q B, d d egion centroid Alper Yilaz,, Mubarak Shah, Fall UCF 7

28 /7/ 8 Central Moents , d d B q p pq dd B q p i pq, Alper Yilaz,, Mubarak Shah, Fall UCF Hu Moents Translation, rotation, scaling invariant, d d B q p pq Alper Yilaz,, Mubarak Shah, Fall UCF

29 /7/ Eaple irror irror, scale, rotate 45 original iage scale scale, rotate Alper Yilaz,, Mubarak Shah, Fall UCF Eaple Alper Yilaz,, Mubarak Shah, Fall UCF 9

30 /7/ Perieter and Copactness Perieter: Su of piels on the boundar of region Copactness Circle is the ost copact perieter P C 4A area Alper Yilaz,, Mubarak Shah, Fall UCF egion Orientation Ais of nd oent Alper Yilaz,, Mubarak Shah, Fall UCF 3

31 /7/ egion Orientation line equation sin cos sin s cos cos s sin Miniize E r B, dd sin, cos Alper Yilaz,, Mubarak Shah, Fall UCF egion Orientation r Substituting, in r Differentiating w.r.t. s Setting it to s cos sin Substituting s in, r sin s cos cos s sin sin cos Alper Yilaz,, Mubarak Shah, Fall UCF 3

32 /7/ egion Orientation r sin cos E r B, dd E sin cos B, dd take derivative wrt and equating it to A sin cos where, is centroid Using, we have E asin bsin cos c cos or E a c a ccos bsin where a B, dd, b B, dd, c B, dd egion Orientation E a c a ccos bsin take derivative wrt and equating it to tan b a c sin cos b b b a c a c a c Alper Yilaz,, Mubarak Shah, Fall UCF 3