SIGGRAPH Interactive Image Cutout. Interactive Graph Cut. Interactive Graph Cut. Interactive Graph Cut. Hard Constraints. Lazy Snapping.
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1 SIGGRAPH 004 Interactve Image Cutout Lazy Snappng Yn L Jan Sun Ch-Keung Tang Heung-Yeung Shum Mcrosoft Research Asa Hong Kong Unversty Separate an object from ts background Compose the object on another mage Carsten Rother Vladmr Kolmogorov Andrew Blake Mcrosoft Research Cambrdge-UK Interactve Graph Cut Interactve Graph Cut (Boykov & Jolly. ICCV 0) Optmzed by s-t mn-cut algorthm Draw Draw foreground and and background Graph Cut Segmentaton Image (Boykov & Jolly. ICCV 0) Interactve Graph Cut Hard Constrants X : Segmentaton. x {" obj", " bkg"} Hard Constrant: (Boykov et al. ICCV 0) O B x = " obj" x = " bkg"
2 Soft Constrants Mnmze the Energy: E( X ) = λ E ( x ) + E( x, x j ) V, j x E x j Image as a Weghted Graph Image Foreground (source S) Mn Cut E : Regon: Color dfference to user marks E : Boundary: Color smlarty between pxels Background (snk T) Graph: source & snk, n-lnks & t-lnks Cut=Segmentaton: Separate source & snk Energy of cut: sum weghts of edges Mn-Cut Max-Flow: Global mnmal enegry n polynomal tme Weghts t-lnks B {, T}: {, S}: 0 U E ( x ) = h ( I ) x E x, x ) exp( -(I I ) ) ( j n-lnks Lazy Snappng L et al. SIGGRAPH 04 Mn Cut = Mnmze Soft Constrants keepng Hard Constrants Lazy Snappng Lazy Snappng Lazy Snappng for Lazy Users Steps UI:. Coarse Step: Obj/Bkg Markng => Graph Cut. Fne Step: a. Border Brush b. Pxel Edtng => Graph-Cut on border
3 Weghts E : Color dfference to user marks Intenstes -> Colors Hstogram -> K-means clusterng E( x = " obj") RGB_dst to closest cluster centrod Per-Px Graph Cut E : Color smlarty between pxels For neghborng pxels of dfferent x E x, x j ) = + C - C ( j Pre-Segmentaton Graph Cut on Regons Graph Cut on Regons Graph Cut on Regons 3
4 Graph Cut Algorthm Regon-based Graph Cut Per-pxel method Pxels Neghbors Pxel color Color dfference Regon based method Small regons Regon connecton Regon mean color Regon color dfference Advantages More than 0 tmes fewer nodes Instant feedback of cutout result Pre-processng overhead ~3 seconds background processng Dvde and Conquer Input Image Frst Step: Object Markng Second Steps: Boundary Edtng Quckly dentfy the object Coarse Boundary Refned Boundary Control the detal boundary Polygon Fttng Frst vertex border pxel wth hghest curvature Next vertces: furthest boundary pxel Stop when dstance < thresh Border Edtng Brush - Replace polygon segment Vertex Edtng: Move/Add/Delete => Graph Cut on border pxels Band of Uncertanty Optmzaton n the Band Pxel Based Graph Cut Segmentaton 4
5 Edt the Polygon Vertces Edt the Polygon Vertces Low Contrast Example Boundary Edtng Boundary Edtng Vdeo Demo (Left boy) For Low Contrast case: In E - Add a term to reflect dstance from polygon Hard Vertex constrant Adjust graph so cut passes through vertex 5
6 Vdeo Demo (Rght Boy) Summary: Two Steps Frst Step: Object Markng Second Steps: Boundary Edtng Input Image Small Regons Coarse Boundary Edtable Polygon Refned Boundary Regon Based Pre-Segmentaton Graph Cut Polygon Fttng Band Pxels Graph Cut Photomontage Interactve Foreground Extracton usng Iterated Graph Cuts Iterated Graph Cut Gaussan Mxture Models (GMMs( GMMs) User Intalzaton? GMM nstead of Hstogram (Color model) Assume dstrbuton s a mxture of Gaussans G μ, Σ ( x) Gaussan GMM estmaton for learnng colour dstrbutons Graph cuts to nfer the segmentaton GMM(x) = w = k K k = w G k μ k, Σk ( x) EM algorthm fnd best wk, μk, Σ for the gven set of samples Dfferent approach k 6
7 Iterated Graph Cuts E GMMs(E No change) Algorthm:. Intalze B, U = B, F = φ Intalze GMMs wk, μk, Σk. Repeat (untl constant energy) a. p U assgn best G k => K clusters b. For each cluster calculate wk, μk, Σk => GMMs c. Fnd Mn Cut => U decreases 3. Apply border mattng 4. Enable user edtng & repeat Incomplete Labelng User specfes border => B, U = B, F = φ F populates through teratons Some F pxels can be retracted. B cannot Edtng (In case of error): User adds F, B (brush) Re-compute Graph Cut can be reused. Iterated Graph Cuts Gaussan Separaton Guaranteed to converge R Foreground & Background Iterated graph cut R Foreground 3 4 Background G Background G Result Energy after each Iteraton Gaussan Mxture Model (typcally K=5) Moderately straghtforward examples Dffcult Examples Camouflage & Low Contrast Fne structure No telepathy Intal Rectangle Intal Result 7
8 Evaluaton Labelled Database Comparson Boykov and Jolly (00) User Input Result Error Rate:.87%.8%.3%.5% 0.7% Error Rate: 0.7% Border Mattng Extract α-values along border Bayes Mattng - Chuang et. al. (00) Create U band Local rectangle ± w Estmate G F, G B Hard Segmentaton Band of Uncertanty Soft Segmentaton F U α B U: μα = α μf + ( α) μb GU ( α) = G( μα, Σα ) Fnd α that maxmzes G U wth respect to pxels n U Border Mattng - Dynamc Programmng Foreground Mx Background 0 Nosy alpha-profle σ Δ Foreground Mx Background Ft a smooth alpha-profle wth parameters Δ, σ t+ t DP Result usng DP Border Mattng Max : G( μ, Σ ) Mn : ( Δ Δ σ α α t= Nosy alpha-profle Regularsaton T t t ) + ( σ t t ) 8
9 Summary G U (α) should match U pxels α should change lke a soft step functon Step functon should change smoothly along contour Mattng Results Input Bayes Mattng (no regularzaton) (wth regularzaton) Lazy Snappng vs. Grab Cut Lazy Snappng Thank You User Interface Algorthm Performance Border Markng brush FG + BG Overrdng brush Vertex edtng Regon-based Graph Cut Border pxel Graph Cut Fully nteractve Includes Pre-Processng Border Edtng Rectangle/lasso BG only Markng brush - [optonal] Iteratve Graph Cut Fast Border Mattng 9
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