regions & segmenttion Eleni Kldoudi Resercher, ICS-FORTH C-472: Mchine Vision Deprtment of Computer Science University of Crete t Herklion 20 Februry 1997
regions nd edges
imge rry - rectngulr tesseltion α[0,0] column j m columns j row i [i,j] 4-neighbours n rows [i,j] 8-neighbours i
number of pixels h(z) grey level histogrm grey level z
some definitions 4-pth 8-pth region boundry
segmenttion segmenttion is the process of prtitioning n imge F[i,j] into regions P 1,, P k, such tht: k P i = entire imge i=1 P i P j =, " i, j = 1, 2,, k, nd i j pixels in ech prtition stisfy logicl predicte pixels in djcent regions do not stisfy the predicte
segmenttion techniques discontinuity edges similrity thresholding regions
h(z) h(z) globl thresholding T = T ( i, j, P[i,j], F[i,j] ) h 1 (z) h 2 (z) 0 μ 1 μ 2 z 0 μ 1 μ 2 z
globl thresholding - exmple
locl thresholding T = T ( i, j, P[i,j], F[i,j] ) divide into subimges determine threshold for ech subimge process ech subimge seprtely
grey level dynmic thresholding T = T ( i, j, P[i,j], F[i,j] ) threshold surfce imge cross section through the imge
region-bsed segmenttion region growing region merging region splitting djcency connectivity homogeneity grey level shpe color size texture model
region growing 0 1 0 2 7 0 1 0 1 6 7 7 6 8 5 5 6 7 7 0 1 5 6 5 6 b b b b b b b b b b b b b b b how do we select : seed points? similrity criteri? stopping rule? less thn 3 less thn 8
region splitting 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 2 3 4 1 12 3 4 1 2 3 4 1 2 3 4 1 3 2 4
region merging segment into mny smll regions merge two djcent regions if similr merge ll djcent regions tht re similr if no two regions cn be merged, stop
hybrid lgorithm for the segmenttion of 2D-3D imges 1. Κ. Χάρης Ένας Υβριδικός Αλγόριθμος για την Τμηματοποίηση Δισδιάστατων και Τρισδιάστατων Εικόνων Μεταπτυχιακό Δίπλωμα Εξειδίκευσης Τμήμα Επιστήμης Υπολογιστών, Πανεπιστήμιο Κρήτης, 1994 2. K. Hris, G. Tzirits, nd S. Orphnoudkis Smoothing of 2D nd 3D Imges Using Locl Clssifiction Signl Processing VII: Theories nd Applictions, M. Holt, C. Cown, P. Grnt, W. Sndhm (eds.), pp. 1504-1507, 1994 3. S. Orphnoudkis, G. Tzirits, nd K. Hris A Hybrid Algorithm for the Segmenttion of 2D-3D Imges in: Proceedings of IPMI 95, Y. Bizis, C. Brillot, nd R. di Pol (eds), Informtion Processing in Medicl Imging, Kluwer Acdemic Publishers, Dordrecht, pp. 385-386, 1995
segmenttion lgorithm overview input 2D or 3D imge edge-preserving smoothing grdient pproximtion wtershed detection hierrchicl region merging segmented imge
smoothing: method N(i,j) 5 5 N(i,j) is homogeneous if smple vrince C x noise vrince μ 1 if N(i,j) is heterogeneous estimte the prmeters of the two distributions μ 2 μ 3
smoothing: method for ech pixel, consider its neighbourhood ssume tht the neighbourhood is either homogeneous or two different regions exist ssign the pixel to one of mximum of two different distribution popultions present within the neighbourhood set the new vlue of the pixel equl to the rithmetic men of the popultion to which the pixel hs been ssigned
smoothing: exmple input imge smoothed imge
grdient pproximtion compute intensity grdient of smoothed imge pply thresholding on the grdient mgnitude imge G T (i,j) = G T (i,j), if G S (i,j)>t 0, otherwise G S : smoothed grdient imge T : threshold vlue
wtershed detection points of low grdient vlue sink first tesseltion of the input grdient imge into ctchment bsins unique lbel to ech ctchment bsin
wtershed detection rw rw smoothed wtersheds grdient superimposed
wtersheds: effect of grdient thresholding oversegmented imge fter wtershed detection T = 0 T = 2 T = 4 T: grdient threshold vlue input imge
region merging - RAG region djcency grph (RAG) 1 2 3 4 6 5 6-prtition of n imge 1 5 2 4 3 6 corresponding RAG for ech step merge the two most similr regions
region merging - RAG similrity mesure merge the pir of regions (R i,r k ) tht minimize the squre error of the men intensity in the resulting region 1,3 3 2,3 1 2 1,4 1,2 2,5 4 5 i.e, minimize: 3 N i N k N i + N k (μ i - μ k ) 2 N: number of pixels in region μ: men intensity of region 4 1,4 1,3 1,2 1,5 5
exmples input smoothed segmenttion (25) overly input 3556 regions 1536 regions 500 regions 50 regions
exmples
summry segmenttion thresholding dynmic, locl, globl region bsed region growing, splitting, merging edge detection to be continued
more detils in : 1. R. Jin, R. Ksturi, B.G. Schunk, Mchine Vision, McGrw-Hill, 1995. (chpter 3) 2. M. Sonk, V. Hlvc, R. Boyle, Imge Processing, Anlysis nd Mchine Vision, Chpmn & Hll Computing, NY, 1993. (chpter 5) 3. K.S. Fu, R.C. Gonzlez, C.S.G. Lee, Robotics: Control, Sensing, Vision, nd Intelligence, McGrw-Hill, NY, 1987. (chpter 8) 4. D.H. Bllrd, C.M. Brown, Computer Vision, Prentice Hll, NJ, 1982. (chpter 5) 5. Κ. Χάρης Ένας Υβριδικός Αλγόριθμος για την Τμηματοποίηση Δισδιάστατων και Τρισδιάστατων Εικόνων, Μεταπτυχιακό Δίπλωμα Εξειδίκευσης, Μεταπτυχιακό Δίπλωμα Εξειδίκευσης, 1994. 6. L. Vincent, P. Soille, Wtersheds in Digitl Spces: An Efficient Algorithm Bsed on Immersion Simultions, IEEE PAMI, vol. 13(6), 583-598, 1991.
cite s Ε. Καλδούδη, Τεχνικές Τμηματοποίησης Ψηφιακών Εικόνων, Σεμινάριο στα πλαίσια του μαθήματος C-472: Μηχανική Όραση, Υπεύθυνος: καθ. Σ. Ορφανουδάκης, Τμήμα Επιστήμης Υπολογιστών του Πανεπιστημίου Κρήτης, 20 Φεβρουαρίου 1997